Master Descriptive Statistics: Measures of Central Tendency and Dispersion

Question 1

Which measure of central tendency is most heavily influenced by extreme values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 2

The standard deviation is a measure of:

Accepted Answer

The spread of the data around the mean

Answer

The average distance of data points from the mean

Answer

The difference between the maximum and minimum values

Question 3

Which graphical representation is most appropriate for displaying the distribution of a large dataset with a wide range of values?

Accepted Answer

Histogram

Answer

Scatterplot

Answer

Box plot

Question 4

The median is the value that:

Accepted Answer

Divides the data set into two equal halves when arranged in order

Answer

Occurs most frequently in the data set

Answer

Is the average of the data set

Question 5

Which of the following is NOT a characteristic of a normal distribution?

Accepted Answer

Mean < median

Answer

Bell-shaped curve

Answer

Symmetrical

Answer

Outliers are uncommon

Question 6

The range is calculated as:

Accepted Answer

Maximum value - minimum value

Answer

Mean / median

Answer

Standard deviation x mean

Question 7

Which measure of central tendency is most stable and least affected by outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 8

The interquartile range (IQR) is:

Accepted Answer

The difference between the upper quartile (Q3) and the lower quartile (Q1)

Answer

The same as the standard deviation

Answer

The range of the data set divided by the mean

Question 9

Which graphical representation is most effective for identifying outliers?

Accepted Answer

Box plot

Answer

Scatterplot

Answer

Stem-and-leaf plot

Question 10

What is a key limitation of using the mean as a measure of central tendency?

Accepted Answer

It can be significantly influenced by outliers.

Answer

It can only be used for qualitative data.

Answer

It is always a whole number.

Answer

It can be used to compare data sets with different distributions.

Question 11

Which measure of central tendency provides the 'average' value of a dataset?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 12

What formula is used to calculate the range of a dataset?

Accepted Answer

Maximum value minus minimum value

Answer

Sum of all values divided by the number of values

Answer

(Maximum value plus minimum value) divided by 2

Answer

Standard deviation multiplied by the mean

Question 13

Which graphical representation is used to display the distribution of data?

Accepted Answer

Histogram

Answer

Pie chart

Answer

Scatterplot

Answer

Box plot

Question 14

What is the main purpose of a stem-and-leaf plot?

Accepted Answer

To display the distribution and outliers

Answer

To show individual data values

Answer

To calculate measures of central tendency

Answer

To compare multiple datasets

Question 15

Which measure of dispersion is most affected by extreme values?

Accepted Answer

Range

Answer

Variance

Answer

Standard deviation

Answer

Interquartile range

Question 16

What is the difference between a biased and an unbiased sample?

Accepted Answer

Biased samples may favor certain groups, while unbiased samples represent the population more accurately

Answer

Unbiased samples are always larger than biased samples

Answer

Biased samples are more precise than unbiased samples

Answer

There is no difference between biased and unbiased samples

Question 17

Which of the following is NOT a key assumption of inferential statistics?

Accepted Answer

Outliers can be safely excluded

Answer

The sample is representative of the population

Answer

The data is normally distributed

Answer

The sample size is sufficiently large

Question 18

What is the purpose of the null hypothesis in a statistical test?

Accepted Answer

The null hypothesis states that there is no significant difference between groups

Answer

The null hypothesis states that there is a significant difference between groups

Answer

The null hypothesis is always true

Answer

The null hypothesis is always false

Question 19

What is the main objective of descriptive statistics?

Accepted Answer

To summarize and describe a dataset

Answer

To make inferences about a population

Answer

To test hypotheses

Answer

To predict future events

Question 20

When analyzing a skewed data distribution, which measure of central tendency is most suitable and why?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 21

How do sample size and sampling method influence the accuracy of descriptive statistics?

Accepted Answer

Larger sample sizes and random sampling generally increase the accuracy of descriptive statistics.

Answer

Smaller sample sizes and convenience sampling generally lead to less accurate descriptive statistics.

Answer

Sample size has no impact on accuracy, but the sampling method does.

Answer

Sampling method has no impact on accuracy, but sample size does.

Question 22

Stem-and-leaf plots can be misleading if:

Accepted Answer

The stem width is not chosen carefully.

Answer

They are difficult to create.

Answer

They are not resistant to outliers.

Answer

They cannot show the distribution of data.

Question 23

Which of the following is NOT a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Mode

Answer

Median

Question 24

Which of the following distributions is represented by a bell-shaped curve?

Accepted Answer

Normal distribution

Answer

Uniform distribution

Answer

Binomial distribution

Answer

Poisson distribution

Question 25

Which of the following is a limitation of descriptive statistics?

Accepted Answer

They do not provide information about causal relationships.

Answer

They can only be applied to small data sets.

Answer

They are challenging to interpret.

Question 26

What is a primary advantage of using graphical representations of data?

Accepted Answer

They can reveal hidden patterns and trends.

Answer

They are more precise than numerical representations.

Answer

They are easier to create than tabular representations.

Question 27

Which measure of central tendency is most appropriate for data sets with outliers?

Accepted Answer

Median

Answer

Mean

Answer

Range

Answer

Mode

Question 28

The standard deviation of a data set reflects its:

Accepted Answer

Dispersion

Answer

Kurtosis

Answer

Skewness

Answer

Central tendency

Question 29

Which step is NOT involved in calculating the variance of a data set?

Accepted Answer

Adding the data points together

Answer

Subtracting the mean from each data point

Answer

Squaring the differences from the mean

Answer

Summing the squared differences

Question 30

The mode of a data set represents:

Accepted Answer

The value that appears most frequently

Answer

The numerical average of the data

Answer

The middle value of the data set when arranged in ascending order

Answer

The value that is most different from the others

Question 31

Which of the following data sets exhibits the largest range?

Accepted Answer

{1, 10, 15, 20, 25}

Answer

{2, 4, 6, 8, 10}

Answer

{5, 5, 5, 5, 5}

Answer

{0, 2, 4, 6, 8}

Question 32

The mean of a data set provides a measure of its:

Accepted Answer

Central tendency

Answer

Dispersion

Answer

Kurtosis

Answer

Skewness

Question 33

Which property of the median is correct?

Accepted Answer

It remains unaffected by outliers.

Answer

It represents the most commonly occurring value in the data set.

Answer

It always equals the mean of the data set.

Answer

It is computed by dividing the sum of all values by the number of values.

Question 34

The variance of a data set is mathematically equivalent to:

Accepted Answer

The square of the standard deviation

Answer

The mean of the data set

Answer

The sum of the data set

Answer

The range of the data set

Question 35

Which data set has the lowest standard deviation?

Accepted Answer

{5, 5, 5, 5, 5}

Answer

{0, 5, 10, 15, 20}

Answer

{1, 2, 3, 4, 5}

Answer

{-5, -2, 1, 4, 7}

Question 36

The median of a data set represents:

Accepted Answer

The middle value

Answer

The least common value

Answer

The most common value

Answer

The average value

Question 37

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Variance

Answer

Standard deviation

Answer

Range

Question 38

Identify a limitation of descriptive statistics:

Accepted Answer

They cannot make predictions about the future

Answer

None of the above

Answer

They can only be used to describe small data sets

Answer

They are not reliable

Question 39

Identify the mode of the following data set: 10, 12, 14, 16, 18, 20, 20

Accepted Answer

20

Answer

14

Answer

10

Answer

16

Question 40

Which measure of central tendency is most sensitive to outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 41

Identify a characteristic of a normal distribution:

Accepted Answer

It is symmetrical around the mean

Answer

It is bimodal

Answer

It is skewed to the right

Answer

It is skewed to the left

Question 42

A researcher wants to find the most common height of students in a college. Which measure of central tendency would be most appropriate?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Range

Question 43

The ages of employees in a department are: 25, 28, 31, 31, 35, 38, 42. What is the median age?

Accepted Answer

31

Answer

28

Answer

35

Answer

33

Question 44

Which measure of dispersion is most affected by extreme values in a dataset?

Accepted Answer

Range

Answer

Interquartile Range

Answer

Standard Deviation

Answer

Variance

Question 45

A company wants to compare the spread of salaries between two departments. Which measure of dispersion would be most appropriate?

Accepted Answer

Standard Deviation

Answer

Median

Answer

Mean

Question 46

A researcher collects data on the number of hours students study per week. The data is skewed to the right. Which measure of central tendency is least affected by this skewness?

Accepted Answer

Median

Answer

Range

Answer

Mean

Answer

Mode

Question 47

If data is normally distributed, approximately what percentage of the data falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

50%

Answer

99.7%

Answer

95%

Question 48

A box-and-whisker plot displays which of the following?

Accepted Answer

Minimum, Maximum, Median, First Quartile, Third Quartile

Answer

Mode, Median, Range

Answer

Frequency, Relative Frequency, Cumulative Frequency

Answer

Mean, Standard Deviation, Variance

Question 49

What type of data is best represented by a histogram?

Accepted Answer

Continuous data

Answer

Categorical data

Answer

Ordinal data

Answer

Nominal data