Paper 4: Fundamentals of Business Mathematics & Statistic

5.48 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Steps of find M.D.

(i) Find weighed A.M. or median.

(ii) Find deviations ignoring ± signs. i.e., | d |

(iii) Get ∑f|d|;

(iv) Divide ∑f|d|by∑f

About Mean

Example 46 : To calculate mean deviation of the following series :

x (marks) f (student)

5 6

10 7

15 8

20 11

25 8

Total 40

Find also the coefficient of dispersion.

Solution :

Table : Computation of Mean Deviation (About Mean)

Marks Deviation

From from actual

Mean (16)

X f (d= x – 15) d′ = d/5 fd′ x x− f x x−

(1) (2) (3) (4) (5) = 2 × (4) (6) (7) = (2) × (6)

5 6 –10 –2 –12 11 66

10 7 –5 –1 –7 6 42

15 8 0 0 0 1 8

20 11 5 1 11 4 44

25 8 10 2 16 9 72

Total 40 – – 8 – 232

A.M.

A fd i 15^8 5 15 1 16

f 40

= +∑ ′× = + × = + =

∑ marks

M.D.

f x x 232

f 40 5.8

−

=∑ = =

∑ marks.

Coefficient of dispersion (about mean) =MeanM.D. =5.8 16 =0.363