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 119.1 - 122.2 46 122.3 - 125.4 38 125.5 - 128.6 24 128.7 - 131.8 19 131.9 - 135.0 27

Heights in Centimeters

Class	Frequency
119.1 - 122.2	46
122.3 - 125.4	38
125.5 - 128.6	24
128.7 - 131.8	19
131.9 - 135.0	27

Answer 1

Solution:

Given that,

Class	Frequency	Midvalue	d	fd	fd2
119.1 - 122.2	46	120.65	-6.4	-294.4	1884.16
122.3 - 125.4	38	123.85	-3.2	-121.4	389.12
125.5 - 128.6	24	127.05	0	0	0
128.7 - 131.8	19	130.25	3.2	60.8	194.56
131.9 - 135.0	27	133.45	6.4	72.8	1105.92
	n = 154			$\sum$fd = -182.4	$\sum$fd2 = 3573.76

b ) The  sample variance S²

  S² = ($\sum$ fd² ) - (( $\sum$ fd )² / n ) / 1 -n ) * h²

= (3573.76 ( ( -182.4 )² / 154 ) / 153 * 1²

   = (3573.76 - 216.0374 / 153 ) * 1

= (3357.7226 / 153 )* 1

= 21.9459*1

= 21.9459

The  sample variance S² is 21.9459

b ) The sample standard deviation is S

S = $\sqrt{}$ variance

= $\sqrt{}$ 21.9459

= 4.6846

sample standard deviation is 4.6846