Paper 4: Fundamentals of Business Mathematics & Statistic

5.50 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Measures of Central Tendency and Measures of Dispersion

Calculate also M.D. about median and hence find coefficient of mean dispersion.

Solution :

Table : Computation of M.D. about A.M.

Wages Mid-value

d x 8.50

2

′= −

fd ́ | d |

(`) x f = x x− f | d |

3.50–5.50 4.50 6 –2 –12 3.68 22.08

5.50–7.50 6.50 14 –1 –14 1.68 23.52

7.50–9.50 8.50 16 0 0 0.32 5.12

9.50–11.50 10.50 10 1 10 2.32 23.20

11.50–13.50 12.50 4 2 8 4.32 17.28

Total – 50 – –8 – 91.20

( ) ( )

x A.M. A fd i 8.50^82

f 50

′ −

= +∑ × = + ×

∑ = 8.50 – 0.32 = 8.18

M.D.

f|d| 91.20

f 50

=∑ =

∑ = 1.824 = ` 1.82

Table : Calculation of M.D. about median

Wages f c.f. mid-value | d | f | d |

(`)

3.50–5.50 6 6 4.50 3.63 21.78

5.50–7.50 14 20 6.50 1.63 22.82

7.50–9.50 16 36 8.50 0.37 5.92

9.50–11.50 10 46 10.50 2.37 23.70

11.50–13.50 4 50 (N) 12.50 4.37 17.48

Total 50 – – – 91.70

Median = value of N/2th item = value of 50/2, i.e., 25^ th item.

So median class is (7.50 – 9.50)

∴ Median 1 211 ( ) ( )

= l +l - l m - c = 7.50 +9.50 - 7.50 25 - 20

f 16

7.50^25

= + 16 × = 7.50 + 0.625 = 8.125 = ` 8.13