# 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

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