HOW TO FIND RANGE AND COEFFICIENT OF RANGE

Example 1 :

Find the range and coefficient of range of the following data.

(i) 63, 89, 98, 125, 79, 108, 117, 68

Solution :

L - 125 and S = 63

Range  =  L - S

  =  125 - 63

Range  =  L - S  =  62

Coefficient of range  =  (L - S)/(L + S)

L + S   =  125 + 63  =  188

Coefficient of range  =  62/188

=  31/94

=  0.33

(ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8

L - 61.4 and S = 13.6

Range  =  L - S

  =  61.4 - 13.6

Range  =  L - S  =  47.8

Coefficient of range  =  (L - S)/(L + S)

L + S   =  61.4 + 13.6  =  75

Coefficient of range  =  47.8/75

=  478/750

=  0.64

Example 2 :

If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.

Solution :

Range  =  36.8, smallest value (S) =  13.4

Range =  L - S

36.8  =  L - 13.4

L  =  36.8 + 13.4

L = 50.2

Hence the largest value is 50.2.

Example 3 :

Calculate the range of the following data.

Solution :

Range  =  650 - 400

  =  250

Example 4 :

A teacher asked the students to complete 60 pages of a record note book. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.

Solution :

Arranging the given data in ascending order, we get 

30, 32, 33, 35, 35, 36, 37, 37.

Σd²/8  =  47/8

(Σd/8)²  =  (-5/8)²  =  25/64  

σ  =  √(47/8) - (25/64)

σ  =  √(376 - 25)/64

σ  =  √351/64

σ  =  √5.48

σ  =  2.34

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