Measures of Dispersion for Competitive Exam Success

Measures of Dispersion

Q. Calculate the interquartile range (IQR) for the data set: 1, 3, 7, 8, 9, 10.

A. 4
B. 5
C. 6
D. 7

Solution

Q1 = 3, Q3 = 9; IQR = Q3 - Q1 = 9 - 3 = 6.

Correct Answer: A — 4

Learn More →

Q. Calculate the mean absolute deviation for the data set: 1, 2, 3, 4, 5.

A. 1
B. 1.5
C. 2
D. 2.5

Solution

Mean = 3. Mean Absolute Deviation = (|1-3| + |2-3| + |3-3| + |4-3| + |5-3|)/5 = (2 + 1 + 0 + 1 + 2)/5 = 1.5.

Correct Answer: B — 1.5

Learn More →

Q. Calculate the mean of the following data: 5, 10, 15, 20.

A. 10
B. 12.5
C. 15
D. 17.5

Solution

Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.

Correct Answer: B — 12.5

Learn More →

Q. Calculate the variance of the data set {2, 4, 4, 4, 5, 5, 7, 9}.

A. 4
B. 6
C. 5
D. 3

Solution

Mean = 5, Variance = [(2-5)² + (4-5)² + (4-5)² + (4-5)² + (5-5)² + (5-5)² + (7-5)² + (9-5)²] / 8 = 4.

Correct Answer: B — 6

Learn More →

Q. Calculate the variance of the data set {4, 8, 6, 5, 3}.

A. 2.5
B. 3.2
C. 1.5
D. 4.0

Solution

Mean = (4+8+6+5+3)/5 = 5.2. Variance = [(4-5.2)² + (8-5.2)² + (6-5.2)² + (5-5.2)² + (3-5.2)²]/5 = 2.5.

Correct Answer: A — 2.5

Learn More →

Q. Find the range of the data set: 10, 15, 20, 25, 30.

A. 15
B. 20
C. 25
D. 30

Solution

Range = Maximum - Minimum = 30 - 10 = 20.

Correct Answer: A — 15

Learn More →

Q. For the data set 10, 20, 30, 40, 50, what is the mean deviation?

A. 10
B. 15
C. 20
D. 25

Solution

Mean = 30; Mean Deviation = (|10-30| + |20-30| + |30-30| + |40-30| + |50-30|) / 5 = 10.

Correct Answer: B — 15

Learn More →

Q. For the data set {10, 12, 23, 23, 16, 23, 21}, what is the mode?

A. 10
B. 12
C. 23
D. 21

Solution

The mode is the number that appears most frequently, which is 23.

Correct Answer: C — 23

Learn More →

Q. For the data set {12, 15, 20, 22, 25}, what is the mode?

A. 12
B. 15
C. 20
D. No mode

Solution

There is no mode as all values appear only once.

Correct Answer: D — No mode

Learn More →

Q. For the data set {2, 4, 6, 8, 10}, what is the mean deviation?

A. 2
B. 1.6
C. 3
D. 2.5

Solution

Mean = 6; Mean deviation = (|2-6| + |4-6| + |6-6| + |8-6| + |10-6|)/5 = (4 + 2 + 0 + 2 + 4)/5 = 12/5 = 2.4.

Correct Answer: B — 1.6

Learn More →

Q. For the data set {4, 8, 6, 5, 3}, what is the mean?

A. 4.5
B. 5.5
C. 6.0
D. 5.0

Solution

Mean = (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.0.

Correct Answer: D — 5.0

Learn More →

Q. For the data set: 1, 2, 3, 4, 5, what is the interquartile range?

A. 1
B. 2
C. 3
D. 4

Solution

Q1 = 2, Q3 = 4; Interquartile Range = Q3 - Q1 = 4 - 2 = 2.

Correct Answer: B — 2

Learn More →

Q. For the data set: 5, 7, 8, 9, 10, what is the mean absolute deviation?

A. 1
B. 2
C. 3
D. 4

Solution

Mean = 7.5; MAD = (|5-7.5| + |7-7.5| + |8-7.5| + |9-7.5| + |10-7.5|) / 5 = 1.

Correct Answer: B — 2

Learn More →

Q. For the data set: 5, 7, 8, 9, 10, what is the standard deviation?

A. 1.5
B. 2
C. 2.5
D. 3

Solution

Mean = 7.5; Variance = [(5-7.5)^2 + (7-7.5)^2 + (8-7.5)^2 + (9-7.5)^2 + (10-7.5)^2] / 5 = 2; Standard Deviation = sqrt(2) = 1.41

Correct Answer: B — 2

Learn More →

Q. If the data set has a mean of 30 and a median of 25, what does this indicate?

A. Data is symmetrical
B. Data is positively skewed
C. Data is negatively skewed
D. Data is uniform

Solution

Since the mean is greater than the median, the data is positively skewed.

Correct Answer: B — Data is positively skewed

Learn More →

Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?

A. 1
B. 0
C. 2
D. -1

Solution

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.

Correct Answer: C — 2

Learn More →

Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of the value 40?

A. 0
B. 1
C. 2
D. 3

Solution

Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1

Correct Answer: C — 2

Learn More →

Q. If the data set has a mean of 30 and a variance of 16, what is the standard deviation?

A. 4
B. 5
C. 6
D. 7

Solution

Standard Deviation = √Variance = √16 = 4.

Correct Answer: A — 4

Learn More →

Q. If the data set has a mean of 50 and a median of 45, what can be said about the data distribution?

A. Symmetric
B. Positively skewed
C. Negatively skewed
D. Uniform

Solution

Since the mean is greater than the median, the distribution is positively skewed.

Correct Answer: B — Positively skewed

Learn More →

Q. If the data set has a mean of 50 and a standard deviation of 10, what is the z-score of the value 70?

A. 1
B. 2
C. 3
D. 4

Solution

Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.

Correct Answer: B — 2

Learn More →

Q. If the data set has a mean of 50 and a variance of 16, what is the standard deviation?

A. 2
B. 4
C. 8
D. 16

Solution

Standard Deviation = √Variance = √16 = 4.

Correct Answer: B — 4

Learn More →

Q. If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?

A. 2
B. 3
C. 4
D. 5

Solution

Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.

Correct Answer: B — 3

Learn More →

Q. If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?

A. 1.58
B. 2.58
C. 3.58
D. 4.58

Solution

Mean = 7.8. Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²]/5 = 2.5. Standard Deviation = √2.5 ≈ 1.58.

Correct Answer: A — 1.58

Learn More →

Q. If the data set is: 3, 7, 7, 19, what is the median?

A. 7
B. 10
C. 11
D. 12

Solution

Median = (7 + 7) / 2 = 7.

Correct Answer: A — 7

Learn More →

Q. If the data set is: 5, 7, 8, 9, 10, what is the median?

A. 7
B. 8
C. 9
D. 10

Solution

Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.

Correct Answer: B — 8

Learn More →

Q. If the data set {1, 2, 3, 4, 5} is transformed to {2, 3, 4, 5, 6}, what happens to the standard deviation?

A. Increases
B. Decreases
C. Remains the same
D. Cannot be determined

Solution

The standard deviation remains the same because the transformation is a shift.

Correct Answer: C — Remains the same

Learn More →

Q. If the data set {10, 20, 30, 40, 50} is transformed to {x + 5}, what happens to the standard deviation?

A. Increases
B. Decreases
C. Remains the same
D. Cannot be determined

Solution

Standard deviation remains the same as adding a constant does not affect dispersion.

Correct Answer: C — Remains the same

Learn More →

Q. If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?

A. 3
B. 7
C. 8
D. 12

Solution

Q1 is the median of the first half of the data set {3, 7}, which is 7.

Correct Answer: B — 7

Learn More →

Q. If the data set {3, 7, 8, 12, 14} is given, what is the median?

A. 8
B. 7
C. 12
D. 10

Solution

Median is the middle value, which is 8.

Correct Answer: A — 8

Learn More →

Q. If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?

A. 0
B. 1
C. 2
D. 3

Solution

The sum of deviations from the mean is always 0.

Correct Answer: A — 0

Learn More →

Showing 1 to 30 of 75 (3 Pages)

Measures of Dispersion

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?