Statistics

22. The given data is converted into continuous frequency duration by subtracting and adding 0.5 from lower and upper limit respectively. Lit the assumed mean be A=42.5 and h=4

21. Let the assumed mean be A=92.5 and h=5

20.

We have,  $N={\displaystyle \sum _{i=1}^{n}fi}=50$ .

So, mean,  $\overline{x}=\frac{1}{N}*{\displaystyle \sum _{i=1}^{n}fi}xi=\frac{1350}{5}=27.$

$\begin{array}{c}=\frac{1}{50}*6600\\ \end{array}$

= 132.

19. Let the assumed mean be A=105 and class width, h=30. The given data can be tabulated as

= 2280 - 4

= 2276.

18. Let the assumed mean be A=64 and it the width, h=1.

17. The given data can be tabulated as follow

16. The given data can be tabulated as follow.

15. We have, first 10 multiples of 3=3,6,9,12,15,18,21,24,27,30.

So,  $\overline{x}=\frac{3+6+9+12+15+18+21+24+27+30}{10}=\frac{165}{10}=16.5$

We can now tabulate the given data as following.

Therefore, variance,  $a^2=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}$

$\begin{array}{c}=\frac{1}{10}*742.5\\ \end{array}$

= 74.25.