Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10th
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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 - Mathematics

Sum

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.

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Solution

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

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APPEARS IN

Samacheer Kalvi Mathematics Class 10 SSLC Tamil Nadu State Board
Chapter 8 Statistics and Probability
Exercise 8.1 | Q 4 | Page 313
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