Calculate Q3, D6, and P80 from the following data and interpret the results.

Respiratory rate 10 15 20 25 30 35 40 45 50
No. of Person 8 12 36 25 28 18 9 12 6

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Solution:

x f cf
10 8 8
15 12 20
20 36 56
25 25 81
30 28 109
35 18 127
40 9 136
45 12 148
50 6 154
N = 154

Now,

Q3 = \(3\left ( \frac{N + 1}{4} \right )^{th}\) item

= \(3 \times \frac{155}{4}\) = 116.25

In c,f column, the value just greater than 116.25 is 127. ∴ Q3 = 35

Also,

D6 = \(6\left ( \frac{N + 1}{10} \right )^{th}\) item

= \(6 \times \frac{155}{10}\) = 93th

In c,f column, the value just greater than 93 is 109. ∴ D6 = 30

Also,

P80 = \(80\left ( \frac{N + 1}{100} \right )^{th}\) item

= \(80 \times \frac{155}{100}\) = 124th

In c,f column, the value just greater than 124 is 127. ∴ P80 = 35

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