Master Descriptive Statistics: A Comprehensive Guide for Sixth Formers

Question 1

Which formula represents the calculation of standard deviation?

Accepted Answer

σ = √(Σ(x - μ)² / N)

Answer

σ = Σ(x - μ) / N

Answer

σ = Σ(x²) - μ² / N

Answer

σ = N / Σ(x - μ)²

Question 2

What is the primary purpose of z-scores?

Accepted Answer

To standardize data and compare values from different distributions

Answer

To calculate the mean and standard deviation of a data set

Answer

To identify outliers in a data set

Answer

To predict the probability of future events

Question 3

Which graphical representation is appropriate for comparing multiple datasets?

Accepted Answer

Bar chart

Answer

Pie chart

Answer

Scatter plot

Answer

Histogram

Question 4

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 5

Which graphical representation is most effective for identifying outliers in a dataset?

Accepted Answer

Box plot

Answer

Bar chart

Answer

Pie chart

Answer

Line graph

Question 6

Identify a limitation of using descriptive statistics.

Accepted Answer

They can be misleading if the data is not representative.

Answer

They do not provide information about individual data points.

Answer

They are only useful for small datasets.

Answer

They are difficult to calculate.

Question 7

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

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Mode

Question 8

Which of the following is the most appropriate measure of central tendency for a data set with outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 9

What is the z-score of a data point that is 2 standard deviations below the mean?

Accepted Answer

-2

Answer

0

Answer

-1

Answer

-3

Question 10

What is the difference between a population and a sample?

Accepted Answer

A population is the entire group of interest, while a sample is a subset of the population selected to represent the population.

Answer

A sample is the entire group of interest, while a population is a subset of the sample selected to represent the sample.

Answer

A population is a group of people, while a sample is a group of objects.

Answer

A sample is a group of people, while a population is a group of objects.

Question 11

Which of these is NOT a measure of the 'middle' of a set of data?

Accepted Answer

Range

Answer

Mean

Answer

Mode

Question 12

Which of the following is a measure of dispersion, or spread, in a data set?

Accepted Answer

Standard deviation

Answer

Mean

Question 13

Which measure of central tendency is strongly influenced by extreme values and can be skewed by outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 14

A dataset has a variance of 36. Calculate its standard deviation.

Accepted Answer

12

Answer

6

Answer

18

Question 15

Which graphical representation is most appropriate for visualizing the distribution of categorical data?

Accepted Answer

Pie chart

Answer

Histogram

Answer

Scatter plot

Question 16

What is the z-score of a value that is 3 standard deviations below the mean?

Accepted Answer

-3

Answer

0

Answer

3

Question 17

Which measure of dispersion indicates the average squared deviation from the mean?

Accepted Answer

Variance

Answer

Range

Answer

Standard deviation

Question 18

A dataset has a mean of 15 and a mode of 12. What can be inferred about the distribution of the data?

Accepted Answer

Skewed to the left

Answer

Symmetrical

Answer

Skewed to the right

Question 19

Which measure of central tendency is least affected by outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 20

The standard deviation of a dataset measures its:

Accepted Answer

Spread or dispersion

Answer

Average value

Answer

Most frequent value

Question 21

The mode of a dataset is the:

Accepted Answer

Value that occurs most frequently

Answer

Average of the data values

Answer

Difference between the highest and lowest data values

Question 22

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

Accepted Answer

Pie chart

Answer

Histogram

Answer

Scatter plot

Question 23

The variance of a dataset is calculated as the:

Accepted Answer

Sum of squared deviations from the mean divided by the number of values

Answer

Square of the standard deviation

Answer

Difference between the highest and lowest data values

Question 24

The range of a dataset is the:

Accepted Answer

Difference between the highest and lowest data values

Answer

Number of data values in the dataset

Answer

Average of the data values

Question 25

A dataset has a mean of 50 and a standard deviation of 10. Which of the following values is most likely not an outlier?

Accepted Answer

45

Answer

20

Answer

80

Question 26

A histogram is a graphical representation that is used to display the:

Accepted Answer

Distribution of a continuous variable

Answer

Relationship between two variables

Answer

Cumulative frequency of a variable

Question 27

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 28

The standard deviation of a data set measures:

Accepted Answer

The spread of data points around the mean

Answer

The average distance of data points from the mean

Answer

The difference between the largest and smallest data points

Answer

The frequency of occurrence of data points

Question 29

Which of the following graphical representations is suitable for displaying a skewed distribution?

Accepted Answer

Histogram

Answer

Bar chart

Answer

Pie chart

Answer

Scatter plot

Question 30

A company collects data on the monthly sales of its products. Which of the following measures would be most appropriate to use to compare the average performance of different products?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Variance

Question 31

Which measure of central tendency is most influenced by extreme values and can be misleading when there are outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 32

The standard deviation primarily measures:

Accepted Answer

The spread or dispersion of a distribution

Answer

The central point of a distribution

Answer

The skewness of a distribution

Question 33

Which type of graphical representation is most appropriate for displaying the frequency distribution of a continuous variable?

Accepted Answer

Histogram

Answer

Pie chart

Answer

Bar chart

Question 34

If the mean of a dataset is greater than the median, what can you infer about the distribution?

Accepted Answer

It is skewed to the right (positively skewed).

Answer

It is skewed to the left (negatively skewed).

Answer

It is symmetric.

Question 35

The variance of a dataset is 36. What is the corresponding standard deviation?

Accepted Answer

6

Answer

2

Answer

12

Question 36

What is the z-score of a value that is 2 standard deviations above the mean in a normal distribution?

Accepted Answer

2

Answer

0

Answer

1

Question 37

Which of the following is a measure of data spread or variability?

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 38

The standard deviation measures:

Accepted Answer

How spread out the data is

Answer

The centre of the data

Answer

The most frequently occurring value

Answer

The difference between the maximum and minimum values

Question 39

Which of the following is a valid interpretation of a variance value?

Accepted Answer

The average squared deviation from the mean

Answer

The units of measurement of the data

Answer

The square root of the standard deviation

Answer

The mean of the absolute deviations from the median

Question 40

The mean of a data set is 10 and the standard deviation is 2. What range of values are within one standard deviation of the mean?

Accepted Answer

8-12

Answer

6-14

Answer

10-14

Answer

12-16

Question 41

A histogram displays:

Accepted Answer

The frequency of values in a data set

Answer

The cumulative frequency of values in a data set

Answer

The mean, median, and mode of a data set

Answer

The standard deviation and variance of a data set

Question 42

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

Accepted Answer

Making predictions about future outcomes

Answer

Summarizing and simplifying data

Answer

Drawing conclusions about a population

Answer

Communicating data clearly and effectively

Question 43

For a skewed distribution, the most suitable measure of central tendency is the:

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 44

Which measure of central tendency is most suitable for skewed data, where the distribution is not symmetric?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 45

If the variance of a dataset is 25, what is the standard deviation?

Accepted Answer

10

Answer

5

Answer

15

Answer

20

Question 46

A survey asks students to rate their satisfaction with a course on a scale of 1 to 5. Which graphical representation would be most appropriate to show the frequency of responses for each rating?

Accepted Answer

Bar chart

Answer

Line graph

Answer

Histogram

Answer

Scatter plot

Question 47

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 48

A company wants to determine the average age of its employees. Which sampling method would be most appropriate to ensure a fair and unbiased representation of the population?

Accepted Answer

Random sampling

Answer

Convenience sampling

Answer

Quota sampling

Answer

Stratified sampling

Question 49

When a scatter plot shows a strong positive correlation, what does this indicate about the relationship between the variables?

Accepted Answer

As the value of one variable increases, the value of the other variable tends to increase

Answer

As the value of one variable increases, the value of the other variable tends to decrease

Answer

There is no relationship between the variables

Answer

The relationship is non-linear

Question 50

Which of the following is NOT a measure of central tendency, which summarizes the "typical" value of a dataset?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 51

The range of a dataset, which measures its spread, is calculated as:

Accepted Answer

Maximum value - Minimum value

Answer

Mean - Median

Answer

Standard deviation / Mean

Answer

Variance / Mean

Question 52

Which of the following graphs is most appropriate for displaying the distribution of a categorical variable, which has distinct categories?

Accepted Answer

Bar chart

Answer

Histogram

Answer

Scatter plot

Answer

Line graph

Question 53

Standard deviation is a measure of dispersion, which quantifies the spread of a dataset. Which of the following is a limitation of using the standard deviation?

Accepted Answer

It is sensitive to outliers, which can distort the measure.

Answer

It can be difficult to interpret its magnitude.

Answer

It is not affected by the shape of the distribution.

Answer

It cannot be used for categorical data.

Question 54

The median of a dataset is the middle value when the data is arranged in ascending order. Which of the following is the correct definition of the median?

Accepted Answer

Middle value when the dataset is arranged in ascending order

Answer

Sum of all values divided by the number of values

Answer

Value that occurs most frequently

Answer

Average of the mean and mode

Question 55

A histogram is a graphical representation that shows the distribution of a quantitative variable by dividing the range of values into bins.

Accepted Answer

The distribution of a quantitative variable

Answer

The relationship between two quantitative variables

Answer

The frequency of different categories of a qualitative variable

Answer

The cumulative frequency of a quantitative variable

Question 56

The mode of a dataset is the value that occurs most frequently.

Accepted Answer

Value that occurs most frequently

Answer

Sum of all values divided by the number of values

Answer

Middle value when the dataset is arranged in ascending order

Answer

Average of the mean and median

Question 57

Which of the following is a measure of central tendency used to describe the average value of a data set?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 58

What is the formula for calculating the mean of a data set?

Accepted Answer

Sum of all data values divided by the number of data values

Answer

Median minus mode

Answer

Range divided by 2

Answer

Standard deviation plus variance

Question 59

What is the term for the square root of the variance?

Accepted Answer

Standard deviation

Answer

Range

Answer

Coefficient of variation

Answer

Mean deviation

Question 60

Which of the following is NOT a type of graphical representation commonly used in descriptive statistics?

Accepted Answer

Equation

Answer

Histogram

Answer

Scatterplot

Answer

Pie chart

Question 61

What information does a histogram provide about a data set?

Accepted Answer

Distribution of data values

Answer

Relationship between two variables

Answer

Mean, median, and mode

Answer

Frequency of occurrence

Question 62

Find the mode of the following data set: 5, 7, 9, 9, 11, 13

Accepted Answer

9

Answer

7

Answer

11

Answer

There is no mode

Question 63

Which of the following data sets has the largest range?

Accepted Answer

4, 8, 12, 16, 20

Answer

1, 3, 5, 7, 9

Answer

2, 4, 6, 8, 10

Answer

3, 6, 9, 12, 15