Question

Consider the following information:

Observations 1 2 3 4 5 6
Num. of defects 10 18 13 15 9 12
The number of runs above and below the sample median is:__________
a) 3.
b) 4.
c) none of these.
d) 5.
e) 6.

Answer 1

A. 3

Explanation:

Formula for locating the Median of a grouped data = (N+1)/2 th where

N is the total number of defects.

Total defects = 10+18+13+15+9+12

Total defects = 77

Median value = (77+1)/2 th value

Median value = 78/2 = 39th value.

We will cummulate the frequency (number of defects up to the 38th value) and locate the corresponding observation value.

On cummulating:

10+18+13 = 41

We can see that the value of 38 falls on the third column(13), hence the median will be the equivalent number of observations i.e 3.

Therefore the sample median is 3