Measures of Central Tendency

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Summary

Measures of Central Tendency

Summary

Measures of central tendency summarize data with a single representative value.
Three commonly used averages: Arithmetic Mean, Median, Mode.
Arithmetic Mean: Sum of all observations divided by the number of observations.
Median: The middle value that divides the data into two equal parts.
Mode: The most frequently occurring value in a dataset.

Key Formulas/Definitions

Arithmetic Mean (A.M.):

$X = \frac{\Sigma X}{N}$
Where:
- $\Sigma X$ = Sum of all observations
- $N$ = Total number of observations
Median:

$\text{Position of Median} = \frac{(N+1)}{2}$
- If N is even, median is the average of the two middle values.
Mode: The value that appears most frequently in a dataset.

Learning Objectives

Understand the need for summarizing data with a single number.
Recognize and distinguish between different types of averages.
Compute different types of averages.
Draw meaningful conclusions from data sets.
Determine the most useful type of average for specific situations.

Common Mistakes/Exam Tips

Remember that the arithmetic mean is affected by extreme values (outliers).
Median is a better measure when data contains outliers.
Mode can be used for qualitative data but may not always exist.

Important Diagrams

Not found in provided text.

Learning Objectives

Understand the need for summarising a set of data by one single number.
Recognise and distinguish between the different types of averages.
Learn to compute different types of averages.
Draw meaningful conclusions from a set of data.
Develop an understanding of which type of average would be the most useful in a particular situation.

Detailed Notes

Measures of Central Tendency

Introduction

Measures of central tendency summarize a set of data by a single representative value.
Common examples include average marks, average rainfall, and average income.

Types of Averages

Arithmetic Mean
- Defined as the sum of all observations divided by the number of observations.
- Example: For marks 40, 50, 55, 78, 58, the mean is calculated as:
  
  $X = \frac{40 + 50 + 55 + 78 + 58}{5} = 56.2$
Median
- The middle value when data is arranged in order.
- Example: For the data set 1, 3, 4, 5, 6, 7, 8, 10, 12, the median is 6.
Mode
- The value that occurs most frequently in a data set.
- Example: In the data set 1, 2, 3, 4, 4, 5, the mode is 4.

Properties of Averages

The sum of deviations from the arithmetic mean is always zero.
The arithmetic mean is sensitive to extreme values.
The median is less affected by outliers and is a better measure for skewed distributions.

Calculation Methods

Arithmetic Mean

Ungrouped Data: Direct method or assumed mean method.
Grouped Data: Direct method and step deviation method.

Median Calculation

For ungrouped data, sort the data and find the middle value.
For grouped data, use cumulative frequency to locate the median class.

Mode Calculation

Can be computed for both discrete and continuous data.
Data can be unimodal, bimodal, or multimodal.

Conclusion

Selecting the appropriate average depends on the nature of the data and the purpose of analysis.

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Misunderstanding Measures of Central Tendency: Students often confuse the definitions and applications of mean, median, and mode. Ensure you understand when to use each measure.
Ignoring Extreme Values: The arithmetic mean is heavily influenced by extreme values. Be cautious when interpreting the mean in datasets with outliers.
Incorrect Calculation Methods: When calculating the mean for grouped data, ensure you are using the correct method (direct, assumed mean, or step deviation).
Misidentifying the Median: The median is not simply the average of the two middle numbers in an even set; it must be calculated correctly based on the ordered dataset.
Failing to Recognize the Mode: In datasets with multiple modes, students may overlook the presence of more than one mode or fail to identify that there may be no mode at all.

Tips for Success

Practice Calculations: Regularly practice calculating mean, median, and mode using both ungrouped and grouped data to build confidence.
Understand the Context: Always consider the context of the data when choosing which measure of central tendency to use. For example, use the median for income data to avoid skew from high earners.
Check Your Work: After performing calculations, double-check your work to ensure accuracy, especially in multi-step processes like finding the mean of grouped data.
Use Visual Aids: When studying, use graphs and charts to visualize data distributions, which can help in understanding where the mean, median, and mode lie in relation to each other.
Review Past Exam Questions: Familiarize yourself with common exam questions related to measures of central tendency to better prepare for what to expect.

Practice & Assessment

Multiple Choice Questions

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: B

Solution:

The median is less affected by extreme values compared to the arithmetic mean, making it a better measure of central tendency for data with outliers.

Median = L + \frac{(N/2 - c.f.)}{f} \times h

Median = \frac{\Sigma X}{N}

Median = \frac{\Sigma fX}{\Sigma f}

Median = \frac{\Sigma WX}{\Sigma W}

Correct Answer: A

Solution:

In a continuous series, the median is calculated using the formula:

\text{Median} = L + \frac{(N/2 - c.f.)}{f} \times h

, where

L

is the lower limit of the median class,

c.f.

is the cumulative frequency before the median class,

f

is the frequency of the median class, and

h

is the class interval.

Half of the data values are less than or equal to 45.

The most frequently occurring value is 45.

The average of the data set is 45.

The sum of deviations from 45 is zero.

Correct Answer: A

Solution:

The median is the central value of the distribution, meaning half of the values are less than or equal to the median.

The median will increase.

The median will decrease.

The median will remain the same.

The effect on the median cannot be determined.

Correct Answer: C

Solution:

The median is the middle value of a data set and is not affected by extreme values. Therefore, increasing the wages of the top 10% earners will not affect the median.

Upper limit of the median class

Lower limit of the median class

Cumulative frequency of the median class

Frequency of the median class

Correct Answer: B

Solution:

In the median formula for a continuous series, 'L' represents the lower limit of the median class.

Correct Answer: B

Solution:

The mode is the value that occurs most frequently in a data set. Here, 20 occurs twice.

$15.67

$16.00

$17.33

$18.00

Correct Answer: C

Solution:

The weighted arithmetic mean is calculated as follows:

\frac{(100 \times 10) + (150 \times 15) + (200 \times 20)}{100 + 150 + 200} = \frac{1000 + 2250 + 4000}{450} = \frac{7250}{450} = 16.11

Mean

Median

Mode

Range

Correct Answer: B

Solution:

The median is the central value of the distribution, where the number of values less than the median is equal to the number greater than the median.

Correct Answer: B

Solution:

The arithmetic mean is calculated as

\frac{10 + 20 + 30 + 40 + 50}{5} = 30

Arithmetic mean

Mode

Median

Geometric mean

Correct Answer: C

Solution:

The median is the value that divides a dataset into two equal parts, with half the values below it and half above.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: B

Solution:

The Median is the central value of a dataset when it is ordered. In this case, the median is 25 minutes.

The sum of deviations is equal to the number of observations.

The sum of deviations is zero.

The sum of deviations is equal to one.

The sum of deviations is equal to the arithmetic mean.

Correct Answer: B

Solution:

The sum of the deviations of a data set from its arithmetic mean is always zero. This is a fundamental property of the arithmetic mean.

Correct Answer: C

Solution:

The mode is the value that appears most frequently in a data set. Here, the number 12 appears three times, which is more frequent than any other number.

2 acres

3 acres

4 acres

5 acres

Correct Answer: B

Solution:

The median is the middle value when the data set is ordered. Here, the median is 3 acres.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: B

Solution:

The median is the middle value of the dataset and is not affected by extreme values, making it the most suitable measure in this scenario.

150 units

175 units

200 units

225 units

Correct Answer: B

Solution:

The arithmetic mean is calculated as the sum of all observations divided by the number of observations: (100 + 150 + 200 + 250) / 4 = 175 units.

1.5 acres

2.5 acres

3.0 acres

4.0 acres

Correct Answer: B

Solution:

The median is the value that divides the dataset into two equal halves. Since 50% of the farmers own between 2-4 acres, the median size of land holdings is 2.5 acres.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: B

Solution:

The median is the measure of central tendency that indicates the value above which half the data lies.

Arithmetic mean

Median

Mode

Geometric mean

Correct Answer: C

Solution:

Mode is generally used to describe qualitative data as it represents the most frequently occurring value.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: A

Solution:

The arithmetic mean provides the average size of land holdings, which Baiju can compare against his 1 acre to determine if it is above average.

74.5

73.5

75.5

Correct Answer: A

Solution:

The total score of 30 students is 30 * 75 = 2250. Removing the score of 90, the new total is 2250 - 90 = 2160. The new mean is 2160 / 29 ≈ 74.5.

Arithmetic mean

Median

Mode

Geometric mean

Correct Answer: C

Solution:

The mode is the most appropriate measure of central tendency for determining the most popular shoe size, as it represents the value that occurs most frequently in the dataset.

It increases by 10

It increases by 2

It remains the same

It decreases by 2

Correct Answer: B

Solution:

Increasing one value by 10 will increase the total sum of the dataset by 10. The mean will increase by

\frac{10}{N}

, where

N

is the number of observations. If

N=5

, the mean increases by 2.

Correct Answer: A

Solution:

The mode is the value that appears most frequently in the dataset. Here, the number 10 appears three times, which is more frequent than any other number.

Correct Answer: A

Solution:

The mode is the value that appears most frequently in a dataset. In this case, the number 3 appears twice, more than any other number.

The median will increase

The median will decrease

The median will remain the same

The effect on the median cannot be determined

Correct Answer: C

Solution:

The median is a positional measure and is not affected by extreme values. Therefore, increasing one of the largest values in the dataset does not affect the median.

Arithmetic Mean

Harmonic Mean

Median

Mode

Correct Answer: B

Solution:

The Harmonic Mean is the appropriate measure for averaging ratios or rates, such as efficiencies.

By using the mid-points of class intervals

By using the mode of class intervals

By using the median of class intervals

By using the sum of frequencies

Correct Answer: A

Solution:

In a continuous series, the arithmetic mean is calculated using the mid-points of the class intervals.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: B

Solution:

The Median is the most appropriate measure of central tendency for skewed distributions as it is not affected by extreme values.

Correct Answer: B

Solution:

When each value in a dataset is increased by a constant, the arithmetic mean also increases by the same constant. Hence, the new arithmetic mean will be 50 + 5 = 55.

Arithmetic Mean

Median

Mode

Harmonic Mean

Correct Answer: A

Solution:

The arithmetic mean is most affected by extreme values because it is calculated by summing all values and dividing by the number of values.

Each observation increases by 2

Each observation decreases by 2

Each observation remains the same

Only the largest observation increases by 2

Correct Answer: A

Solution:

If the arithmetic mean increases by 2, it implies that each observation in the dataset increases by 2.

The data set is symmetric

The median is the arithmetic mean

The median divides the data into two equal parts

The mode is equal to the median

Correct Answer: C

Solution:

The median is the central value of the distribution, meaning it divides the data into two equal parts.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: C

Solution:

The mode is the value that appears most frequently in a dataset. In this case, 30 appears most frequently.

Arithmetic Mean

Median

Mode

Harmonic Mean

Correct Answer: C

Solution:

The Mode is the measure of central tendency that identifies the most frequently occurring value in a dataset. In this case, the mode is 12.

Arithmetic mean

Median

Mode

Geometric mean

Correct Answer: B

Solution:

The median would be most useful to determine if Baiju's land size is above or below what half the farmers own.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: C

Solution:

The mode is the most appropriate measure for identifying the most popular shoe size, as it indicates the size that occurs most frequently.

Arithmetic mean

Median

Mode

None of the above

Correct Answer: B

Solution:

Median is a better summary for data with extreme values as it is the middle value and not affected by outliers.

Arithmetic Mean

Weighted Arithmetic Mean

Median

Mode

Correct Answer: B

Solution:

To calculate the average price per unit of production with weights proportional to the production quantities, the Weighted Arithmetic Mean should be used. This accounts for the different quantities of each product.

Arithmetic mean

Median

Mode

Geometric mean

Correct Answer: A

Solution:

The arithmetic mean is calculated by summing all the observations and dividing by the number of observations.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: B

Solution:

The median is a better measure for datasets with extreme values as it is not affected by them, unlike the arithmetic mean.

The sum will be equal to the number of observations

The sum will be zero

The sum will be equal to one

The sum will be equal to the median

Correct Answer: B

Solution:

The algebraic sum of deviations of a set of values from their arithmetic mean is always zero.

135

145

125

115

Correct Answer: C

Solution:

The sum of the original data is 1450. The incorrect data adds 190 instead of 90, making the sum 1550. Correcting this gives 1450 - 190 + 90 = 1350. The mean is 1350/10 = 135. The correct mean is 125.

Arithmetic mean

Median

Mode

Geometric mean

Correct Answer: A

Solution:

The arithmetic mean is most affected by extreme values because it considers all values in the data set.

Direct Method

Assumed Mean Method

Step Deviation Method

Weighted Mean Method

Correct Answer: C

Solution:

The step deviation method is suitable for calculating the arithmetic mean in a continuous series with unequal class intervals, as it simplifies calculations by reducing the size of numerical figures.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: B

Solution:

The median is the most appropriate measure of central tendency when the data set contains extreme outliers because it is not affected by extreme values, unlike the arithmetic mean.

Half of the data points are less than or equal to 50.

All data points are equal to 50.

The most frequent data point is 50.

The average of the data points is 50.

Correct Answer: A

Solution:

The median is the central value that divides the dataset into two equal halves, so half of the data points are less than or equal to the median.

248 kWh

252 kWh

249 kWh

251 kWh

Correct Answer: C

Solution:

The incorrect total consumption is 100 * 250 = 25000 kWh. Correcting the error, the new total is 25000 - 500 + 300 = 24800 kWh. The corrected mean is 24800 / 100 = 248 kWh.

Median

Mode

Arithmetic Mean

Geometric Mean

Correct Answer: C

Solution:

The sum of deviations of items from the arithmetic mean is always equal to zero.

Correct Answer: A

Solution:

The arithmetic mean is calculated as the sum of all observations divided by the number of observations:

\frac{10 + 20 + 30 + 40 + 50}{5} = 25

140

210

230

Correct Answer: C

Solution:

When each observation in a dataset is multiplied by a constant, the arithmetic mean is also multiplied by that constant. Therefore, the new arithmetic mean will be

70 \times 3 = 210

Arithmetic Mean

Median

Mode

Harmonic Mean

Correct Answer: C

Solution:

The mode is the most appropriate measure of central tendency for determining the most popular shoe size, as it identifies the value that appears most frequently in the data set.

Correct Answer: B

Solution:

When a constant is added to each observation in a dataset, the arithmetic mean increases by that constant. Therefore, the new arithmetic mean will be 50 + 5 = 55.

Correct Answer: A

Solution:

The arithmetic mean is calculated as

\frac{5 + 10 + 15 + 20 + 25}{5} = 15

Quartiles

Deciles

Percentiles

Medians

Correct Answer: A

Solution:

Quartiles divide a dataset into four equal parts, providing a way to understand the spread and center of the data.

By taking the average of the two middle values.

By selecting the middle value directly.

By selecting the most frequently occurring value.

By calculating the weighted average of all values.

Correct Answer: A

Solution:

For a data set with an even number of observations, the median is calculated by taking the average of the two middle values.

130

120

140

135

Correct Answer: A

Solution:

To find the median, arrange the data in ascending order: 100, 110, 120, 130, 140, 150, 160. The median is the middle value, which is 130.

The distribution is positively skewed.

The distribution is negatively skewed.

The distribution is symmetric.

The distribution cannot be determined.

Correct Answer: A

Solution:

If the mode is greater than the mean, the distribution is positively skewed, indicating that the tail on the right side is longer or fatter than the left side.

Correct Answer: B

Solution:

The original mean is (40 + 50 + 60 + 70 + 80 + 90 + 100) / 7 = 70. If each score is increased by 5, the new mean is 70 + 5 = 75.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: B

Solution:

The median is the most appropriate measure of central tendency when a dataset contains outliers because it is not affected by extreme values.

Arithmetic Mean

Median

Mode

Harmonic Mean

Correct Answer: C

Solution:

Mode is the value which occurs most frequently in a dataset.

100

None of the above

Correct Answer: B

Solution:

The sum of deviations of items from the arithmetic mean is always equal to zero.

Correct Answer: B

Solution:

Arranging the data in ascending order gives: 1, 3, 4, 5, 6, 7, 8, 10, 12. The middle value is 6, so the median is 6.

Arithmetic Mean

Median

Mode

Geometric Mean

Correct Answer: C

Solution:

The mode is the most appropriate measure of central tendency for determining the most frequently occurring value, such as the most popular shoe size.

Correct Answer: A

Solution:

To find the missing value, use the formula for arithmetic mean:

\frac{10 + 20 + 30 + 40 + x}{5} = 28

. Solving for

x

gives

x = 32

Arithmetic mean

Median

Mode

Geometric mean

Correct Answer: C

Solution:

Mode is suitable for determining the average size of readymade garments as it represents the most frequently occurring size.

True or False

Correct Answer: True

Solution:

The mode, being the most frequent value, can often be identified graphically in a histogram or bar chart.

Correct Answer: True

Solution:

The median is defined as the middle value in an ordered data set, dividing it into two equal halves.

Correct Answer: False

Solution:

In a continuous series, the median is calculated by locating the median class and using the formula involving the lower limit, cumulative frequency, and frequency of the median class.

Correct Answer: True

Solution:

Mode is defined as the value that appears most frequently in a data set.

Correct Answer: True

Solution:

The mode is defined as the value that occurs most frequently in a data set.

Correct Answer: True

Solution:

The weighted arithmetic mean assigns weights to different items based on their importance, which affects the calculation of the mean.

Correct Answer: True

Solution:

The arithmetic mean is sensitive to extreme values because it considers all values in the data set.

Correct Answer: True

Solution:

In a perfectly symmetrical distribution, all three measures of central tendency coincide at the same point.

Correct Answer: True

Solution:

The arithmetic mean is affected by extreme values because it considers all data points in its calculation.

Correct Answer: True

Solution:

The mode is the most frequently occurring value and can be determined for both types of data.

Correct Answer: False

Solution:

The arithmetic mean and median are not always equal. The mean is affected by extreme values, while the median is not.

Correct Answer: False

Solution:

The median is not necessarily equal to the arithmetic mean; they are different measures of central tendency.

Correct Answer: True

Solution:

The median is less affected by extreme values and skewed distributions, providing a better central value in such cases.

Correct Answer: False

Solution:

The arithmetic mean is not always greater than the median. The relationship between the mean and median depends on the distribution of the data. In a symmetric distribution, they are equal, while in a skewed distribution, the mean can be either greater or less than the median.

Correct Answer: True

Solution:

Mode is defined as the value that appears most frequently in a data set, as mentioned in the excerpts.

Correct Answer: True

Solution:

The median is defined as the central value of a distribution, where half of the values are less than the median and half are greater.

Correct Answer: True

Solution:

Mode is the value that occurs most frequently in a data set and it can be located graphically using a histogram or a frequency polygon.

Correct Answer: True

Solution:

By definition, the sum of deviations of items from the arithmetic mean is always zero, as stated in the excerpts.

Correct Answer: True

Solution:

The median divides a data set into two equal parts, with half of the values below it and half above it, making it the central value.

Correct Answer: True

Solution:

For continuous data, the arithmetic mean is computed by taking the mid-points of class intervals.

Correct Answer: True

Solution:

In a positively skewed distribution, the arithmetic mean is typically greater than the median due to the influence of higher values.

Correct Answer: False

Solution:

The median is a positional measure and is not affected by extreme values, unlike the arithmetic mean.

Correct Answer: False

Solution:

The median is a positional value and is not affected by extreme values, unlike the arithmetic mean.

Correct Answer: True

Solution:

The arithmetic mean is widely used because it is simple to calculate and considers all data points.

Correct Answer: True

Solution:

In a perfectly symmetric distribution, the arithmetic mean, median, and mode are equal, as implied by the relative positions of these measures.

Correct Answer: False

Solution:

The median is the middle value when a data set is ordered, but it is not necessarily at the exact middle if the number of observations is even.

Correct Answer: False

Solution:

The sum of deviations from the median is not zero; this property holds for the arithmetic mean.

Correct Answer: True

Solution:

The arithmetic mean can be calculated for both grouped and ungrouped data using different methods such as the direct method, assumed mean method, and step deviation method.

Correct Answer: True

Solution:

The sum of deviations of items from the arithmetic mean is zero because it is a property of the arithmetic mean.

Correct Answer: True

Solution:

In a distribution, the median is typically positioned between the mean and the mode.

Correct Answer: False

Solution:

The sum of deviations of items from the median is not zero. This property holds true for the arithmetic mean, not the median.

Correct Answer: True

Solution:

The mode is defined as the value that appears most frequently in a data set. It is one of the measures of central tendency.

Correct Answer: False

Solution:

In a symmetric distribution, the arithmetic mean, median, and mode are equal. The arithmetic mean can be less than, equal to, or greater than the median depending on the distribution of the data.

Correct Answer: True

Solution:

Median is less affected by extreme values and provides a better central tendency measure in such cases.

Correct Answer: True

Solution:

For continuous data, the arithmetic mean is calculated using the midpoints of class intervals to represent each class.

Correct Answer: False

Solution:

The arithmetic mean is affected by extreme values, which can skew the mean towards the extremes.

Measures of Central Tendency

AI Learning Assistant

Summary

Measures of Central Tendency

Summary

Key Formulas/Definitions

Learning Objectives

Common Mistakes/Exam Tips

Important Diagrams

Learning Objectives

Learning Objectives

Detailed Notes

Measures of Central Tendency

Introduction

Types of Averages

Properties of Averages

Calculation Methods

Arithmetic Mean

Median Calculation

Mode Calculation

Conclusion

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Tips for Success

Practice & Assessment

Multiple Choice Questions

Q1.Which measure of central tendency is most appropriate for data with extreme values?

Correct Answer: B

Q2.In a continuous series, what is the formula to calculate the median?

Correct Answer: A

Q3.If the median of a data set is 45, which of the following statements is true?

Correct Answer: A

Q4.A survey of daily wages in a factory shows that the median wage is $50. If a new policy increases the wages of the top 10% earners significantly, how will the median be affected?

Correct Answer: C

Q5.In a continuous series, the median is found using the formula: Median = L + ((N/2 - c.f.)/f) * h. What does 'L' represent in this formula?

Correct Answer: B

Q6.A dataset consists of the following numbers: 10, 20, 20, 30, 40. What is the mode?

Correct Answer: B

Q7.A factory produces three types of products: A, B, and C. The production quantities are 100, 150, and 200 units respectively. The selling prices per unit are 10,10, 10,15, and $20. Calculate the weighted arithmetic mean of the selling prices.

Correct Answer: C

Q8.In a dataset, if the number of values less than a certain value is equal to the number of values greater than that value, what is this value called?

Correct Answer: B

Q9.In a dataset, the arithmetic mean is calculated as the sum of all observations divided by the number of observations. If the dataset consists of the numbers 10, 20, 30, 40, and 50, what is the arithmetic mean?

Correct Answer: B

Q10.Which measure of central tendency divides a dataset into two equal parts?

Correct Answer: C

Q11.A researcher is analyzing the time taken by different employees to complete a task. The times (in minutes) are as follows: 15, 18, 22, 25, 30, 35, 40. If the researcher wants to find the central value of the dataset, which measure should be used?

Correct Answer: B

Q12.If the sum of the deviations of a data set from its arithmetic mean is calculated, what will be the result?

Correct Answer: B

Q13.A data set has the following values: 5, 7, 9, 9, 10, 12, 12, 12, 15. What is the mode of this data set?

Correct Answer: C

Q14.In a village, the size of land holdings is given as 1 acre, 2 acres, 3 acres, 4 acres, and 5 acres. What is the median size of land holdings?

Correct Answer: B

Q15.A group of students scored the following marks in a test: 45, 50, 55, 60, 65, 70, 75, 80, 85, 90. If the teacher wants to summarize the performance of the class using a measure of central tendency that is least affected by extremely high or low scores, which measure should she use?

Correct Answer: B

Q16.A factory produces 100 units, 150 units, 200 units, and 250 units in four different shifts. What is the arithmetic mean of production per shift?

Correct Answer: B

Q17.In a village, the size of land holdings of farmers is distributed as follows: 10% own less than 1 acre, 20% own between 1-2 acres, 50% own between 2-4 acres, and 20% own more than 4 acres. What is the median size of land holdings?

Correct Answer: B

Q18.Baiju is a farmer in Balapur village. If Baiju's land size is above the size of what half the farmers own, which measure of central tendency does this represent?

Correct Answer: B

Q19.Which measure of central tendency is most suitable for qualitative data?

Correct Answer: C

Q20.Baiju, a farmer in Balapur, wants to know if his 1 acre of land is above the average size of land holdings in his village. Which measure of central tendency should he use to determine this?

Correct Answer: A

Q21.In a class of 30 students, the arithmetic mean of their test scores is 75. If one student's score of 90 is removed, what will be the new mean?

Correct Answer: A

Q22.A shoe company wants to determine the most popular shoe size among adults. Which measure of central tendency is most appropriate for this purpose?

Correct Answer: C

Q23.If the arithmetic mean of a dataset is 50 and one of the values is increased by 10, what happens to the arithmetic mean?

Correct Answer: B

Q24.A dataset has the following values: 10, 15, 10, 20, 25, 10, 30. What is the mode of this dataset?

Correct Answer: A

Q25.A dataset has the following values: {3,3,6,7,8,9,10}\{3, 3, 6, 7, 8, 9, 10\}{3,3,6,7,8,9,10}. What is the mode of this dataset?

Correct Answer: A

Q26.If the median of a dataset is 50 and one of the largest values in the dataset is increased significantly, how will this affect the median?

Correct Answer: C

Q27.A company wants to determine the average efficiency of its machines, where efficiency is defined as the ratio of output to input. The efficiencies of the machines are given as 0.8, 0.9, 0.85, and 0.95. Which measure of central tendency should be used to calculate the average efficiency?