Question

13. 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.​

Answer 1

Step-by-step explanation:

Answer:

75 Boys

10.07

Step-by-step explanation:

The mean height of 200 students is 65 inches

=> total height = 200 * 65 = 13000 inches

Let say Boys = B

then girls = 200 - B

The mean height of boys and girls are 70 inches and 62 inches respectively

Total height of boys = 70B inches

total height of girls = 62(200 - B) = 12400 - 62 B inches

70B + 12400 - 62 B = 13000

=> 8B = 600

=> B = 75

Number of Boys = 75

number of girls = 125

Combined Variance = ( 75 * ( 8² + (70 - 65)²) + 125 * ( 10² + (62 - 65)²) )/200

= (75 * 89 + 125*109)/200

= 101.5

combined standard deviation. = √101.5 = 10.07