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