# Answer the following : The mean and S.D. of a group of 50 observation are 40 and 5 respectively. If two more observations 60 and 72 are added to the set, find the mean and S.D. of 52 items. - Mathematics and Statistics

Sum

The mean and S.D. of a group of 50 observations are 40 and 5 respectively. If two more observations 60 and 72 are added to the set, find the mean and S.D. of 52 items.

#### Solution

n = 50, bar(x) = 40, sigma_x = 5   ...(given)

bar(x) = 1/"n"sumx_"i"

∴ sumx_"i" = "n"bar(x) = 50 × 4 = 2000

New sumx_"i" = sumx_"i" + 60 + 72

= 2000 + 60 + 72

= 2132

∴ New Mean = 2132/52 = 41

Now, sigma_x  = 5

∴ sigma_x^2 = 25

sigma_x^2 = 1/"n"(sumx_"i"^2) - (barx)^2

∴ 25 = 1/50(sumx_"i"^2) - (40)^2

∴ 25 =  1/50(sumx_"i"^2) - 1600

∴ (sumx_"i"^2)/50 = 25 + 1600 = 1625

∴ sumx_"i"^2 = 50 × 1625 = 81250

New sumx_"i"^2 = sumx_"i"^2 + (60)^2 + (72)^2

= 81250 + 3600 + 5184

= 90034

∴ New S.D. = sqrt(("New" sumx_"i"^2)/"n" -("New mean")^2

= sqrt(90034/52 - (41)^2

= sqrt(90034/52- 1681)

= sqrt((90034 - 87412)/52)

= sqrt(2622/52)

= sqrt(50.42)

= 7.1

Concept: Standard Deviation for Combined Data
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 8 Measures of Dispersion
Miscellaneous Exercise 8 | Q II. (12) | Page 191