Paper 4: Fundamentals of Business Mathematics & Statistic

5.8 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Example 8 : Arithmetic mean of the following frequency distribution is 8.8. Find the missing frequencies :

Wages (`) 4–6 6–8 8–10 10 –12 12–14 Total

No. workers : 6 –– 16 –– 5 50

Solution:

Table : Calculation of Arithmetic Mean

wages (`) x f fx

4–6 5 6 30

6–8 7 f 1 7f 1

8–10 9 16 96

10–12 11 f 2 11f 2

12–14 13 5 65

Total N =27+f 1 +f 2 191+7f 1 +11f 2 = fx

∴ 27 + f 1 + f 2 = 50 or, f 1 + f 2 = 23

x = fx

f

or,

1 2

1 2

8.8 191 7f 11f

27 f f

= + +

+ + ,

8.8 191 7f 11 23 f^1 (^1 )

27 23

= + + −

+

or, 8.8 × 50 = 191 + 253 – 4f 1 or, 4 f 1 = 444 – 440= 4 or, f 1 = 1 i.e. f 2 = 23 –1 = 22

5.1.1.3. Wrong Observation:

After calculating A.M. (x) of n observations if it is detected that one or more observations have been taken

wrongly (or omitted), then corrected calculation of A.M. will be as follows :

Let wrong observations x 1 , y 1 being taken instead of correct values x, y then corrected x = given

x– (x 1 + y 1 ) + (x + y), in this case total no. of observations will be same.

Example 9. The mean of 20 observations is found to be 40. Later on, it was discovered that a marks 53 was

misread as 83. Find the correct marks.

Wrong x= 20 × 40 = 800, Correct x= 800 – 83 + 53 = 770

∴ Correct x=^77020 =38.5

Example 10. A.M. of 5 observations is 6. After calculation it has been noted that observations 4 and 8 have

been taken in place of observations 5 and 9 respectively. Find the correct A.M.

x x

n

=∑ or, 6 x

5

=∑ or, ∑x 30= , corrected ∑x 30= –(4+8) + (5+9) = 32

Corrected A.M. =^325 = 6.4

5.1.1.4. Calculation of A.M. from Cumulative Frequency Distribution

At first we are to change the given cumulative frequency distribution into a general form of frequency

distribution, then to apply the usual formula to compute A.M. the idea will be clear from the following

examples.