Question

Dr. Paul Oswiecmiski randomly selects 40 of his 20- to 29-year old patients. Below is a frequency distribution of their Serum HDL cholesterol levels.

HDL Cholesterol	Frequency
20-29	1
30-39	0
40-49	6
50-59	9
60-69	14
70-79	10

A. what is the class width?

B. Which is most true regarding the HDL cholesterol levels of these 40 patients?

I. Mean>Median

II. Mean< Median

III. Mean=Median

Answer 1

A)

Class width is the difference between the upper or lower class limits of consecutive classes.

All classes should have the same class width.

In this case, class width equals to the difference between the lower limits of the first two classes.

Therefore,

Class Width = 30 - 20 = 10

B)

Class Midpoints = (Lower class limit + Upper class limit) / 2

For First class,

Midpoint = (20+29)/2 = 24.5

Similarly solve for other classess.....

Computational Table:

Class	Frequency (Fi)	Midpoint (Xi)	FiXi	Cumulative Frequency
20 - 29	1	24.5	24.5	1
30 - 39	0	34.5	0	=1 + 0 = 1
40 - 49	6	44.5	267	= 1 + 6 = 7
50 - 59	9	54.5	490.5	= 7 + 9 = 16
60 - 69	14	64.5	903	= 16 + 14 = 30
70 - 79	10	74.5	745	= 30 + 10 = 40
Total	40		2430

Mean =

Where, N = 40

Median =

For CONTINUOUS DISTRIBUTION

Median =

Median class = size of (N/2)th item

Median class = size of (40/2)th item

Median class = size of 20th item

Median class = 60 - 69

L = Lower limit of median class = 60

h = length of the median class = 9

f = frequency of median class = 14

C.F = Cummulative frequency of previous class = 16

Therefore,

Median =

Median = 62.57

Therefore,

Mean < Median

i.e. 60.75 < 62.57

ANSWER: B

B. Mean < Median