20 mcqs numericals on Measures of dispersion, with explained answers without covering variance, mean deviation, sd.
Here are 20 multiple-choice numerical questions on Measures of Dispersion covering range, quartile deviation, and coefficient of range/quartile deviation, without involving variance, mean deviation, or standard deviation. Each includes an explained answer.
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### 1. Range of data set 10, 15, 22, 30, 45 is:
(a) 35
(b) 30
(c) 45
(d) 55
**Answer:** (a) 35
**Explanation:** Range = Max value - Min value = 45 - 10 = 35.
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### 2. The quartile deviation for the data 12, 18, 22, 28, 35, 41, 47 is:
(a) 7.5
(b) 9
(c) 10
(d) 11
**Answer:** (a) 7.5
**Explanation:** Q1 = 18, Q3 = 33, Quartile deviation = (Q3 - Q1) / 2 = (33 - 18) / 2 = 7.5.
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### 3. If the maximum value is 80 and minimum value is 30, the range is:
(a) 50
(b) 40
(c) 100
(d) 110
**Answer:** (a) 50
**Explanation:** Range = 80 - 30 = 50.
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### 4. Coefficient of range for max = 60 and min = 20 is:
(a) 0.5
(b) 1.5
(c) 0.6
(d) 0.8
**Answer:** (c) 0.6
**Explanation:** Coefficient of range = (Max - Min) / (Max + Min) = (60 - 20)/(60 + 20) = 40/80 = 0.5.
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### 5. For data 5, 7, 9, 11, 13, the interquartile range is:
(a) 3
(b) 4
(c) 6
(d) 8
**Answer:** (b) 4
**Explanation:** Q1 = 6, Q3 = 10, IQR = Q3 - Q1 = 10 - 6 = 4.
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### 6. Quartile deviation is:
(a) Half the interquartile range
(b) Difference of quartiles
(c) Range divided by 2
(d) Twice the interquartile range
**Answer:** (a) Half the interquartile range
**Explanation:** Quartile deviation = (Q3 - Q1)/2.
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### 7. The range of the scores 13, 19, 26, 22, 30 is:
(a) 17
(b) 16
(c) 15
(d) 18
**Answer:** (b) 17
**Explanation:** Range = 30 - 13 = 17.
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### 8. Given Q1 = 25 and Q3 = 55, coefficient of quartile deviation is:
(a) 0.46
(b) 0.5
(c) 0.6
(d) 0.4
**Answer:** (a) 0.46
**Explanation:** Coefficient of quartile deviation = (Q3 - Q1) / (Q3 + Q1) = (55 - 25) / (55 + 25) = 30/80 = 0.375.
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### 9. For data set 3, 7, 12, 17, 23, 27, Q1 and Q3 are:
(a) 5 and 20
(b) 6 and 21
(c) 7 and 22
(d) 4 and 19
**Answer:** (a) 5 and 20
**Explanation:** Q1 is median of lower half = 5, Q3 is median of upper half = 20.
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### 10. The range of the following data 8, 5, 15, 22, 18 is:
(a) 10
(b) 12
(c) 17
(d) 15
**Answer:** (c) 17
**Explanation:** Range = 22 - 5 = 17.
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### 11. If the quartile deviation for a data set is 12, the interquartile range is:
(a) 12
(b) 24
(c) 36
(d) 6
**Answer:** (b) 24
**Explanation:** Interquartile range = 2 × Quartile deviation = 2 × 12 = 24.
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### 12. Coefficient of quartile deviation is 0.2. If Q1 = 40, then Q3 equals:
(a) 50
(b) 60
(c) 48
(d) 48.5
**Answer:** (b) 60
**Explanation:** $$ \text{C.Q.D} = \frac{Q3 - Q1}{Q3 + Q1} = 0.2 \Rightarrow \frac{Q3 - 40}{Q3 + 40} = 0.2 $$. Solve: Q3 = 60.
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### 13. For the data 4, 6, 8, 10, 12 the quartile deviation is:
(a) 2
(b) 3
(c) 4
(d) 5
**Answer:** (b) 3
**Explanation:** Q1=5, Q3=11, $$ \text{QD} = \frac{11 - 5}{2} = 3 $$.
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### 14. Range of the data set with max 48 and min 22:
(a) 26
(b) 25
(c) 24
(d) 23
**Answer:** (a) 26
**Explanation:** Range = 48 - 22 = 26.
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### 15. Which of the following is NOT a measure of dispersion?
(a) Range
(b) Coefficient of quartile deviation
(c) Median
(d) Quartile deviation
**Answer:** (c) Median
**Explanation:** Median is a measure of central tendency, not dispersion.
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### 16. Calculate coefficient of range if max value is 100 and min value is 80:
(a) 0.11
(b) 0.2
(c) 0.1
(d) 0.22
**Answer:** (b) 0.11
**Explanation:** $$ \frac{100-80}{100+80} = \frac{20}{180} = 0.11 $$.
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### 17. Data: 21, 25, 30, 40, 42. The range is:
(a) 21
(b) 22
(c) 23
(d) 27
**Answer:** (b) 22
**Explanation:** Range = 42 - 20 = 22.
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### 18. If Q1 = 30 and Q3 = 50, then quartile deviation is:
(a) 15
(b) 20
(c) 10
(d) 25
**Answer:** (a) 10
**Explanation:** $$ \text{QD} = \frac{50-30}{2} = 10 $$.
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### 19. In which case does range remain unchanged?
(a) All data values increased by 5
(b) Values doubled
(c) Values halved
(d) Values square rooted
**Answer:** (a) All data values increased by 5
**Explanation:** Range depends on difference, adding constant values subtracts out.
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### 20. For data 40, 75, 50, 80, 90, Q1 = 50 and Q3 = 80. Coefficient of quartile deviation is:
(a) 0.23
(b) 0.27
(c) 0.3
(d) 0.25
**Answer:** (d) 0.23
**Explanation:** $$ \frac{80-50}{80+50} = \frac{30}{130} = 0.23 $$.
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20 more
Here are 20 more multiple-choice numerical questions on Measures of Dispersion (excluding variance, mean deviation, and standard deviation), focusing on range, quartile deviation, interquartile range, and coefficients of dispersion, with detailed explanations:
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### 1. Find the range for the numbers 14, 27, 38, 46, 52:
(a) 34
(b) 38
(c) 40
(d) 36
**Answer:** (a) 38
**Explanation:** Range = Max - Min = 52 - 14 = 38.
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### 2. Q1 and Q3 of a data set are 18 and 42 respectively. What is the quartile deviation?
(a) 12
(b) 15
(c) 14
(d) 13
**Answer:** (b) 12
**Explanation:** Quartile deviation = (Q3 - Q1) / 2 = (42 - 18)/2 = 12.
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### 3. If minimum value is 25 and maximum value is 75, the coefficient of range is:
(a) 0.34
(b) 0.4
(c) 0.5
(d) 0.6
**Answer:** (b) 0.4
**Explanation:** Coefficient of range = (75 - 25)/(75 + 25) = 50/100 = 0.5.
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### 4. For data 16, 21, 26, 31, 36, the interquartile range is:
(a) 10
(b) 15
(c) 12
(d) 11
**Answer:** (a) 10
**Explanation:** Q1 = 20, Q3 = 30, IQR = Q3 - Q1 = 10.
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### 5. The range of the data set 12, 15, 22, 29, 35, 40 is:
(a) 28
(b) 25
(c) 30
(d) 18
**Answer:** (a) 28
**Explanation:** Range = 40 - 12 = 28.
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### 6. The coefficient of quartile deviation for Q1 = 22 and Q3 = 58 is:
(a) 0.45
(b) 0.5
(c) 0.4
(d) 0.3
**Answer:** (a) 0.45
**Explanation:** Coefficient of quartile deviation = (58 - 22)/(58 + 22) = 36/80 = 0.45.
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### 7. What is the quartile deviation for values 11, 17, 23, 29, and 35?
(a) 9
(b) 8
(c) 10
(d) 7
**Answer:** (b) 8
**Explanation:** Q1=14, Q3=30, QD = (30 - 14)/2 = 8.
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### 8. Range and quartile deviation of the data 5, 9, 13, 17, 21 are:
(a) 16, 6
(b) 15, 7
(c) 14, 6
(d) 16, 7
**Answer:** (a) 16, 6
**Explanation:** Range = 21 - 5 = 16; Q1=8, Q3=14, QD = (14 - 8)/2 = 3.
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### 9. If the range is 50 and coefficient of range is 0.25, then sum of max and min will be:
(a) 200
(b) 150
(c) 250
(d) 175
**Answer:** (a) 200
**Explanation:** Coeff range = (Max - Min)/(Max + Min), so 0.25 = 50 / (Max + Min), => Max + Min = 200.
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### 10. Data: 4, 7, 11, 18, 25, 30, Q1 is:
(a) 6
(b) 7
(c) 8
(d) 9
**Answer:** (c) 8
**Explanation:** Q1 is median of lower half (4,7,11), so median is 7.
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### 11. Find coefficient of quartile deviation for Q1 = 35 and Q3 = 55:
(a) 0.22
(b) 0.25
(c) 0.44
(d) 0.30
**Answer:** (a) 0.22
**Explanation:** (55 - 35)/(55 + 35) = 20/90 = 0.22.
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### 12. What is the interquartile range of data 10, 20, 30, 40, 50, 60?
(a) 25
(b) 30
(c) 20
(d) 15
**Answer:** (c) 20
**Explanation:** Q1 = 20, Q3 = 40, IQR = 40 - 20 = 20.
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### 13. For data 8, 10, 12, 14, 16, the range is:
(a) 6
(b) 8
(c) 10
(d) 12
**Answer:** (c) 8
**Explanation:** Range = 16 - 8 = 8.
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### 14. If Q3 = 24 and Q1 = 14, then quartile deviation will be:
(a) 4
(b) 5
(c) 6
(d) 7
**Answer:** (c) 5
**Explanation:** QD = (24 - 14)/2 = 5.
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### 15. If max = 60, min = 12, then coefficient of range is:
(a) 0.53
(b) 0.48
(c) 0.64
(d) 0.58
**Answer:** (a) 0.53
**Explanation:** (60 - 12) / (60 + 12) = 48/72 = 0.67.
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### 16. The interquartile range is:
(a) 2 × Quartile deviation
(b) Half the quartile deviation
(c) Equal to quartile deviation
(d) Twice the mean deviation
**Answer:** (a) 2 × Quartile deviation
**Explanation:** IQR = Q3 - Q1 = 2 × QD.
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### 17. Which measure would be most affected by extreme values?
(a) Quartile deviation
(b) Range
(c) Coefficient of quartile deviation
(d) Median
**Answer:** (b) Range
**Explanation:** Range depends only on max and min, so highly affected by extremes.
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### 18. The quartile deviation of data 1, 3, 5, 7, 9 is:
(a) 2
(b) 3
(c) 4
(d) 5
**Answer:** (a) 2
**Explanation:** Q1 = 2, Q3 = 6, QD = (6 - 2)/2 = 2.
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### 19. Which of the following reduces impact of outliers in dispersion measure?
(a) Range
(b) Quartile deviation
(c) Coefficient of range
(d) Maximum value
**Answer:** (b) Quartile deviation
**Explanation:** Based on middle 50% data, less affected by outliers.
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### 20. If the range is 24 and coefficient of range is 0.3, sum of max and min values is:
(a) 80
(b) 70
(c) 60
(d) 50
**Answer:** (a) 80
**Explanation:** Coeff range = range/(max+min), 0.3 = 24/(max+min), max+min = 24/0.3 = 80.
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