Advertisement Remove all ads

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

Answer the following :

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.

Advertisement Remove all ads

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
  Is there an error in this question or solution?
Advertisement Remove all ads

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
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×