Question

1. The data below show the prices of a slice of cheese pizza at various locations around Snohomish County:

$3.05	$2.57	$2.32	$2.07	$2.49	$2.12	$2.63	$2.42
$2.71	$2.19	$2.96	$2.80	$3.30	$3.48	$2.26	$2.84

1. make a histogram, then describe the center, spread and shape.

2. Find the 5-number summary (min, Q1, median, Q3, max). Show all the steps.

3. Suppose there was one more restaurant that sold a slice of cheese pizza for $5.00. Would this affect the mean or median more? Would it affect the IQR or standard deviation more?

Answer 1

C I	f
2.00-2.30	4
2.30-2.60	4
2.60-2.90	4
2.90-3.20	2
3.20-3.50	2

center lies 2.6-2.9
Range =	3.48-2.07=
	1.41

	s.n.	x	Min =	2.07
	1	2.07	Q1 =	(n+1)4 th item=
	2	2.12		17/4 th item=
	3	2.19		4.25th item=
	4	2.26	2.26+	0.25(2.32-2.26)
	5	2.32	2.26+	0.015
	6	2.42	Q1 =	2.275
	7	2.49	Median=	(8th+9th)/2=
	8	2.57		(2.57+2.63)/2 =
	9	2.63		2.6
	10	2.71	Q3=	3(n+1)4 th item=
	11	2.8	Q3=	12.75 th
	12	2.84	Q3=	2.84+ 0.75(2.96-2.84)
	13	2.96	Q3=	2.96
	14	3.05	Max =	3.48
	15	3.3	IQR =	Q3-Q1
	16	3.48	IQR =	0.685
	sum=	42.21
	Mean=	42.21/16=
		2.638125
If 5 is added then	mean=	47.21/17 =	2.777058824
		medain=	9th item=	2.63
	Change in	mean=	0.138934	more
	Change in	median=	0.03

If we add $5 then standard deviation is more affected than IQR

Histogram 5 4 3 2 1 0 1 12.00-2.30 12.30-2.60 12.60-2.90 2.90-3.20 13.20-3.50