Measures of Central Tendency: Master Statistics with Confidence

Question 1

A distribution has a mean of 50 and a median of 45. Which best describes the distribution?

Accepted Answer

Skewed to the left

Answer

Skewed to the right

Answer

Symmetric

Answer

Cannot be determined from the given information

Question 2

Which of the following is not considered a quartile?

Accepted Answer

Median

Answer

Q1

Answer

Q2

Answer

Q3

Question 3

Approximately what percentage of data is within one standard deviation of the mean in a normal distribution?

Accepted Answer

68%

Answer

34%

Answer

95%

Answer

99%

Question 4

Which measure of central tendency would be most appropriate for the following data set: [20, 22, 21, 19, 23, 20, 22]?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 5

Which limitation is associated with using standard deviation as a measure of dispersion?

Accepted Answer

It is influenced by outliers

Answer

It cannot be used for non-normal distributions

Answer

It provides an absolute measure of variability

Answer

It is difficult to calculate

Question 6

Which of the following describes a percentile?

Accepted Answer

A value that divides a data set into 100 equal parts

Answer

A value that represents the most frequently occurring data point

Answer

A measure of central tendency

Answer

A measure of variability

Question 7

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

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 8

Which of the following is NOT a measure of dispersion?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 9

The sum of deviations from the mean of a data set is always:

Accepted Answer

0

Answer

1

Answer

Equal to the mean

Answer

Equal to the median

Question 10

Which of the following is not a percentile?

Accepted Answer

90th decile

Answer

25th percentile

Answer

50th percentile

Answer

75th percentile

Question 11

The range of a data set is calculated as the:

Accepted Answer

Difference between the maximum and minimum values

Answer

Sum of all values divided by the number of values

Answer

Square root of the variance

Question 12

Which measure of central tendency is not affected by the units of measurement used?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 13

What is a characteristic of the variance of a data set?

Accepted Answer

It is always a positive value

Answer

It is always a negative value

Answer

It can be either positive or negative

Question 14

The first quartile (Q1) represents:

Accepted Answer

The median of the lower half of the data

Answer

The median of the upper half of the data

Answer

The average of the lowest 25% of the data

Question 15

Which measure of central tendency is most appropriate for data that is skewed or has outliers?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Question 16

The standard deviation measures:

Accepted Answer

The average distance of data points from the mean

Answer

The average value of the data

Answer

The range of the data

Question 17

The mode of a dataset is:

Accepted Answer

The value that occurs most frequently

Answer

The sum of all values divided by the number of values

Answer

The value that divides the data into two equal halves

Question 18

The interquartile range (IQR) is:

Accepted Answer

The difference between the first and third quartiles

Answer

The difference between the mean and the median

Answer

The average value of the data

Question 19

What is the precise definition of the mean?

Accepted Answer

The mean is the sum of all values in a dataset divided by the number of values.

Answer

The mean is the whole number that appears most often in a dataset.

Answer

The mean is the middle value when a dataset is arranged in order from smallest to largest.

Question 20

Which of the following statements correctly describes a key characteristic of the range of a dataset?

Accepted Answer

It is always a positive value.

Answer

It is a measure of the central tendency of the data.

Answer

It is unaffected by the presence of outliers.

Answer

It is the most commonly used measure of dispersion.

Question 21

Which measure of central tendency is most susceptible to the influence of extreme values, i.e., outliers?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 22

The formula for calculating the standard deviation of a dataset is:

Accepted Answer

Σ(x - μ)² / (N-1)

Answer

Σ(x - μ)² / N

Answer

Σ(x)² / N

Question 23

The variance of a dataset represents:

Accepted Answer

The average squared distance of data points from the mean

Answer

The square root of the standard deviation

Answer

The range of the dataset

Question 24

Calculate the mode of the following dataset: 5, 7, 7, 9, 11

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Question 25

Which of the following is the definition of a percentile?

Accepted Answer

The value below which a certain percentage of the data falls

Answer

The difference between the maximum and minimum values

Answer

The average of the data points

Question 26

The mean of a dataset is defined as:

Accepted Answer

The sum of all data points divided by the number of data points

Answer

The middle value of the dataset when assorted in numerical order

Answer

The value that occurs most frequently in the dataset

Question 27

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

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 28

Which of the following is not a measure of variability (dispersion)?

Accepted Answer

Median

Answer

Range

Answer

Variance

Answer

Standard deviation

Question 29

The standard deviation of a data set is 3.5. What does this imply about the data?

Accepted Answer

The data is widely spread out from the mean.

Answer

The data is clustered closely around the mean.

Answer

The mean of the data is 3.5.

Answer

The mode of the data is 3.5.

Question 30

Which value represents the 25th percentile of a data set?

Accepted Answer

The value below which 25% of the data falls.

Answer

The value below which 50% of the data falls.

Answer

The value below which 75% of the data falls.

Answer

The value that occurs most frequently in the data.

Question 31

A data set has the following frequencies: Mode A (4), Mode B (3), Mode C (3). What type of distribution does this data exhibit?

Accepted Answer

Trimodal

Answer

Unimodal

Answer

Bimodal

Answer

Multimodal

Question 32

Outliers can significantly influence which measure of central tendency?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 33

Which measure of central tendency best represents the average value in a distribution?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Question 34

Determine the range of the dataset: 5, 10, 15, 20, 25, 30.

Accepted Answer

25

Answer

5

Answer

10

Question 35

Identify the option that is not a measure of central tendency:

Accepted Answer

Correlation

Answer

Mean

Answer

Median

Question 36

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

Accepted Answer

Range

Answer

Mean

Answer

Median

Answer

Mode

Question 37

In an even-sized data set, the median is:

Accepted Answer

The average of the two middle values

Answer

The middle value

Answer

The sum of all values divided by the number of values

Answer

The most frequently occurring value

Question 38

Which quartile divides a data set in half?

Accepted Answer

Second quartile

Answer

First quartile

Answer

Third quartile

Answer

Fourth quartile

Question 39

The variance of a data set measures:

Accepted Answer

Spread or dispersion

Answer

Central tendency

Answer

Skewness

Answer

Kurtosis

Question 40

Which percentile represents the value below which 25% of the data falls?

Accepted Answer

25th percentile

Answer

50th percentile

Answer

75th percentile

Answer

95th percentile

Question 41

The standard deviation of a data set is most sensitive to:

Accepted Answer

Outliers

Answer

Extreme values

Answer

Changes in the mean

Answer

Changes in the median

Question 42

What formula is used to calculate the mean of a data set?

Accepted Answer

Sum of all values divided by the number of values

Answer

Sum of the highest and lowest values divided by 2

Answer

Value that occurs most frequently in the data set

Answer

Difference between the highest and lowest values

Question 43

Which percentile divides a data set into two halves?

Accepted Answer

Median

Answer

Quartile 1

Answer

Quartile 3

Answer

Interquartile range

Question 44

What is the variance of a data set with a standard deviation of 5?

Accepted Answer

25

Answer

5

Answer

10

Answer

50

Question 45

Which of the following is not a measure of spread?

Accepted Answer

Mean

Answer

Range

Answer

Standard deviation

Answer

Variance

Question 46

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

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 47

The mean of a dataset is calculated by

Accepted Answer

Summing all values and dividing by the number of observations

Answer

Finding the value that occurs most frequently

Answer

Determining the average of the highest and lowest values

Answer

Subtracting the standard deviation from the median

Question 48

What is the key distinction between the range and the standard deviation?

Accepted Answer

The range is the difference between the highest and lowest values, while the standard deviation measures the spread of data around the mean

Answer

The range represents the spread of data around the mean, while the standard deviation measures the difference between the highest and lowest values

Answer

The range and standard deviation convey the same information about data dispersion

Answer

The standard deviation is the square of the range

Question 49

Quartiles divide a ranked dataset into?

Accepted Answer

Four equal parts

Answer

Two equal parts

Answer

Three equal parts

Answer

Five equal parts

Question 50

Percentiles are calculated by

Accepted Answer

Dividing the data into 100 equal intervals and identifying the values at the boundaries

Answer

Subtracting the minimum value from the maximum value and dividing by the number of observations

Answer

Adding the minimum and maximum values and dividing by the number of observations

Answer

Calculating the mean and standard deviation of the data

Question 51

A potential limitation of using the mean as a measure of central tendency is that it

Accepted Answer

Can be affected by outliers

Answer

Assumes the data is normally distributed

Answer

Is not applicable to all types of data

Answer

Requires complex calculations

Question 52

The mode is often preferred as a measure of central tendency when

Accepted Answer

The data contains a significant number of outliers

Answer

The data is normally distributed

Answer

The data is measured on a nominal scale

Answer

The mean and median are equal

Question 53

The median of a dataset can be described as the value that?

Accepted Answer

Splits the data into two equal halves

Answer

Appears most frequently

Answer

Is the average of all values

Answer

Represents the difference between the highest and lowest values

Question 54

For a skewed distribution, which measure of central tendency provides the most representative value?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 55

The standard deviation of a dataset primarily measures:

Accepted Answer

The spread or dispersion of the data

Answer

The average value of the data

Answer

The frequency of occurrence of values

Answer

The difference between the highest and lowest values

Question 56

Which measure of central tendency is calculated by summing all values and dividing by the number of values in a dataset?

Accepted Answer

Mean

Answer

Median

Answer

Mode

Answer

Range

Question 57

The variance of a dataset is defined as:

Accepted Answer

The sum of squared deviations from the mean divided by the count

Answer

The square of the standard deviation

Answer

The difference between the mean and the median

Answer

The range of the data

Question 58

Which measure of central tendency remains unaffected by missing values?

Accepted Answer

Median

Answer

Mean

Answer

Mode

Answer

Range

Question 59

The mode of a dataset refers to the value that:

Accepted Answer

Appears most frequently

Answer

Divides the dataset into two equal halves

Answer

Is the lowest value in the dataset

Answer

Is the average value of the dataset

Question 60

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

Accepted Answer

Correlation

Answer

Mean

Answer

Median

Answer

Mode

Question 61

Calculate the mean of the following numbers: 5, 7, 9, 11, 13

Accepted Answer

9

Answer

7

Answer

11

Answer

13

Question 62

The range of a dataset refers to the difference between which values?

Accepted Answer

The smallest and largest values

Answer

The mean and median

Answer

The first and third quartiles

Answer

The mode and median

Question 63

Which of the following is a measure of dispersion or spread in a dataset?

Accepted Answer

Variance

Answer

Mean

Answer

Median

Answer

Quartiles

Question 64

The standard deviation measures:

Accepted Answer

The average distance of data points from the mean

Answer

The square of the variance

Answer

The difference between the maximum and minimum values

Answer

The number of times a value occurs in a dataset