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A factory manufactures nuts and bolts of various sizes. The measurement of inner diameters of 1000 nuts gave the following frequency table:

Diameter (mm) 43-45 46-48 49-51 52-54 55-57
No. of Nuts 175 236 200 196 193

Determine the mean inner diameter per nut.

Option: 1

48


Option: 2

50


Option: 3

52


Option: 4

54


Answers (1)

best_answer

As we have learnt @3143 

The given table is in inclusive form of frequency distribution. We first convert it into an

exclusive form and write it in the form

Diameter (in mm) 42.5-45.5 45.5-48.5 48.5-51.5 51.5-54.5 54.5-57.5
No. of Nuts 175 236 200 196 193

the width of the class intervel is h = 3

Let the Shift (Assumed mean) be  a = 50

using \:\:d_i=\frac{x_i-a}{h},\:\;\:we\:\: construct \:\:the \:\:following \:\:frequency \:\:distribution:

Diameter (mm) mid \:value (x_i) frequency(f_i) d_i=\frac{x_i-50}{h} f_id_i

42.5-45.5

45.5-48.5

48.5-51.5

51.5-54.5

54.5-57.5

 

44

47

50

53

56

 

175

236

200

196

193

\sum f_i=1000

-2

-1

0

1

2

 

-350

-236

0

196

286

\sum f_id_i=-4

Thus the mean inner diameter is

mean =a+ \frac{\sum f_id_i}{\sum f_i}h=50-\frac{(4)(3)}{1000}=49.998mm=50mm\:approx

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Anam Khan

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