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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:

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 learened

Short cut Method for A.M -

Let

 u_{i}= \frac{x_{i}-A}{h}

\bar{x}= A+\frac{h\sum f_{i}u_{i}}{\sum f_{i}}

- wherein

Where A is assumed mean h is width of class interval

 

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


The width of the class interval is h = 3.

                        Let the shift (assumed mean) be a = 50.

                        Using di = \frac{x_i-a}{h}, we construct the following frequency distribution:

 

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

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