Suppose you have a height of 20 children at the day care center as follows 65, 8

Question

Suppose you have a height of 20 children at the day care center as follows 65, 83, 69, 67, 69, 67, 67, 72, 85, 68, 73, 65, 67, 65, 72, 71, 75, 76, 67, 68 Arrange: 65, 65, 65, 67, 67, 67, 67, 67, 68, 68, 69, 69, 71, 72, 72, 73, 75, 76, 83, 85 Find the (P_25) 25^th percentile = 25/100 times 20 = 5 & 6 = 67 + 67/2 = 67 Find the (p_47) 47^th percentile = 47/100 times 20 = 9.4 round up = 10 = 68 Find the (P_50) 50^th percentile = 50/100 times 20 = 10 & 11 68 + 69/2 = 68.5 Find the (P_60) 60^th percentile = 60/100 times 2 = 12 & 13 = 69 + 71/2 = 70 Find the percentile rank of 76: 17/20 times 100 = 85 Find the percentile rank of 83.: 18/20 times 100 = 90

Explanation / Answer

for calculating percentile, data are arranged in ascending order and it was done in question

here total observation is 20,

(1)so P25=25th percentile is the observation of 20*25/100=5

so sixth observation will be P25 i.e.67

(2)P47=20*47/25=9.4 so next obsevation will be 10th

so P47=68

(3) for P50, 20*50/100=10, so 11th observation is P50 i.e.69

(4)for P60, 20*60/100=12, 13th observation is P60 i.e.71

(5) 76 is 18th observation, so its percentile is 100*18/20=90, i.e. 90th percentile

(6)83 is 19th observation, so its percentile is 100*19/20=95, i.e. 95th percentile

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