Question

In: Math

For the following data, approximate the sample mean, sample variance and sample standard deviation weekly grocery...

For the following data, approximate the sample mean, sample variance and sample standard deviation weekly grocery bill.

Bill (in dollars) Frequency

135-139 11

140-144 20

145-149 19

150-154 7

155-159 5

Expert Solution

Solution:

Given that,

Class	Frequancy ( f )	Mid value ( x )	d = x -A /h	*fd**	fd²
135-139	11	137	-2	-22	44
140 - 144	20	142	-1	-20	20
145 -149	19	147	0	0	0
150 - 154	7	152	1	7	7
155 - 159	5	157	2	10	20
	n = 62			fd -25	fd² = 91

a ) The sample mean is

Mean = (A + (fd / n) * h)

= (147 +( - 25 / 62 ) * 5

= 147 + - 0.4032 * 5

= 147 + - 2.0161

= 144.9839

b ) The sample variance S²

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

= ( 91 ( (- 25 )² / 62 ) / 61 * 5²

= ( 91 -10.0806 / 61 ) * 25

= (80.9194 / 61 )* 25

= 1.3262 *25

= 33.1637

The sample variance S² is 33.1637

c ) The sample standard is S

S = ( fd² ) - (( fd )² / n ) / 1 -n ) * h²

= ( 91 ( (- 25 )² / 62 ) / 61 * 5²

= ( 91 -10.0806 / 61 ) * 25

= (80.9194 / 61 )* 25

= 1.3262 *25

= 33.1637

= 5.7588

The sample standard is = 5.7588

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