Question

a)     Estimate the 7th decile and the 32nd percentile for the frequency table below

 

Height (cm)        140-144        144-148     148-152      152-156     156-160       160-164

No of students          4                   5                8                 7                  5                  1

              

Answer 1

The 32nd percentile is some score k from data such 32% of observations lies below this score. There are totally $4+5+8+7+5+1=30$ observations. 32% of the number of observations would be the sought percentile.

$0.32*30=9.6$. Since we obtain non-integer value, we should round it to the highest integer, so we get 10. The element of number 10 is the first observation in the group 148-152cm, that totally has 8 observations, which means every observation is approximately ${\frac {152-148} 8}=0.5 cm$ higher than the previous one. The first observation corresponds to 148cm.

148cm is a 32nd percentile of the given data

7th decile means 70nd percentile. So, the algorithm is similar

$0.7*30=21$. The 21 observation is the 4th observation in the group 152-156. In that group every observation is approximately ${\frac {156-152} 7}=0.57$ cm higher than previous one. The 4th observation would be approximately $152+3*0.57=153.71 cm$

153.71cm is a 7th decile of the given data