Question

A teacher asked the students to complete 60 pages of a record notebook. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.

Answer 1

The remaining number of pages to be completed is 60 – 32, 60 – 35, 60 – 37, 60 – 30, 60 – 33, 60 – 36, 60 – 35 and 60 – 37

The pages to be completed are, 28, 25, 23, 30, 27, 24, 25, and 23

Arrange in ascending order we get, 23, 23, 24, 25, 25, 27, 28 and 30

xi	xi2
23	529
23	529
24	576
25	625
25	625
27	729
28	784
30	900
`sumx_"i"` = 205	`sumx_"i"^2` = 5297

Here n = 8, `sumx_"i"` = 205, `sumx_"i"^2` = 5297

Standard deviation (σ) = `sqrt((sumx_"i"^2)/"n" - ((sumx_"i")/"n")^2`

= `sqrt(5297/8 - (205/8)^2`

= `sqrt(662.13 - 42025/64)`

= `sqrt(662.13 - 656.64)`

= `sqrt(5.49)`

= 2.34

Standard deviation (σ) = 2.34