Paper 4: Fundamentals of Business Mathematics & Statistic

5.6 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

2 3

r

r j = 1 1 j

1 1 2 3 r r

1 2 r j

j = 1

n x

x =n x + n x + n x +... + n x =

n + n + ... + n n

Example 5: The means of two samples of sizes 50 and 100 respectively are 54.1 and 50.3. Obtain the mean

of the sample size 150 obtained by combining the two sample.

Here, n 1 = 50, n 2 = 100, x 1 = 54.1, x 2 = 50.3

∴Mean (x) = 1 1 1 22 2

n x + n x =50 × 54.1+100 × 50.3

n + n 50 +100

2705 5030 7735 51.57 (approx.)

150 150

= + = =

5.1.1.2. Finding of missing frequency:

In a frequency distribution if one (or more) frequency be missing (i.e. not known) then we can find the

missing frequency provided the average of the distribution is known. The idea will be clear from the following

example :

For one missing frequency :

Example 6 : The AM of the following frequency distribution is 67.45. Find the value of f 3 ,

Let A = 67. Now using the formula.

Height (inch) Frequency

61 15

64 54

67 f 3

70 81

73 24

Solution:

Calculation of missing frequency

Table : Calculation of Mean

Height (x) Frequency(f) d = x – A d ́ = d / 3 fd ́

61 15 –6 –2 – 30

64 54 –3 –1 – 54

67 f 3 0 0 0

70 81 3 1 81

73 24 6 2 48

Total N =174 + f 3 – – Σfd′= 45