Question

# Cholesterol levels: A national health survey measured the serum HDL cholesterol levels in a large number...

Cholesterol levels: A national health survey measured the serum HDL cholesterol levels in a large number of women. Following is a sample of

37

HDL levels (in milligrams per deciliter) that are based on the results of that survey. The list has been sorted into numerical order.

 25 25 25 26 27 27 27 28 28 29 34 35 35 38 38 39 42 42 43 44 45 45 45 45 46 46 47 48 51 52 56 57 65 67 69 72 75

(a) What is the 16th percentile?

(b) What is the 70th percentile?

Solution :

Arranging Observations in the ascending order, We get :
25,25,25,26,27,27,27,28,28,29,34,35,35,38,38,39,42,42,43,44,45,45,45,45,46,46,47,48,

51,52,56,57,65,67,69,72,75

Here, n = 37

P 16 = (16(n+1) / 100 )th value of the observation

= (16⋅38 / 100)th value of the observation

= (6.08)th value of the observation

= 6th observation +0.08[7th-6th]

= 27 + 0.08[27 - 27]

= 27 + 0.08(0)

= 27+0

= 27

16th percentile = 27

(b)

70=(70(n+1) / 100)th value of the observation

= (70⋅38 / 100)th value of the observation

= (26.6)th value of the observation

= 26th observation + 0.6[27th-26th]

= 46 + 0.6[47-46]

= 46 + 0.6(1)

= 46 + 0.6

= 46.6

70th percentile = 46.6

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