Question

c) The marks scored by (17 students in a class test are
15,14,20,8,17,25,27,20,16,17,0,5,19,17,30, 6 and 13.
Find: i) Median (ii) Lower Quartile (iii) Upper Quartile
(iv Mode​

Answer 1

1) Median = 17

2) Lower quartile = 21/2

3) Upper quartile = 20

4) Mode = 17

Arranging the marks obtained by the 17 students in the test in increasing order -

0,5,6,8,13,14,15,16,17,17,17,19,20,20, 25,27,30.

Median = (n/2)th term , for odd number of terms

Median = ((n/2)th term + (n/2 +1)th term)/2 , for even number of terms.

Median of the observations= middle term of the observations

Median = 9th term = 17

Mode = The observation which is repeated most number of times

Mode = 17 (it is repeated three times)

Lower quartile will be equal to the median of the lower half of the observations .

Upper half observations - 0,5,6,8,13,14,15,16

Lower quartile = (8+13)/2 = 21/2

Upper quartile will be equal to the median of the upper half of the observations .

Lower half observations - 17,17,19,20,20,25,27,30

Upper quartile = (20+20)/2 = 20