Paper 4: Fundamentals of Business Mathematics & Statistic

5.36 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Calculation of missing frequency :

Example 39 : Mode of the given distribution is 44, find the missing frequency

Marks 10–20 20–30 30–40 40–50 50–60 60–70

No. of students 5 8 12 –– 10 8

Solution :

Since mode is 44, so modal class is 40–50.

Table : Showing the Frequency Distribution

Marks Frequency(f)

10–20 5

20–30 8

30–40 12

40–50 ––

50–60 10

60–70 8

let the missing frequency be f 1

Now mode = 11

l f^1210

2f 12 10

+ − ×

− −

or, 44 =^11

40 f^1210

2f 22

+ − ×

−

or,^11

4 f^1210

2f 22

= − ×

− or, f^1 = 16 (on reduction)

Miscellaneous examples :

1. If two variates x and y are related by 2x = 3y – 1, and mean of y be 9 ; find the mean of x.
   2x = 3y –1 or, 2x = 3y -1 or, 2x = 3 ×9 -1= 26 or, x = 13


2. If 2u = 5x is the relation between two variables x and u and harmonic mean of x is 0.4, find the harmonic
   mean of u.

u^5 x or, u^5 0.4 1.0

= 2 = 2 × = ∴ reqd. H.M is 1.0

3. The relation between two variables x and y is 3y – 2x + 5 = 0 and median of y is 40, find the median of x.

From 3y – 2x + 5 = 0 we get, x=^32 y+ 25. As the median is located by position, so median of x is^32. 40+^52 =62.5

4. Mode of the following frequency distribution is 24 and total frequency is 100. Find the values
   of f 1 and f 2.
   C.I : 0 –10 10–20 20–30 30–40 40–50
   Frequency : 14 f 1 27 f 2 15