Question

1-Find the standard deviation and the average of the final grades (final grade page is attached) .

2-the average of n= 10 will be close to the average of the whole population ( central limit theorem) so take a random grab of 10 people and find the avarge of x of this group.

Do this 5 times and answer the question in the page that is attached.

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Answer 1

$Average~grade~\mu=\frac{\sum X_i}{N}=\frac{2746}{39}=70.4103$

$Standard ~deviation ~of ~entire~class~\sigma=\sqrt{\frac{\sum (X_{i}-\mu)^2}{39}}=13.6583$

Sr. No	X1	X2	X3	X4	X5
1	96	60	50	82	69
2	50	72	92	69	96
3	60	88	80	80	50
4	69	96	88	50	88
5	82	50	74	60	74
6	74	74	50	74	72
7	80	69	60	88	80
8	69	78	74	50	74
9	84	50	72	50	60
10	50	70	60	60	84
Mean	71.4	70.7	70	66.3	74.7

$\bar{X_1}=71.4 ~~\bar{X_2}=70.7 ~~\bar{X_3}=70~~\bar{X_4}=66.3~~\bar{X_5}=74.7$

$The~average~of~sample~average~ is~\frac{\sum \bar{X_i}}{5}=70.62$

$The~standard~deviation ~of~X_1,X_2,X_3,X_4,X_5~is~\sqrt{208.86}=14.452$

$\frac{\sigma}{\sqrt{n}}=\frac{13.6583}{\sqrt{10}}=4.3191$