Paper 4: Fundamentals of Business Mathematics & Statistic

5.22 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Example 26 : To find the median of marks : 4, 12, 7, 9, 14, 17, 16, 21

(i) Arrangement : 4, 7, 9, 12, 14, 16, 17, 21. (ii) n = 8 = an even number.

(iii) Median = average value of n 2 th item and

n 1

2

 +

  th i.e.

= average value of^82 th item and the next item

= average value of 4th item and the 5th item

= average value of 12 and 14 marks = 12 14 2 + = 13 marks.

Alternative way

Median = value of n 1 2 + th item = value of 8 1 2 + th item = value 4.5th item = 21 (value of 4th item and value

of 5th item) =

1

2 (12+14) =

1

2 × 26 = 13 marks.

(B) For Direct Series (or simple Frequency Distribution)

Cumulative frequency (less than type) is calculated. Now the value of the variable corresponding to the

cumulative frequency n 1 2 + gives the median, when N is the total frequency.

Example 27 : To find the median of the following

x : 1 2 3 4 5 6

y : 7 12 17 19 21 24

Solution :

Table : Calculation of Median

x f cum. freq. (c.f)

1 7 7

2 12 19

3 17 36

4 19 55

5 21 76

6 24 100 (= N)

N = 100

Now, median = value of n 1 2 + th item = value of 100 1 2 + th item = value of 50.5th item.

From the last column, it is found 50.5 is greater than the cumulative frequency 36, but less than the next

cum. Freq. 55 corresponding to x = 4. All the 19 items (from 37, to 55) have the same variate 4. And 50.5

item is also one of those 19 item.

∴ Median = 4.