Maharashtra State BoardHSC Commerce 11th
Advertisement Remove all ads

The mean and S.D. of a group of 48 observations are 40 and 8 respectively. If two more observations 60 and 65 are added to the set, find the mean and S.D. of 50 items. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

The mean and S.D. of a group of 48 observations are 40 and 8 respectively. If two more observations 60 and 65 are added to the set, find the mean and S.D. of 50 items.

Advertisement Remove all ads

Solution

n = 48, `bar"x" = 40,  sigma_"x"` = 8 ........[Given]

`bar"x" = 1/"n" sum"x"_"i"`

∴ `sum"x"_"i" = "n"bar"x"` = 48 × 40 = 1920

New  `sum"x"_"i" = sum"x"_"i" + 60 + 65`
= 1920 + 60 + 65
= 2045
∴ New mean = `2045/50` = 40.9
Now, `sigma_"x"` = 8
∴ `sigma_"x"^2` = 64
Since, `sigma_"x"^2 = 1/"n"(sum"x"_"i"^2) - (bar"x")^2`

∴ 64 = `1/48(sum"x"_"i"^2) - (40)^2`

∴ 64 = `1/48(sum"x"_"i"^2) - 1600`

∴ `(sum"x"_"i"^2)/48` = 64 + 1600 = 1664

∴ `sum"x"_"i"^2` = 48 × 1664 = 79872

New `sum"x"_"i"^2 = sum"x"_"i"^2 + (60)^2  (65)^2`

= 79872 + 3600 + 4225
= 87697
∴ New S.D. = `sqrt(("New" sum"x"_"i"^2)/"n" - ("New mean")^2`

= `sqrt(87697/50 - (40.9)^2`

= `sqrt(1753.94 - 1672.81)`

= `sqrt(81.13)`

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 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 2 Measures of Dispersion
Miscellaneous Exercise 2 | Q 12 | Page 35
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×