Measures of Dispersion, Skewness and Kurtosis MCQs 2026

If mean = 30, mode = 24, SD = 3, Pearson skewness (mode) is

1. A 6 ✓
2. B 0.5 ✓
3. C −2 ✓
4. D 2 ✓

Dispersion measures

1. A only central location ✓
2. B only sample size ✓
3. C how spread out or scattered the data are ✓
4. D only data collection year ✓

Range is defined as

1. A maximum divided by minimum ✓
2. B maximum value minus minimum value ✓
3. C sum of all values ✓
4. D median minus mode ✓

Range of 4, 7, 9, 15 is

1. A 7 ✓
2. B 11.5 ✓
3. C 9 ✓
4. D 11 ✓

Mean deviation (MD) is

1. A the square root of variance always ✓
2. B only maximum minus minimum ✓
3. C only Q3 minus Q1 ✓
4. D the average of absolute deviations from a reference point (usually mean) ✓

For 2, 4, 6 with mean 4, mean deviation from mean is

1. A 0 ✓
2. B 4/3 (approximately 1.33) ✓
3. C 2 ✓
4. D 4 ✓

Variance measures

1. A only the centre of data ✓
2. B average squared deviation from the mean ✓
3. C only the most frequent value ✓
4. D only rank correlation ✓

Population variance is Σ(x − μ)² /

1. A n−1 ✓
2. B n+1 ✓
3. C 2N ✓
4. D N ✓

Sample variance s² uses divisor

1. A n+1 ✓
2. B n − 1 (Bessel correction) ✓
3. C N always ✓
4. D n−2 ✓

For data 2, 4, 6 (sample), sample variance is

1. A 8/3 ✓
2. B 2 ✓
3. C 4 ✓
4. D 8 ✓

For data 2, 4, 6 (population), population variance is

1. A 8/3 ✓
2. B 4 ✓
3. C 2 ✓
4. D 0 ✓

Standard deviation is

1. A variance squared ✓
2. B mean of absolute deviations always ✓
3. C range divided by 2 ✓
4. D the positive square root of variance ✓

If sample variance is 25, standard deviation is

1. A 12.5 ✓
2. B 625 ✓
3. C 5 ✓
4. D −5 ✓

Coefficient of variation (CV) is

1. A (Standard deviation / Mean) × 100% ✓
2. B Mean / SD × 100 ✓
3. C SD squared / Mean ✓
4. D Range / Mean only ✓

If mean = 50 and SD = 10, CV is

1. A 20% ✓
2. B 10% ✓
3. C 5% ✓
4. D 200% ✓

A dataset with SD = 0 must have

1. A mean zero only ✓
2. B median undefined ✓
3. C all values identical ✓
4. D positive skew always ✓

Pearson's coefficient of skewness using mode is (Mean − Mode) /

1. A Standard deviation ✓
2. B Variance ✓
3. C Range ✓
4. D IQR ✓

Quartile deviation is (Q3 − Q1) /

1. A 4 ✓
2. B 2 ✓
3. C 1 ✓
4. D N ✓

Negative skewness means

1. A right tail longer ✓
2. B zero variance ✓
3. C the left tail is longer; mean typically below median ✓
4. D mean above median ✓

A larger standard deviation indicates

1. A lower spread ✓
2. B greater spread around the mean ✓
3. C always higher mean ✓
4. D always symmetric data ✓

If all values in a dataset are identical, standard deviation is

1. A 1 ✓
2. B 0 ✓
3. C undefined ✓
4. D equal to the mean ✓

Bowley's coefficient of skewness uses

1. A quartiles: (Q3 + Q1 − 2Q2)/(Q3 − Q1) ✓
2. B only mean and mode ✓
3. C only range and mean ✓
4. D only variance ✓

For symmetric data, coefficient of skewness is

1. A always +1 ✓
2. B approximately zero ✓
3. C always −1 ✓
4. D undefined ✓

Kurtosis measures

1. A only centre of data ✓
2. B the peakedness and tail heaviness relative to a normal distribution ✓
3. C only sample mean only ✓
4. D only class width ✓

For a normal (mesokurtic) distribution, kurtosis (Pearson, moment-based) equals

1. A 0 ✓
2. B 1 ✓
3. C 3 ✓
4. D 6 ✓

Excess kurtosis is defined as

1. A kurtosis plus 3 ✓
2. B kurtosis times 3 ✓
3. C skewness minus 3 ✓
4. D kurtosis minus 3 ✓

Leptokurtic distribution has

1. A higher peak and heavier tails than normal (excess kurtosis > 0) ✓
2. B flatter peak than normal ✓
3. C exactly normal tails ✓
4. D zero variance ✓

Platykurtic distribution has

1. A flatter peak and lighter tails than normal (excess kurtosis < 0) ✓
2. B heavier tails than normal ✓
3. C infinite peak ✓
4. D negative variance ✓

Chebyshev's inequality states that for any k > 1, at least (1 − 1/k²) of data lie within

1. A k standard deviations of the mean ✓
2. B k variances of the median ✓
3. C k ranges of the mode ✓
4. D exactly 95% for k=2 always ✓

By Chebyshev, at least what fraction lies within 2 SD of the mean

1. A 50% ✓
2. B 95% ✓
3. C 100% ✓
4. D 75% (1 − 1/4) ✓

By Chebyshev, at least what fraction lies within 3 SD of the mean

1. A 99% ✓
2. B 8/9 (approximately 88.9%) ✓
3. C 50% ✓
4. D 2/3 ✓

Mean deviation is generally considered

1. A always larger than range ✓
2. B less mathematically tractable than variance for inference ✓
3. C always equal to SD ✓
4. D always zero for samples ✓

Standard deviation is preferred in inference because

1. A it ignores all outliers completely ✓
2. B it equals range always ✓
3. C squared deviations are differentiable and lead to normal theory ✓
4. D it requires no assumptions ✓

If two datasets have the same mean but different SD, the riskier investments typically have

1. A lower SD ✓
2. B SD = 0 ✓
3. C higher standard deviation ✓
4. D equal CV always ✓

Comparing variability of heights (cm) and weights (kg) fairly uses

1. A raw range only ✓
2. B raw variance only ✓
3. C only IQR without mean ✓
4. D coefficient of variation ✓

For grouped data, variance can be computed using

1. A only the modal class frequency ✓
2. B class midpoints and frequencies ✓
3. C only the first class ✓
4. D only graph area ✓

Root mean square deviation equals

1. A mean deviation always ✓
2. B range ✓
3. C IQR ✓
4. D standard deviation for population definition ✓

A distribution with mean 100 and SD 5 has CV of

1. A 20% ✓
2. B 0.05% ✓
3. C 500% ✓
4. D 5% ✓

If variance increases by multiplying each value by 2, new variance is

1. A 2 times ✓
2. B unchanged ✓
3. C 4 times the old variance ✓
4. D 8 times ✓

Semi-average range is

1. A Q3 − Q1 ✓
2. B full range ✓
3. C average of ranges of two halves of the data ✓
4. D SD/2 ✓

Skewness zero and kurtosis 3 suggest

1. A always uniform distribution ✓
2. B always bimodal distribution ✓
3. C always negative skew ✓
4. D bell-shaped symmetric mesokurtic distribution ✓

In PPSC/CSS, dispersion questions often include

1. A only trigonometric identities ✓
2. B variance, SD, CV and Chebyshev ✓
3. C only chemical bonding ✓
4. D only matrix rank ✓

Population variance of 1, 4, 7 is

1. A 4 ✓
2. B 6 ✓
3. C 8 ✓
4. D 18 ✓

Population standard deviation of 1, 4, 7 is

1. A 6 ✓
2. B 3 ✓
3. C 2 ✓
4. D √6 (approximately 2.45) ✓

Variance is expressed in

1. A squared units of the original variable ✓
2. B the same units as the variable always ✓
3. C percent only ✓
4. D unit-free always ✓

Range is most affected by

1. A extreme values at the ends ✓
2. B the median class only ✓
3. C the mode only ✓
4. D middle 50% of data ✓

If IQR = 12, semi-interquartile range (quartile deviation) is

1. A 12 ✓
2. B 24 ✓
3. C 6 ✓
4. D 3 ✓

For Q1 = 10, Q2 = 20, Q3 = 30, Bowley skewness is

1. A 0 ✓
2. B 1 ✓
3. C −1 ✓
4. D 0.5 ✓

The third central moment is related to

1. A only sample size ✓
2. B skewness of the distribution ✓
3. C only range ✓
4. D only kurtosis only without skew ✓

The fourth central moment is related to

1. A only the median ✓
2. B only range ✓
3. C kurtosis of the distribution ✓
4. D only Chebyshev bound ✓

By Chebyshev, at least what fraction lies within 4 SD of the mean

1. A 75% ✓
2. B 88% ✓
3. C 15/16 (93.75%) ✓
4. D 99% ✓

Positive skewness means

1. A left tail longer ✓
2. B perfect symmetry ✓
3. C the right tail is longer; mean typically exceeds median ✓
4. D mean below median always ✓

Skewness measures

1. A lack of symmetry in a distribution ✓
2. B only central tendency ✓
3. C only sample size ✓
4. D only counting categories ✓

The second moment about the mean (average squared deviation) is

1. A variance (population definition) ✓
2. B standard deviation ✓
3. C skewness ✓
4. D kurtosis only ✓

The first moment about the mean is always

1. A one ✓
2. B equal to variance ✓
3. C equal to skewness ✓
4. D zero ✓

Multiplying every value by 3 multiplies standard deviation by

1. A 3 ✓
2. B 9 ✓
3. C unchanged ✓
4. D 1/3 ✓

Adding a constant to every value changes standard deviation by

1. A not at all (SD unchanged) ✓
2. B increasing SD by that constant ✓
3. C multiplying SD by the constant ✓
4. D halving SD ✓

Interquartile range equals

1. A Q3 + Q1 ✓
2. B Median − Q1 ✓
3. C Range ✓
4. D Q3 − Q1 ✓

If Q1 = 20 and Q3 = 40, quartile deviation is

1. A 20 ✓
2. B 30 ✓
3. C 10 ✓
4. D 60 ✓

Mean deviation from the median for 1, 3, 9 is

1. A 4 ✓
2. B 3 ✓
3. C 2 ✓
4. D 8/3 (approximately 2.67) ✓