# CLASS-10INTRODUCTION & DEFINATION OF RANGE

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.)