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.
The distances in metres for seven throws of a shot-putter are: 14.5, 15.2, 16.8, 17.1, 15.9, 16.3, 14.7. Calculate the sample mean and sample standard deviation. Round to two decimals.
A. 15.79, 1.02B. 15.79, 0.96C. 14.79, 1.15D. 14.79, 0.88
mediumAsked in NIMCET 2026View solution ›
Q2.
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 ›
Q3.
An investigator has missed a value while collecting data in an experiment. Denoting the missing value by $x$ , the observations are: 10, 4, 11, 6, 17, 15, 9, 8, $x$ . What should be the value of $x$ , if he wants mean = median = mode for this data set?
A. 9B. 10C. 11D. 12
mediumAsked in NIMCET 2026View solution ›
Q4.
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 ›
Q5.
The mean of 5 observations is 5 and their variance is 12.4. If three of the observations are 1, 2 and 6, then the mean deviation from the mean of the data is:
A. 2.5B. 2.6C. 2.8D. 2.4
mediumAsked in NIMCET 2023 +1View solution ›
Q6.
For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation are
A. 39.9, 14.97B. 39.5, 14C. 39.55, 14.97D. 40.19, 15.1
mediumAsked in NIMCET 2023View solution ›
Q7.
Consider the following frequency distribution table. Class interval 10-20 20-30 30-40 40-50 50-60 60-70 70-80 Frequency 180 $f_{1}$ 34 180 136 $f_{2}$ 50 If the total frequency is 685 and the median is 42.6, then the values of $f_{1}$ and $f_{2}$ are
A. 80, 25B. 83, 22C. 79, 26D. 82, 23
hardAsked in NIMCET 2023View solution ›
Q8.
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 ›
Q9.
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 ›
Q10.
The two regression lines are $3 x + 2 y = 26$ and $6 x + y = 31$ . The coefficient of correlation between $x$ and $y$ is
A. $0.5$ B. $0.7$ C. $- 0.7$ D. $- 0.5$
mediumAsked in NIMCET 2011View solution ›
Q11.
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 ›
Q12.
Standard deviation for the following distribution is Size of item: 6, 7, 8, 9, 10, 11, 12 Frequency: 3, 6, 9, 13, 8, 5, 4
A. 1.607B. 9.0C. 5.0D. 1.88
mediumAsked in NIMCET 2020View solution ›
Q13.
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 ›
Q14.
If a variable takes the values $0, 1, 2, \dots, 50$ with frequencies $1,^{50} C_{1},^{50} C_{2}, \dots,^{50} C_{50}$ , then the AM is
A. 50B. 25C. $\frac{2 ^{50}}{50}$ D. 51
mediumAsked in NIMCET 2021View solution ›
Q15.
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 ›
Q16.
The first three moments of a distribution about 2 are 1, 16 and $- 40$ respectively. The mean and variance of the distribution are
A. (2, 16)B. (2, 15)C. (3, 15)D. (1, 16)
mediumAsked in NIMCET 2022View solution ›
Q17.
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 ›
Q18.
The mean deviation from the mean of the AP $a, a + d, a + 2 d, \dots, a + 2 n d$ is:
A. $\frac{n}{n + 1} d$ B. $\frac{n}{2 n + 1} d$ C. $\frac{n + 1}{2 n + 1} d$ D. $\frac{n ( n + 1 )}{2 n + 1} d$
mediumAsked in NIMCET 2014View solution ›
Q19.
If the mean deviation of the numbers $1, 1 + d, 1 + 2 d, \dots, 1 + 100 d$ from their mean is 255, then the value of $d$ is
A. 20.0B. 10.1C. 20.2D. 10.0
mediumAsked in NIMCET 2015View solution ›
Q20.
If the mean deviation of the numbers $1, 1 + d, 1 + 2 d, \dots, 1 + 100 d$ from their mean is 255, then d is equal to
A. 10.1B. 10.2C. 10.02D. 10.4
mediumAsked in NIMCET 2019View solution ›

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