Question

Avalon Bagel provides take-out service for a variety of breakfast items. The following table shows the number of orders that have been recently placed grouped by the size of the order in dollars.

$0-under $5---10

$5-under $10---12

$10-under $15---14

$15-under $20---5

$20-under $25---9

What is the approximate variance for the order size for this sample?

Round to one decimal place.

Answer 1

The concept is based on the variance calculation of grouped sample ,

formula for the same as,

Size of order	Mid point (x)	No. (f)	fX	(x-M)^2	f*(x-M)^2
$0-$5	$2.50	10	$25.00	82.81	828.1
$5-$10	$7.50	12	$90.00	16.81	201.72
$10-$15	$12.50	14	$175.00	0.81	11.34
$15-$20	$17.50	5	$87.50	34.81	174.05
$20-$25	$22.50	9	$202.50	118.81	1069.29
	sum	N=50	$580.00	Sum	2284.5
		Mean	$11.60	Variance	46.62
			580/50		2284.5/(50-1)

Mean = 580/50 = $11.60

Variance = 2284.5/(50-1)=46.62