Question

Calculate the sample variance and sample standard deviation for the following frequency distribution of heights in centimeters for a sample of 8-year-old boys. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Heights in Centimeters

Class Frequency

120.6 - 123.6 26

123.7 - 126.7 22

126.8--129.8 34

129.9-132.9 26

133-136 44

Answer 1

Solution:

We have to find  the sample variance and sample standard deviation for the given frequency distribution of heights in centimeters for a sample of 8-year-old boys.

Formula:

Sample variance:

where mi = mid values of class intervals.

Thus we need to make following table:

Class	fi: Frequency	mi	mi*fi	mi2* fi
120.6-123.6	26	=(120.6+123.6)/2=122.1	3174.6	387618.66
123.7-126.7	22	=(123.7+126.7)/2=125.2	2754.4	344850.88
126.8-129.8	34	=(126.8+129.8)/2=128.3	4362.2	559670.26
129.9-132.9	26	=(129.9+132.9)/2=131.4	3416.4	448914.96
133.0-136.0	44	=(133.0+136.0)/2=134.5	5918	795971
	N = 152

Thus

Sample variance:

and

Sample standard deviation: