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Answer the following : There are two companies U and V which manufacture cars. A sample of 40 cars each from these companies are taken and the average running life (in years) is recorded Life (in yea - Mathematics and Statistics

Sum

Answer the following :

There are two companies U and V which manufacture cars. A sample of 40 cars each from these companies are taken and the average running life (in years) is recorded

Life (in years) No of Cars
Company U Company V
0 - 5 5 14
5 - 10 18 8
10 - 15 17 18

Which company shows greater consistency?

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Solution

We construct the following table to compute C.V.:

For both companies, U and V, the mid-values of the class-intervals are 2.5, 7.5, 12.5

Company U
xi fi

ui = `(x_"i" - "A")/"h"`

A = 7.5,
h = 5

fiui fiui2 = fiui × ui
2.5 5 – 1 – 5 5
7.5 18 0 0 0
12.5 17 1 17 17
  `sumf_"i"` = 40   `sumf_"i"u_"i"` = 12 `sumf_"i"u_"i"^2` = 22

Company U

`bar(u) = (sumf_"i"u_"i")/(sumf_"i") = 12/40` = 0.3

∴ `bar(x) = "A" + "h"bar(u)`

= 7.5 + 5 × 0.3 = 9

`sigma_u^2 = (sumf_"i"u_"i"^2)/(sumf_"i") - (baru)^2`

= `22/40 - (0.3)^2`

= 0.55 – 0.09 = 0.46

∴ `sigma_u = sqrt(0.46)` = 0.678

∴ `sigma_x = "h"sigma_u`  = 5 × 0.678 = 3.39

C.V. = `sigma_x/bar(x) xx 100`

= `(3.39)/9 xx 100`

= 37.67

Company V
xi fi

ui = `(x_"i" - "A")/"h"`

A = 7.5,
h = 5

fiui fiui2 = fiui × ui
2.5 14 – 1 – 14 14
7.5 8 0 0 0
12.5 18 1 18 18
  `sumf_"i"` = 40   `sumf_"i"u_"i"` = 4 `sumf_"i"u_"i"^2` = 32

Company V

`bar(u) = (sumf_"i"u_"i")/(sumf_"i") = 4/40` = 0.1

∴ `bar(x) = "A" + "h"bar(u)`

= 7.5 + 5 × 0.1 = 8

`sigma_u^2 = (sumf_"i"u_"i"^2)/(sumf_"i") - (baru)^2`

= `32/40 - (0.1)^2`

= 0.8 – 0.01 = 0.79

∴ `sigma_u = sqrt(0.79)` = 0.889

∴ `sigma_x = "h"sigma_u`  = 5 × 0.889 = 4.445

C.V. = `sigma_x/bar(x) xx 100`

= `(4.445)/8 xx 100`

= 55.56

Since `("C.V")_("company U")<("C.V.")_("company V")`

company U shows greater consistency in performance.

Concept: Coefficient of Variation
  Is there an error in this question or solution?
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 8 Measures of Dispersion
Miscellaneous Exercise 8 | Q II. (21) | Page 192
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