Statistics Questions with Solutions

25 questions11 easy13 medium1 hard

Statistics deals with collecting, summarising and interpreting data. This topic covers measures of central tendency (mean, median and mode) for ungrouped and grouped data, and measures of dispersion such as range, mean deviation, variance, standard deviation and the coefficient of variation. Exam questions test calculating these measures, the effect of adding or multiplying every observation by a constant, combined mean and variance of two groups, and comparing the consistency of two data sets. Remember that adding a constant to every value changes the mean but not the variance or standard deviation, while multiplying by k multiplies the standard deviation by |k|. Facts like these solve many questions without any calculation. Practise the statistics questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
Consider the following grouped data. Find the mode. Class interval: 20–25, 25–30, 30–35, 35–40, 40–45, 45–50 Number of students: 8, 14, 20, 18, 10, 6
A. 32.14B. 31.67C. 33.75D. 34.12
easyAsked in NIMCET 2026View solution ›
Q2.
For a given sample, the computed values of the variance and fourth central moment are 3 and 63 respectively. Then the underlying frequency distribution is classified as:
A. NormalB. MesokurticC. PlatykurticD. Leptokurtic
easyAsked in NIMCET 2026View solution ›
Q3.
If $\overline{X_{1}}$ and $\overline{X_{2}}$ are the means of two distributions such that $\overline{X_{1}} < \overline{X_{2}}$ and $\overline{X}$ is the mean of the combined distribution, then
A. $\overline{X} < \overline{X_{1}}$ B. $\overline{X} > \overline{X_{2}}$ C. $\overline{X} = \frac{X _{1} + X _{2}}{2}$ D. $\overline{X_{1}} < \overline{X} < \overline{X_{2}}$
easyAsked in NIMCET 2013View solution ›
Q4.
If the mean of the squares of the first $n$ natural numbers is $11$ , then $n$ is equal to
A. $- \frac{13}{2}$ B. $11$ C. $5$ D. $4$
easyAsked in NIMCET 2011 +1View solution ›
Q5.
If the mean of the first $n$ natural numbers is $\frac{n + 7}{3}$ , then $n$ is equal to
A. $9$ B. $10$ C. $11$ D. $12$
easyAsked in NIMCET 2011View solution ›
Q6.
The standard deviation of 20 numbers is 30. If each of the numbers is increased by 4, then the new standard deviation will be
A. 24B. 34C. 30D. 20
easyAsked in NIMCET 2021View solution ›
Q7.
The 10th and 50th percentiles of the observations 32, 49, 23, 29, 118 respectively are
A. 21, 32B. 23, 32C. 23, 33D. 22, 31
easyAsked in NIMCET 2022View solution ›
Q8.
The mean of 25 observations was found to be 38. It was later discovered that 23 and 38 were misread as 25 and 36, then the mean is
A. 32B. 36C. 38D. 42
easyAsked in NIMCET 2022View solution ›
Q9.
Let $x_{i}$ , $i = 1, 2, \dots, n$ be n observations and $w_{i} = p x_{i} + k$ , $i = 1, 2, \dots, n$ , where p and k are constants. If the mean of the $x_{i}$ 's is 48 and their standard deviation is 12, whereas the mean of the $w_{i}$ 's is 55 and their standard deviation is 15, then the values of p and k should be:
A. p = 1.25, k = -5B. p = -1.25, k = 5C. p = 2.5, k = -5D. p = 25, k = 5
easyAsked in NIMCET 2019View solution ›
Q10.
In a reality show, two judges independently provided marks based on the performance of the participants. The marks provided by the second judge are given by $Y = 10.5 + 2 X$ , where $X$ is the marks provided by the first judge. If the variance of the marks provided by the second judge is 100, then the variance of the marks provided by the first judge is
A. 49.5B. 25C. 50D. 99
easyAsked in NIMCET 2024View solution ›
Q11.
Which one of the following is NOT a correct statement?
A. The value of standard deviation changes by a change of scaleB. The standard deviation is greater than or equal to the mean deviation (about mean)C. The sum of squares of deviations is minimum when taken from the meanD. The variance is expressed in the same units as the units of observation
easyAsked in NIMCET 2025View solution ›