Standard deviation, variance and mean deviation — practice questions

Question 1 · difficulty L2 · understanding

The mean deviation about the mean for the data $$\begin{array}{|c|c|c|c|c|c|c|} \hline x_i & 5 & 7 & 9 & 10 & 12 & 15 \\ \hline f_i & 8 & 6 & 2 & 2 & 2 & 6 \\ \hline \end{array}$$ $$\text { is equal to: }$$

• A. $$\frac{40}{13}$$
• B. $$\frac{42}{13}$$
• C. $$\frac{44}{13}$$
• D. $$\frac{46}{13}$$

Question 2 · difficulty L2 · understanding

If the mean and the variance of the data $$\begin{array}{|c|c|c|c|c|} \hline \text { Class } & 4-8 & 8-12 & 12-16 & 16-20 \\ \hline \text { Frequency } & 3 & \lambda & 4 & 7 \\ \hline \end{array}$$ are $\mu$ and 19 respectively, then the value of $\lambda+\mu$ is :

• A. 21
• B. 19
• C. 18
• D. 20

Question 3 · difficulty L2 · understanding

For a statistical data $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}$ of 10 values, a student obtained the mean as 5.5 and $\sum_{i=1}^{10} x_i^2=371$. He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respectively. The variance of the corrected data is

• A. 5
• B. 7
• C. 9
• D. 4

Question 4 · difficulty L2 · understanding

If the variance of the frequency distribution $$x$$ $$c$$ $$2c$$ $$3c$$ $$4c$$ $$5c$$ $$6c$$ $$f$$ 2 1 1 1 1 1 is 160, then the value of $$c\in N$$ is

• A. 5
• B. 8
• C. 6
• D. 7

Question 5 · difficulty L2 · understanding

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :

• A. 1792
• B. 1216
• C. 1456
• D. 1072

Question 6 · difficulty L2 · understanding

If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $${{20} \over 3}$$, respectively, then the value of | a $$-$$ b | is equal to :

• A. 9
• B. 11
• C. 7
• D. 1

Question 7 · difficulty L2 · understanding

The variance $$\sigma^2$$ of the data $$x_i$$ 0 1 5 6 10 12 17 $$f_i$$ 3 2 3 2 6 3 3 is _________.

Question 8 · difficulty L2 · understanding

If the mean of the frequency distribution Class : 0-10 10-20 20-30 30-40 40-50 Frequency : 2 3 $$x$$ 5 4 is 28, then its variance is __________.

Question 9 · difficulty L2 · understanding

Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14. Then n is equal to _____________.

Question 10 · difficulty L2 · understanding

Consider a data consisting of 10 observations $x_1, x_2, \ldots, x_{10}$, whose mean is 5 and variance is 7 . If the mean and the variance of the first 8 observations $x_1, x_2, \ldots, x_8$ are 4 and 3.5 , respectively, and $x_9 < x_{10}$, then the value of $3 x_9+2 x_{10}$ is $\_\_\_\_$ .