Question

**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?

Answer #1

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

A national health survey measured the serum HDL cholesterol
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25
26
26
26
27
28
28
32
34
34
35
36
36
36
37
38
40
43
44
47
47
48
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34
35
35
36
36
36
38
38
38
38
38
39
40 40
41
42 43
43
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48
38
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49
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Stretching/Yoga – and instructed to follow the program for 8 weeks.
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48
38
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41
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1
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