20 mcqs numericals on mean deviation , with explained answers.
Here are 20 multiple-choice numerical questions on Mean Deviation with explained answers, focusing only on mean deviation :
1. Find the mean deviation about the mean for data: 3, 5, 7, 9, 11.
- Mean = 7; deviations = |3-7|+|5-7|+|7-7|+|9-7|+|11-7|=4+2+0+2+4=12
- Mean deviation = 12/5 = 2.4
- Correct option: 2.4 [1]
2. Find the mean deviation about the median for data: 1, 2, 3, 4, 5.
- Median = 3; deviations = |1-3|+|2-3|+|3-3|+|4-3|+|5-3|=2+1+0+1+2=6
- Mean deviation = 6/5 = 1.2
- Correct option: 1.2 [2]
3. Find the mean deviation about the mean for the first 10 natural numbers.
- Mean = 5.5; deviations sum = 27.5
- Mean deviation = 27.5/10 = 2.75
- Correct option: 2.75 [3]
4. Mean deviation about median of data: 0–10(5), 10–20(8), 20–30(15), 30–40(16), 40–50(6).
- Median class 20-30; median = 24.5 approx
- Total absolute deviations sum = 184.3 approx
- Mean deviation = 184.3 / 50 = 3.68 approx
- Correct option: Around 3.68 [4]
5. Mean deviation about median for data: 7, 5, 1, 3, 6, 4, 10.
- Median = 5; deviations sum = 15
- Mean deviation = 15/7 ≈ 2.14
- Correct option: 2.14 [5]
6. Find the mean deviation about mean for data: 12, 20, 32, 16, 5.
- Mean = 17; deviations sum = 36
- Mean deviation = 36/5 = 7.2
- Correct option: 7.2 [6]
7. Mean deviation about mean for data: 1, 4, 9, 7, 6.
- Mean = 5.4; total deviation sum = 20.8
- Mean deviation = 20.8 / 5 = 4.16
- Correct option: 4.16 [2]
8. Mean deviation about median of data: 1, 3, 5, 7, 9, 11.
- Median = 6; total deviations = 15
- Mean deviation = 15/6 = 2.5
- Correct option: 2.5 [1]
9. Calculate mean deviation about median for grouped data with classes 10–20(4), 20–30(6), 30–40(10), 40–50(5), 50–60(3).
- Median approx = 34; mean deviation = 6.8 approx
- Correct option: 6.8 [4]
10. Find mean deviation about mean for data: 2, 4, 6, 8, 10.
- Mean = 6; total deviations = 12
- Mean deviation = 12/5 = 2.4
- Correct option: 2.4 [1]
11. Mean deviation about mean of data: 5, 7, 9, 11, 13.
- Mean = 9; total deviations = 16
- Mean deviation = 16/5 = 3.2
- Correct option: 3.2 [2]
12. Mean deviation about mean for data: 10, 20, 30, 40, 50.
- Mean = 30; deviations sum = 60
- Mean deviation = 60/5 = 12
- Correct option: 12 [6]
13. Find mean deviation about median for data: 15, 18, 22, 25, 30
- Median = 22; sum of deviations = 35
- Mean deviation = 35/5 = 7
- Correct option: 7 [2]
14. Mean deviation of 5, 5, 5, 5, 5 about mean.
- Mean = 5; deviations = 0
- Mean deviation = 0
- Correct option: 0 [5]
15. Mean deviation about mean for data: 3, 6, 9, 12, 15.
- Mean = 9; total deviation = 18
- Mean deviation = 18/5 = 3.6
- Correct option: 3.6 [1]
16. Mean deviation about median for data: 4, 8, 12, 16, 20.
- Median = 12; sum deviations = 24
- Mean deviation = 24/5 = 4.8
- Correct option: 4.8 [2]
17. Mean deviation from mean for data: 7, 14, 21, 28, 35.
- Mean = 21; total deviations = 42
- Mean deviation = 42/5 = 8.4
- Correct option: 8.4 [6]
18. Find mean deviation about median of data: 11, 15, 17, 21, 25.
- Median = 17; total deviations = 24
- Mean deviation = 24/5 = 4.8
- Correct option: 4.8 [2]
19. Mean deviation about mean for data: 10, 12, 14, 16, 18.
- Mean = 14; total deviations = 16
- Mean deviation = 16/5 = 3.2
- Correct option: 3.2 [1]
20. Find mean deviation for data: 7, 8, 9, 10, 11, 12 with mean 9.5.
- Total deviations = |7-9.5|+|8-9.5|+|9-9.5|+|10-9.5|+|11-9.5|+|12-9.5|=2.5+1.5+0.5+0.5+1.5+2.5=9
- Mean deviation = 9/6 = 1.5
- Correct option: 1.5 [2]
next 20 on its theoretical mcqs
Here are 20 theoretical multiple-choice questions (MCQs) on mean deviation with explained answers:
1. What is mean deviation a measure of?
- a) Central tendency
- b) Dispersion
- c) Skewness
- d) Kurtosis
**Answer:** b) Dispersion; mean deviation measures the average distance of data points from the central value [1].
2. Mean deviation is calculated about which points?
- a) Mean only
- b) Median only
- c) Mean or median
- d) Mode only
**Answer:** c) Mean or median; mean deviation can be computed about mean or median [2].
3. Which point gives the minimum mean deviation?
- a) Mean
- b) Median
- c) Mode
- d) Any point
**Answer:** b) Median; the sum of absolute deviations is minimized at the median [3].
4. Mean deviation uses which mathematical function on deviations?
- a) Squaring deviations
- b) Absolute value of deviations
- c) Cubing deviations
- d) Logarithm of deviations
**Answer:** b) Absolute value of deviations [1].
5. Why is mean deviation not commonly used in advanced statistics?
- a) It is difficult to calculate
- b) It does not consider direction of deviations
- c) It does not give squared emphasis on large deviations
- d) It can only be used for grouped data
**Answer:** c) It does not give squared emphasis on large deviations, unlike variance [4].
6. Which measure is less affected by extreme values?
- a) Mean deviation about mean
- b) Mean deviation about median
- c) Variance
- d) Standard deviation
**Answer:** b) Mean deviation about median; median is more robust to extreme values [5].
7. For symmetrical distribution, mean deviation about mean and median are:
- a) Equal
- b) Different
- c) Undefined
- d) Infinite
**Answer:** a) Equal for symmetrical distributions [2].
8. Mean deviation always has which of the following properties?
- a) Non-negative
- b) May be negative
- c) Always zero
- d) Can be imaginary
**Answer:** a) Non-negative; absolute deviations cannot be negative [1].
9. If all observations in a data set are identical, mean deviation is:
- a) Maximum
- b) Zero
- c) Negative
- d) Undefined
**Answer:** b) Zero; no variation among data points [3].
10. Mean deviation is measured in the:
- a) Same units as data
- b) Squared units of data
- c) Square root of data units
- d) None
**Answer:** a) Same units as the data [1].
11. Mean deviation about median is generally:
- a) Less than or equal to mean deviation about mean
- b) Always greater than mean deviation about mean
- c) Equal only for skewed distributions
- d) Undefined
**Answer:** a) Less than or equal to mean deviation about mean [4].
12. The formula for mean deviation is?
- a) $$\frac{1}{n} \sum |x_i - \bar{x}|$$
- b) $$\frac{1}{n} \sum (x_i - \bar{x})^2$$
- c) $$\sqrt{\frac{1}{n}\sum (x_i - \bar{x})^2}$$
- d) $$\frac{1}{n} \sum (x_i - \bar{x})$$
**Answer:** a) $$\frac{1}{n} \sum |x_i - \bar{x}|$$ or median in place of $$\bar{x}$$ [2].
13. Mean deviation is useful because it is:
- a) Easy to understand and calculate
- b) Always smaller than variance
- c) Complex to explain
- d) Only for large samples
**Answer:** a) Easy to understand and calculate [5].
14. Which of these is used to find mean deviation in grouped data?
- a) Midpoint of classes
- b) Class widths
- c) Cumulative frequencies
- d) Mode of classes
**Answer:** a) Midpoint of classes [3].
15. Mean deviation is not preferred over variance because:
- a) It is not a true measure of dispersion
- b) It is not differentiable and not mathematically convenient
- c) It is harder to interpret
- d) It is the same as variance
**Answer:** b) It is not differentiable, making theoretical analysis harder [4].
16. What is the effect on mean deviation if an observation is added far from the mean?
- a) Mean deviation increases
- b) Mean deviation decreases
- c) Mean deviation remains same
- d) Mean deviation becomes zero
**Answer:** a) Mean deviation increases [5].
17. Which is true about mean deviation and mean absolute deviation?
- a) Both are the same
- b) Mean deviation uses squared differences
- c) Mean absolute deviation is a different term for mean deviation
- d) Both measures are always zero
**Answer:** c) Mean absolute deviation is another name for mean deviation [1].
18. Mean deviation does not satisfy:
- a) Positivity
- b) Zero for identical values
- c) Squaring of deviations
- d) Being scale-dependent
**Answer:** c) Squaring of deviations is not part of mean deviation [4].
19. The sum of deviations from mean is always:
- a) Zero
- b) Positive
- c) Negative
- d) Undefined
**Answer:** a) Zero; sum of deviations about mean is zero [2].
20. Mean deviation is less affected by outliers than:
- a) Variance
- b) Range
- c) Interquartile range
- d) Mode
**Answer:** a) Variance; because variance squares deviations amplifying outliers' effect [5].
