Measures of Dispersion, Skewness and Kurtosis MCQs 2026

The fourth central moment is related to

1. Aonly the median✓
2. Bonly range✓
3. Ckurtosis of the distribution✓
4. Donly Chebyshev bound✓

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

1. A75%✓
2. B88%✓
3. C15/16 (93.75%)✓
4. D99%✓

A dataset with SD = 0 must have

1. Amean zero only✓
2. Bmedian undefined✓
3. Call values identical✓
4. Dpositive skew always✓

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

1. A1✓
2. B0✓
3. Cundefined✓
4. Dequal to the mean✓

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

1. A4✓
2. B3✓
3. C2✓
4. D8/3 (approximately 2.67)✓

Population variance of 1, 4, 7 is

1. A4✓
2. B6✓
3. C8✓
4. D18✓

Population standard deviation of 1, 4, 7 is

1. A6✓
2. B3✓
3. C2✓
4. D√6 (approximately 2.45)✓

Variance is expressed in

1. Asquared units of the original variable✓
2. Bthe same units as the variable always✓
3. Cpercent only✓
4. Dunit-free always✓

In PPSC/CSS, dispersion questions often include

1. Aonly trigonometric identities✓
2. Bvariance, SD, CV and Chebyshev✓
3. Conly chemical bonding✓
4. Donly matrix rank✓

Range is most affected by

1. Aextreme values at the ends✓
2. Bthe median class only✓
3. Cthe mode only✓
4. Dmiddle 50% of data✓

A larger standard deviation indicates

1. Alower spread✓
2. Bgreater spread around the mean✓
3. Calways higher mean✓
4. Dalways symmetric data✓

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

1. A12✓
2. B24✓
3. C6✓
4. D3✓

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

1. A0✓
2. B1✓
3. C−1✓
4. D0.5✓

The third central moment is related to

1. Aonly sample size✓
2. Bskewness of the distribution✓
3. Conly range✓
4. Donly kurtosis only without skew✓

Semi-average range is

1. AQ3 − Q1✓
2. Bfull range✓
3. Caverage of ranges of two halves of the data✓
4. DSD/2✓

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

1. A2 times✓
2. Bunchanged✓
3. C4 times the old variance✓
4. D8 times✓

A distribution with mean 100 and SD 5 has CV of

1. A20%✓
2. B0.05%✓
3. C500%✓
4. D5%✓

Root mean square deviation equals

1. Amean deviation always✓
2. Brange✓
3. CIQR✓
4. Dstandard deviation for population definition✓

For grouped data, variance can be computed using

1. Aonly the modal class frequency✓
2. Bclass midpoints and frequencies✓
3. Conly the first class✓
4. Donly graph area✓

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

1. Araw range only✓
2. Braw variance only✓
3. Conly IQR without mean✓
4. Dcoefficient of variation✓

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

1. Alower SD✓
2. BSD = 0✓
3. Chigher standard deviation✓
4. Dequal CV always✓

Standard deviation is preferred in inference because

1. Ait ignores all outliers completely✓
2. Bit equals range always✓
3. Csquared deviations are differentiable and lead to normal theory✓
4. Dit requires no assumptions✓

Mean deviation is generally considered

1. Aalways larger than range✓
2. Bless mathematically tractable than variance for inference✓
3. Calways equal to SD✓
4. Dalways zero for samples✓

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

1. A99%✓
2. B8/9 (approximately 88.9%)✓
3. C50%✓
4. D2/3✓

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

1. A50%✓
2. B95%✓
3. C100%✓
4. D75% (1 − 1/4)✓

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

1. Ak standard deviations of the mean✓
2. Bk variances of the median✓
3. Ck ranges of the mode✓
4. Dexactly 95% for k=2 always✓

Platykurtic distribution has

1. Aflatter peak and lighter tails than normal (excess kurtosis < 0)✓
2. Bheavier tails than normal✓
3. Cinfinite peak✓
4. Dnegative variance✓

Leptokurtic distribution has

1. Ahigher peak and heavier tails than normal (excess kurtosis > 0)✓
2. Bflatter peak than normal✓
3. Cexactly normal tails✓
4. Dzero variance✓

Excess kurtosis is defined as

1. Akurtosis plus 3✓
2. Bkurtosis times 3✓
3. Cskewness minus 3✓
4. Dkurtosis minus 3✓

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

1. A0✓
2. B1✓
3. C3✓
4. D6✓

Kurtosis measures

1. Aonly centre of data✓
2. Bthe peakedness and tail heaviness relative to a normal distribution✓
3. Conly sample mean only✓
4. Donly class width✓

For symmetric data, coefficient of skewness is

1. Aalways +1✓
2. Bapproximately zero✓
3. Calways −1✓
4. Dundefined✓

Bowley's coefficient of skewness uses

1. Aquartiles: (Q3 + Q1 − 2Q2)/(Q3 − Q1)✓
2. Bonly mean and mode✓
3. Conly range and mean✓
4. Donly variance✓

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

1. A6✓
2. B0.5✓
3. C−2✓
4. D2✓

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

1. AStandard deviation✓
2. BVariance✓
3. CRange✓
4. DIQR✓

Negative skewness means

1. Aright tail longer✓
2. Bzero variance✓
3. Cthe left tail is longer; mean typically below median✓
4. Dmean above median✓

Positive skewness means

1. Aleft tail longer✓
2. Bperfect symmetry✓
3. Cthe right tail is longer; mean typically exceeds median✓
4. Dmean below median always✓

Skewness measures

1. Alack of symmetry in a distribution✓
2. Bonly central tendency✓
3. Conly sample size✓
4. Donly counting categories✓

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

1. Avariance (population definition)✓
2. Bstandard deviation✓
3. Cskewness✓
4. Dkurtosis only✓

The first moment about the mean is always

1. Aone✓
2. Bequal to variance✓
3. Cequal to skewness✓
4. Dzero✓

Multiplying every value by 3 multiplies standard deviation by

1. A3✓
2. B9✓
3. Cunchanged✓
4. D1/3✓

Adding a constant to every value changes standard deviation by

1. Anot at all (SD unchanged)✓
2. Bincreasing SD by that constant✓
3. Cmultiplying SD by the constant✓
4. Dhalving SD✓

Interquartile range equals

1. AQ3 + Q1✓
2. BMedian − Q1✓
3. CRange✓
4. DQ3 − Q1✓

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

1. A20✓
2. B30✓
3. C10✓
4. D60✓

Quartile deviation is (Q3 − Q1) /

1. A4✓
2. B2✓
3. C1✓
4. DN✓

If mean = 50 and SD = 10, CV is

1. A20%✓
2. B10%✓
3. C5%✓
4. D200%✓

Coefficient of variation (CV) is

1. A(Standard deviation / Mean) × 100%✓
2. BMean / SD × 100✓
3. CSD squared / Mean✓
4. DRange / Mean only✓

If sample variance is 25, standard deviation is

1. A12.5✓
2. B625✓
3. C5✓
4. D−5✓

Standard deviation is

1. Avariance squared✓
2. Bmean of absolute deviations always✓
3. Crange divided by 2✓
4. Dthe positive square root of variance✓

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

1. A8/3✓
2. B4✓
3. C2✓
4. D0✓

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

1. A8/3✓
2. B2✓
3. C4✓
4. D8✓

Sample variance s² uses divisor

1. An+1✓
2. Bn − 1 (Bessel correction)✓
3. CN always✓
4. Dn−2✓

Population variance is Σ(x − μ)² /

1. An−1✓
2. Bn+1✓
3. C2N✓
4. DN✓

Variance measures

1. Aonly the centre of data✓
2. Baverage squared deviation from the mean✓
3. Conly the most frequent value✓
4. Donly rank correlation✓

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

1. A0✓
2. B4/3 (approximately 1.33)✓
3. C2✓
4. D4✓

Mean deviation (MD) is

1. Athe square root of variance always✓
2. Bonly maximum minus minimum✓
3. Conly Q3 minus Q1✓
4. Dthe average of absolute deviations from a reference point (usually mean)✓

Range of 4, 7, 9, 15 is

1. A7✓
2. B11.5✓
3. C9✓
4. D11✓

Range is defined as

1. Amaximum divided by minimum✓
2. Bmaximum value minus minimum value✓
3. Csum of all values✓
4. Dmedian minus mode✓

Dispersion measures

1. Aonly central location✓
2. Bonly sample size✓
3. Chow spread out or scattered the data are✓
4. Donly data collection year✓

Skewness zero and kurtosis 3 suggest

1. Aalways uniform distribution✓
2. Balways bimodal distribution✓
3. Calways negative skew✓
4. Dbell-shaped symmetric mesokurtic distribution✓