Descriptive Statistics: Master the Basics of Data Analysis

Question 1

When a dataset contains outliers, which measure of central tendency is least affected by their presence?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 2

What is a primary benefit of using descriptive statistics in data analysis?

Accepted Answer

Summarizes large data sets

Answer

Easily calculated by hand

Answer

Used to test statistical hypotheses

Answer

Predicts future trends

Question 3

Which of the following is a measure of central tendency, indicating the average value of a dataset?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 4

The median of a dataset is the middle value when arranged in ascending or descending order. True or False?

Accepted Answer

True

Answer

False

Question 5

Which measure of variability indicates the average squared difference from the mean?

Accepted Answer

Variance

Answer

Range

Answer

Standard deviation

Answer

Coefficient of variation

Question 6

The formula for calculating variance involves summing the squared deviations from the mean and dividing by the number of observations. True or False?

Accepted Answer

True

Answer

False

Question 7

When the mean, median, and mode of a dataset are all equal, what does this suggest?

Accepted Answer

The data is symmetrically distributed.

Answer

The data is skewed.

Answer

The data has a large variance.

Answer

The data is bimodal.

Question 8

The standard deviation of a dataset has the same units of measurement as the data itself. True or False?

Accepted Answer

True

Answer

False

Question 9

Which of the following is a limitation of descriptive statistics?

Accepted Answer

They cannot make generalizations beyond the sample.

Answer

They are always accurate.

Answer

They are easy to interpret.

Answer

They can be used for predictive purposes.

Question 10

Which measure of central tendency signifies the value that appears most frequently in a dataset?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Question 11

The range of a dataset represents:

Accepted Answer

The difference between the highest and lowest values

Answer

The average of all the values

Answer

The most frequently occurring value

Question 12

Given a dataset with a mean of 50 and a variance of 25, what is its standard deviation?

Accepted Answer

10

Answer

5

Answer

15

Question 13

Which characteristic is NOT associated with a normal distribution?

Accepted Answer

Tails extend infinitely

Answer

Symmetrical bell shape

Answer

Mean, median, and mode are equal

Question 14

The median of a dataset divides the data into two equal parts. What is the median of {2, 4, 6, 8, 10}?

Accepted Answer

5

Answer

4

Answer

6

Question 15

A study gathers data on student heights, with a mean of 64 inches and a standard deviation of 3 inches. If a student is 67 inches tall, how many standard deviations above the mean is their height?

Accepted Answer

1

Answer

0.5

Answer

1.5

Question 16

Which of the following describes a key feature of the mode?

Accepted Answer

It may occur multiple times

Answer

It is always unique

Answer

It can represent any value in the dataset

Question 17

The mean of a dataset is affected by:

Accepted Answer

Extreme values

Answer

Number of data points

Answer

Shape of the distribution

Question 18

Which of these datasets exhibits the greatest variability?

Accepted Answer

{0, 10, 20, 30, 40}

Answer

{1, 2, 3, 4, 5}

Answer

{1, 3, 5, 7, 9}

Question 19

Which measure of central tendency is significantly influenced by extreme values?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 20

Which characteristic is NOT associated with the normal distribution?

Accepted Answer

Always having mode at the center

Answer

Bell-shaped curve

Answer

Symmetry

Answer

Equal mean and median

Question 21

What is the standard deviation of a dataset with a variance of 25?

Accepted Answer

10

Answer

5

Answer

15

Answer

2.5

Question 22

Distinguish between range and standard deviation as measures of variability. Provide an example to illustrate your explanation.

Accepted Answer

Range, the difference between the highest and lowest data points, shows the data's spread. Standard deviation measures how much the data varies around its mean, indicating its fluctuation.

Answer

Both range and standard deviation measure the average distance of data points from the mean.

Answer

Range, the square root of the variance, differs from standard deviation, which is the square of the variance.

Answer

Range is a more reliable measure of variability compared to standard deviation.

Question 23

Identify the measure of central tendency that represents the most frequently occurring data value.

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Standard deviation

Question 24

Which of the following is NOT considered a measure of variability?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 25

Consider two datasets: Dataset A with a mean of 10 and a variance of 4, and Dataset B with a mean of 12 and a variance of 6. Which dataset would you conclude to have a greater dispersion of data?

Accepted Answer

Dataset B

Answer

Dataset A

Answer

They have the same spread

Answer

Cannot be determined from the given information

Question 26

Which type of statistical distribution is characterized by being symmetrically distributed around its mean?

Accepted Answer

Normal distribution

Answer

Skewed distribution

Answer

Uniform distribution

Answer

Bimodal distribution

Question 27

Which of the following is NOT a measure used to describe a distribution of data in descriptive statistics?

Accepted Answer

Linear regression

Answer

Mean

Answer

Standard deviation

Answer

Variance

Question 28

Which measure of central tendency is calculated by adding all the data points and then dividing by the number of data points?

Accepted Answer

Mean

Answer

Median

Answer

Range

Answer

Mode

Question 29

Find the median of the following dataset: [2, 4, 6, 8, 10]

Accepted Answer

6

Answer

5

Answer

8

Answer

7

Question 30

Which of the following is the value in a dataset that appears most frequently?

Accepted Answer

Mode

Answer

Range

Answer

Median

Answer

Mean

Question 31

Which measure of variability represents the average of the squared differences between each data point and the mean?

Accepted Answer

Variance

Answer

Standard deviation

Answer

Range

Answer

Mean

Question 32

Which of the following is NOT a purpose of descriptive statistics?

Accepted Answer

Making predictions about future events

Answer

Summarizing and describing data

Answer

Identifying patterns and trends

Question 33

When should the median be used instead of the mean as a measure of central tendency?

Accepted Answer

When the data is skewed or contains outliers

Answer

When the data has a small number of data points

Answer

When the data is normally distributed

Answer

When the data is symmetric

Question 34

Which measure of central tendency represents the middle value of a dataset when arranged in ascending order?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 35

A dataset with a larger variance is likely to have:

Accepted Answer

Data points more spread out

Answer

Data points more clustered around the mean

Answer

Data points normally distributed

Answer

Data points evenly distributed

Question 36

Which of the following is NOT a measure of descriptive statistics?

Accepted Answer

Correlation coefficient

Answer

Mean

Answer

Standard deviation

Answer

Range

Question 37

In a skewed distribution, which measure of central tendency is typically most representative of the data?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 38

Which measure of variability is the average of the squared deviations from the mean?

Accepted Answer

Variance

Answer

Skewness

Answer

Standard deviation

Answer

Kurtosis

Question 39

A dataset with a mean of 10 and a standard deviation of 5 is said to be:

Accepted Answer

Normally distributed with a probability of 68% of data points falling within one standard deviation of the mean

Answer

Negatively skewed

Answer

Positively skewed

Answer

Bimodal

Question 40

In a symmetric distribution, the mean and median are:

Accepted Answer

Equal

Answer

Cannot be determined without more information

Answer

Different

Question 41

Which of the following is NOT a common use of descriptive statistics?

Accepted Answer

Predicting future events

Answer

Describing data patterns

Answer

Making inferences about a population

Answer

Summarizing data

Question 42

The range of a dataset is calculated as:

Accepted Answer

Maximum value - Minimum value

Answer

Variance + Standard deviation

Answer

Mean - Median

Answer

Sum of all data points

Question 43

Which of the following is **not** a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Mode

Answer

Median

Question 44

The mean of a set of numbers is calculated by summing all the numbers and dividing by the:

Accepted Answer

Number of numbers

Answer

Standard deviation of the numbers

Answer

Range of the numbers

Question 45

The range of a set of numbers is the difference between the:

Accepted Answer

Maximum and minimum values

Answer

Mean and median

Answer

Median and mode

Answer

Standard deviation and variance

Question 46

The variance of a set of numbers measures the:

Accepted Answer

Spread of the numbers

Answer

Kurtosis of the numbers

Answer

Skewness of the numbers

Answer

Central tendency of the numbers

Question 47

The standard deviation of a set of numbers is the:

Accepted Answer

Square root of the variance

Answer

Mean of the numbers

Answer

Sum of the numbers

Answer

Range of the numbers

Question 48

A normal distribution is a symmetrical distribution where the:

Accepted Answer

Mean, median, and mode are equal

Answer

Median is greater than the mode

Answer

Mode is greater than the range

Answer

Mean is greater than the median

Question 49

A skewed distribution is a distribution where the:

Accepted Answer

Mean and median are not equal

Answer

Median and mode are equal

Answer

Mean and standard deviation are equal

Answer

Range and variance are equal

Question 50

Which of the following is a measure of central tendency?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Range

Answer

Variance

Question 51

Which of the following definitions of median is correct?

Accepted Answer

The middle value when the data is arranged in ascending order.

Answer

The sum of all values divided by the total number of values.

Answer

The most frequently occurring value in the data set.

Question 52

What is the range of the data set {2, 5, 7, 10, 12}?

Accepted Answer

10

Answer

5

Answer

7

Question 53

Which of the following measures of variability is most sensitive to extreme values?

Accepted Answer

Range

Answer

None of the above

Answer

Standard deviation

Answer

Variance

Question 54

Which of the following formulas is used to calculate the standard deviation?

Accepted Answer

Square root of Variance

Answer

Variance / Mean

Answer

Variance + Mean

Answer

Mean - Variance

Question 55

Which of the following statements about the relationship between measures of central tendency and measures of variability is correct?

Accepted Answer

Measures of variability describe the spread of data around the central tendency.

Answer

Measures of central tendency and measures of variability are unrelated.

Answer

Measures of central tendency describe the variability of data.

Question 56

In a data set, the mean is 10 and the standard deviation is 2. What is the z-score of a value that is 12?

Accepted Answer

1

Answer

-1

Answer

0.5

Answer

2