Advertisement Remove all ads

# Answer the following : The mean height of 200 students is 65 inches. The mean heights of boys and girls are 70 inches and 62 inches respectively and the standard deviations are 8 and 10 respectively. - Mathematics and Statistics

Sum

Answer the following :

The mean height of 200 students is 65 inches. The mean heights of boys and girls are 70 inches and 62 inches respectively and the standard deviations are 8 and 10 respectively. Find the number of boys and the combined S.D.

Advertisement Remove all ads

#### Solution

Let suffix 1 denote quantities for boys and suffix 2 for girls.

Given : bar(x)_1 = 70, sigma_1 = 8, bar(x)_2 = 62, sigma_2 = 10, n1 + n2 = 200

∴ n2 = 200 – n1

Combined mean = bar(x) = 65, where

bar(x) = ("n"_1bar(x)_1 + "n"_2bar(x)_2)/("n"_1 + "n"_2)

∴ 65 = (70"n"_1 + 62(200 - "n"_1))/200

∴ 13000 = 8n1 + 12400

∴ 600 = 8n1

∴ n1 = 75

∴ n2 = 200 – 75 = 125

d1 = bar(x)_1 - bar(x) = 70 – 65 = 5

d2 = bar(x)_2 - bar(x) = 62 – 65 = – 3

If combined S.D. is sigma, then

sigma = sqrt(("n"_1("d"_1^2 + sigma_1^2) + "n"_2("d"_2^2 + sigma_2^2))/("n"_1 + "n"_2)

= sqrt((75(25 + 64) + 125(9 + 100))/200

= sqrt((6675 + 13625)/200

= sqrt(101.5)

= 10.07

Hence, the number of boys = 75 and combined S.D. = 10.07.

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. (13) | Page 191
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?