Master Descriptive Statistics: A Comprehensive Guide for Mechanical Engineering Students

Question 1

The standard deviation is a measure of:

Accepted Answer

Variability

Answer

Central tendency

Answer

Frequency

Answer

Correlation

Question 2

What is the distinction between a population and a sample?

Accepted Answer

Population is larger than sample; sample is representative of population

Answer

Sample is larger than population; population is representative of sample

Answer

Population is unknown; sample is known

Answer

Sample is unknown; population is known

Question 3

What does the range of a dataset represent?

Accepted Answer

Difference between the highest and lowest values

Answer

Average of the highest and lowest values

Answer

Sum of all the values

Answer

Product of all the values

Question 4

Which of the following measures the strength of a linear relationship between two variables?

Accepted Answer

Correlation coefficient

Answer

Standard deviation

Answer

Mean

Answer

Variance

Question 5

What is the primary goal of descriptive statistics?

Accepted Answer

To summarize and characterize the main features of a dataset

Answer

To make inferences about a population based on a sample

Answer

To predict future outcomes

Answer

To perform hypothesis testing

Question 6

Which characteristic is NOT associated with a normal distribution?

Accepted Answer

Standard deviation = Variance

Answer

Bell-shaped

Answer

Symmetrical

Answer

Mean = Median

Question 7

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

Accepted Answer

To display the distribution of a dataset

Answer

To calculate measures of central tendency

Answer

To identify outliers

Answer

To perform statistical inference

Question 8

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

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 9

A scatter plot exhibits a positive correlation between variables. What does this imply?

Accepted Answer

As one variable increases, the other also increases.

Answer

As one variable decreases, the other also decreases.

Answer

The variables are not related.

Question 10

Which measure of central tendency is most resistant to the influence of outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 11

Which of the following measures of central tendency describes the typical or average value in a data set?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 12

Which of the following graphical representations is most suitable for displaying the distribution of a data set?

Accepted Answer

Histogram

Answer

Scatter plot

Answer

Pie chart

Answer

Bar graph

Question 13

What does a standard deviation of 0 indicate about a data set?

Accepted Answer

The data has no variation.

Answer

The data is spread out over a wide range.

Answer

The data is skewed towards one extreme.

Answer

The data contains missing values.

Question 14

What is the purpose of a histogram?

Accepted Answer

To show the frequency distribution of data.

Answer

To compare two or more data sets.

Answer

To predict future trends.

Answer

To identify outliers.

Question 15

Which of these is NOT a measure of central tendency?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 16

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 17

A data set with a high standard deviation is likely to be:

Accepted Answer

Widely dispersed

Answer

Clustered around the mean

Answer

Symmetrically distributed

Answer

Normally distributed

Question 18

Which graphical representation is most appropriate for displaying the distribution of a categorical variable?

Accepted Answer

Bar chart

Answer

Histogram

Answer

Scatter plot

Answer

Line graph

Question 19

Which of the following is true about the mode of a data set?

Accepted Answer

It can occur multiple times.

Answer

It is always unique.

Answer

It is not affected by outliers.

Answer

It is the most extreme value in the data set.

Question 20

Which of the following is a measure of variability?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 21

Which measure of central tendency provides the most reliable estimate when data is skewed, meaning it has a disproportionate number of values on one side of the distribution?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 22

The standard deviation is a measure of:

Accepted Answer

The average distance of data points from the mean

Answer

The frequency of occurrence of data values

Answer

The central value of a dataset

Question 23

Which of the following is NOT a measure of variability, which describes how spread out data is?

Accepted Answer

Median

Answer

Range

Answer

Variance

Question 24

A histogram is a graphical representation used to:

Accepted Answer

Display the distribution of continuous data by dividing it into bins

Answer

Show the relationship between two variables

Answer

Summarize categorical data

Question 25

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

Accepted Answer

Drawing inferences about a population from a sample

Answer

Summarizing data

Answer

Describing data patterns

Question 26

The interquartile range (IQR) represents:

Accepted Answer

The range of the middle 50% of data, excluding the lowest and highest 25%

Answer

The difference between the maximum and minimum values

Answer

The spread of all data points

Question 27

Which graphical representation is most suitable for comparing multiple datasets by displaying their distributions?

Accepted Answer

Box plot

Answer

Bar chart

Answer

Scatter plot

Question 28

The mode is defined as:

Accepted Answer

The value that occurs most frequently in a dataset

Answer

The arithmetic average of all data points

Answer

The value that divides a dataset into two equal halves

Question 29

Which measure of central tendency is least affected by extreme values, also known as outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 30

Descriptive statistics is a type of statistics that:

Accepted Answer

Uses numerical and graphical methods to describe and summarize data

Answer

Involves making inferences about a population based on a sample

Answer

Predicts future events based on historical data

Question 31

Which measure of central tendency represents the data point that occurs most frequently in a dataset?

Accepted Answer

Mode

Answer

Mean

Answer

Median

Answer

Range

Question 32

The variance of a dataset is a measure of its:

Accepted Answer

Spread or dispersion

Answer

Central value

Answer

Shape

Answer

Outliers

Question 33

Which graphical representation is ideal for displaying the frequency distribution of a continuous dataset?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Pie chart

Answer

Scatter plot

Question 34

According to the Empirical Rule, approximately what percentage of data points in a normal distribution lies within one standard deviation from the mean?

Accepted Answer

68.3%

Answer

34.1%

Answer

95.5%

Answer

99.7%

Question 35

Which of the following is an incorrect characteristic of a normal distribution?

Accepted Answer

Skewed

Answer

Symmetrical

Answer

Bell-shaped

Answer

Unimodal

Question 36

Which statement accurately describes the range of a dataset?

Accepted Answer

It can be affected by outliers.

Answer

It is a measure of central tendency.

Answer

It is expressed in standard deviation units.

Answer

It is appropriate for comparing two datasets.

Question 37

Which measure of central tendency is most suitable for representing the typical salary in a dataset of employee salaries?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 38

In a normal distribution with a mean of 50 and a standard deviation of 5, what is the probability of randomly selecting a value between 45 and 55?

Accepted Answer

0.683

Answer

0.383

Answer

0.955

Answer

0.997

Question 39

Which of the following is a measure of central tendency, indicating the typical value around which data is clustered?

Accepted Answer

Mean

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 40

What does the interquartile range (IQR) represent?

Accepted Answer

The range of values between the 25th and 75th percentiles, indicating the middle 50% of the data

Answer

The difference between the maximum and minimum values

Answer

The average value of the data set

Answer

The standard deviation of the data set

Question 41

Which graphical representation is most appropriate for displaying a distribution that may have extreme values or outliers?

Accepted Answer

Box plot

Answer

Histogram

Answer

Stem-and-leaf plot

Answer

Pie chart

Question 42

How is the mean, representing the average value of a data set, calculated?

Accepted Answer

Sum of all values divided by the number of values

Answer

Sum of all values squared divided by the number of values

Answer

Square root of the variance

Answer

Median value of the data set

Question 43

Which of the following is not an advantage of using a histogram?

Accepted Answer

Requires interpolation to determine exact values, limiting precision

Answer

Can reveal patterns and outliers

Answer

Shows the frequency of values

Answer

Can be used to compare different distributions

Question 44

What does the coefficient of variation indicate about a data set?

Accepted Answer

The relative variability compared to the mean, indicating the extent to which data is dispersed

Answer

The mean value of the data set

Answer

The range of values in the data set

Answer

The number of outliers in the data set

Question 45

According to the empirical rule for a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

Accepted Answer

68%

Answer

95%

Answer

99.7%

Answer

50%

Question 46

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

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 47

Which measure of central tendency represents the value that divides a dataset into two equal halves?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 48

Which of the following is not a measure of variability?

Accepted Answer

Quartile

Answer

Standard deviation

Answer

Variance

Answer

Range

Question 49

The interquartile range (IQR) is a measure of:

Accepted Answer

Variability

Answer

Central tendency

Answer

Skewness

Answer

Kurtosis

Question 50

For a skewed dataset, which measure of central tendency best represents the typical value?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 51

The coefficient of variation (CV) measures:

Accepted Answer

Relative variability

Answer

Absolute variability

Answer

Central tendency

Answer

Distribution shape

Question 52

When dealing with data that may contain outliers, which measure of central tendency is most appropriate?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Standard deviation

Question 53

A box plot displays:

Accepted Answer

The minimum, maximum, median, and quartiles

Answer

The mode, range, and standard deviation

Answer

The mean, median, and distribution shape

Answer

The variability and outliers