INTRODUCTION & DEFINATION OF RANGE –
The difference between the values of the biggest and the smallest observation is called the range.
Interquartile Range –
The difference between the upper quartile and the lower quartile is called the inter-quartile range. Thus, interquartile range = (Q₃ - Q₁)
Semi-Interquartile Range –
1
------- (Q₃ - Q₁) is called the semi-interquartile range
2
Example.) In a class test, the marks obtained by 11 students are –
15, 18, 13, 5, 11, 20, 3, 17, 8, 15, 6
Findd : (i) Range (ii) Median (iii) Lower quartile
(iv) Upper quartile (v) IInterquartile Range
(vi) Semi-Interquartile Range
Ans.) On arranging the given marks in an ascending order, we get –
3, 5, 6, 8, 11, 13, 15, 15, 17, 18, 20.
So, n = 11, which is odd
(i) Highest marks = 20, lowest marks = 3
Range = (20 – 3) = 17
n + 1 11 + 1
(ii) Median Marks = (--------)th observation = (---------)th observation
2 2
= 6th observation = 13 (Ans.)
n + 1 11 + 1
(iii) Lower Quartile Q₁ = (-------)th observation = (---------)th
4 4
observation = 3rd observation = 6 (Ans.)
3(n + 1)
(iv) Upper quartile Q₃ = -----------th observation
4
3(11 + 1)
= ------------ = 9th observation = 17 (Ans.)
4
(v) Interquartile range = (Q₃ - Q₁) = (17 – 6) = 11
1 11
(vi) Semi-interquartile Range = ------- (Q₃ - Q₁) = ------- = 5.5
2 2
(Ans.)
Your second block of text...