Descriptive Statistics: Measures of Central Tendency and Variability

Question 1

Which measure of central tendency is most affected by extremely high or low values (outliers)?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 2

Which of the following is NOT a measure of variability?

Accepted Answer

Mean

Answer

Range

Answer

Interquartile range

Question 3

The coefficient of variation measures:

Accepted Answer

Relative variability

Answer

Absolute variability

Answer

Central tendency

Question 4

A limitation of descriptive statistics is that they:

Accepted Answer

Cannot make inferences about the population from which the data was sampled

Answer

Are always sensitive to outliers

Answer

Provide too much detail about the data

Question 5

The median of a dataset is the value that:

Accepted Answer

Splits the data into two equal halves

Answer

Occurs most frequently in the dataset

Answer

Is the average of the highest and lowest values in the dataset

Question 6

If the range of a dataset is 10 and the minimum value is 5, determine the maximum value.

Accepted Answer

15

Answer

10

Answer

20

Question 7

Which of these is a measure of variability, not central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Mode

Answer

Median

Question 8

Which measure of central tendency is least affected by a skewed distribution?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 9

A company's sales data shows an average (mean) of $10,000 and a variation (standard deviation) of $2,000. What does this information tell us about the company's sales?

Accepted Answer

Most sales are close to $10,000, but there is some difference in sales amounts.

Answer

Sales are very steady, with little difference in sales amounts.

Answer

Sales are unpredictable, with no clear pattern.

Question 10

In a symmetrical distribution, which of the following statements correctly describes the relationship between the mean, median, and mode?

Accepted Answer

Mean = Median = Mode

Answer

Mean ≠ Median ≠ Mode

Answer

Mean ≠ Median = Mode

Answer

Mean = Median > Mode

Question 11

How does increasing the sample size generally affect the accuracy of descriptive statistics?

Accepted Answer

Increases accuracy

Answer

Decreases accuracy

Answer

No effect on accuracy

Question 12

The range of a dataset is defined as:

Accepted Answer

Maximum value minus the minimum value

Answer

The most frequently occurring value

Answer

The average of all data points

Answer

The difference between the median and the mean

Question 13

The standard deviation of a dataset measures:

Accepted Answer

How spread out the data is

Answer

The difference between the highest and lowest values

Answer

The most frequently occurring value

Answer

The average value of the data

Question 14

Which of the following is a limitation of descriptive statistics?

Accepted Answer

It cannot establish cause-and-effect relationships

Answer

It can be time-consuming to calculate

Answer

It is only suitable for small datasets

Answer

It cannot identify trends or patterns

Question 15

The median of a dataset is defined as:

Accepted Answer

The middle value when assorted in ascending order

Answer

The most frequently occurring value

Answer

The sum of all data points

Question 16

An example of a categorical variable is:

Accepted Answer

Gender

Answer

Weight

Answer

Age

Answer

Height

Question 17

Which measure of central tendency is most significantly influenced by extreme values (outliers)?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 18

Which of the following is NOT a measure of variability in a dataset?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 19

When working with a dataset with a skewed distribution, which measure of central tendency would be most appropriate?

Accepted Answer

Median

Answer

Standard deviation

Answer

Mode

Answer

Mean

Question 20

Which of the following is NOT an advantage of using descriptive statistics?

Accepted Answer

Provides detailed insights into individual data points.

Answer

Summarizes data concisely.

Answer

Identifies trends and patterns.

Question 21

When analyzing a dataset, it is crucial to consider the:

Accepted Answer

Context and relevance of the data.

Answer

Statistical measures solely.

Answer

Type of data solely.

Answer

Number of data points solely.

Question 22

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

Accepted Answer

Range

Answer

Mean

Answer

Mode

Answer

Median

Question 23

The interquartile range (IQR) of a dataset is 12. If the lower quartile (Q1) is 40, determine the upper quartile (Q3).

Accepted Answer

52

Answer

46

Answer

64

Answer

32

Question 24

Identify a primary limitation of descriptive statistics.

Accepted Answer

They do not establish causal relationships.

Answer

They are complex to interpret.

Answer

They are not precise enough.

Answer

They can be biased.

Question 25

To compare the mean heights of two groups, which statistical test is appropriate?

Accepted Answer

Two-sample t-test

Answer

One-sample t-test

Answer

Chi-square test

Question 26

Which graphical representation effectively displays the distribution of a continuous variable?

Accepted Answer

Histogram

Answer

Scatterplot

Answer

Pie chart

Answer

Bar chart

Question 27

Which measure of central tendency is least affected by outliers?

Accepted Answer

Median

Answer

Mode

Answer

Standard deviation

Answer

Mean

Question 28

Which of the following is NOT a measure of variability?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 29

Calculate the range of the dataset {1, 3, 5, 7, 9}.

Accepted Answer

8

Answer

12

Answer

10

Answer

14

Question 30

What is the variance of the dataset with values {2, 4, 6, 8, 10}?

Accepted Answer

8

Answer

14

Answer

10

Answer

12

Question 31

Which measure of central tendency is most appropriate for a dataset with extreme values?

Accepted Answer

Median

Answer

Standard deviation

Answer

Mean

Answer

Mode

Question 32

What is the probability of obtaining a z-score between -1.96 and 1.96?

Accepted Answer

0.95

Answer

0.025

Answer

0.05

Answer

0.10

Question 33

Which of the following is NOT a type of bar chart?

Accepted Answer

Pie chart

Answer

Histogram

Answer

Clustered bar chart

Answer

Stacked bar chart

Question 34

Which of the following is a measure that describes the center of a dataset?

Accepted Answer

Mean

Answer

Variance

Answer

Range

Question 35

Which of these measures tells us how spread out a dataset is?

Accepted Answer

Standard deviation

Answer

Mode

Answer

Median

Answer

Mean

Question 36

What is the range of the following set of numbers: 3, 7, 12, 18, 24?

Accepted Answer

21

Answer

30

Answer

15

Answer

25

Question 37

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

Accepted Answer

Range

Answer

Standard deviation

Answer

Mean

Answer

Variance

Question 38

What is the mode of the following numbers: 4, 6, 8, 8, 10?

Accepted Answer

8

Answer

There is no mode

Answer

6

Answer

10

Question 39

Why might the mean not be the best way to represent the center of a dataset?

Accepted Answer

It can be heavily influenced by extreme values.

Answer

It is difficult to calculate.

Answer

It doesn't represent the typical value well.

Answer

It is not a commonly used measure.

Question 40

How are variance and standard deviation related?

Accepted Answer

The standard deviation is the square root of the variance.

Answer

The standard deviation is twice the variance.

Answer

The variance is the square of the standard deviation.

Question 41

What is a common use for descriptive statistics?

Accepted Answer

Analyzing and summarizing data.

Answer

Testing specific hypotheses about data.

Answer

Building complex mathematical models.

Question 42

What is the key difference between a parameter and a statistic?

Accepted Answer

A parameter describes a whole population, while a statistic describes a sample from that population.

Answer

A parameter is a variable, while a statistic is a constant.

Question 43

The data set: 2, 4, 6, 8, 10 has a mean of 6. What is the variance of this data set?

Accepted Answer

8

Answer

16

Answer

4

Answer

2

Question 44

A data set has a mean of 10 and a standard deviation of 2. Which of the following values is most likely to be an outlier in this data set?

Accepted Answer

16

Answer

14

Answer

8

Answer

12

Question 45

In a data set, the mode is 5. What does this tell us about the data?

Accepted Answer

The value 5 occurs most frequently in the data set.

Answer

The data set is evenly distributed around the value 5.

Answer

The average value of the data set is 5.

Question 46

A researcher is analyzing the distribution of test scores. Which measure of central tendency would be most appropriate to use if the data is skewed?

Accepted Answer

Median

Answer

Range

Answer

Mode

Answer

Mean

Question 47

A data set has a range of 20. What does this tell us about the data?

Accepted Answer

The difference between the highest and lowest values in the data set is 20.

Answer

The data set is evenly distributed across a range of 20.

Answer

The average value of the data set is 20.

Question 48

A data set has a standard deviation of 0. What does this tell us about the data?

Accepted Answer

All the values in the data set are the same.

Answer

The average value of the data set is 0.

Answer

There are no outliers in the data set.

Answer

The data set is evenly distributed.

Question 49

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

Accepted Answer

Interquartile range

Answer

Mode

Answer

Median

Answer

Mean

Question 50

A researcher is analyzing the heights of a group of people. They find that the mean height is 170 cm, the median height is 168 cm, and the mode height is 165 cm. What can we conclude about the distribution of heights?

Accepted Answer

The distribution of heights is slightly skewed to the right.

Answer

The distribution of heights is symmetrical.

Answer

The distribution of heights is skewed to the left.