Measures of Dispersion
Q. Calculate the interquartile range (IQR) for the data set: 1, 3, 7, 8, 9, 10.
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.
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}.
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.
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?
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?
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?
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?
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?
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?
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 the value 40?
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 a value 40?
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?
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?
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?
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?
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?
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?
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?
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?
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?
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)
