Question

3.2 Samples of aluminum-alloy channels were tested for stiffness. The following frequency distribution was obtained. The distribution is assumed to be normal Stiffness Frequency 2480 2440 35 2400 2360 33 2320 21 What is the approximate mean of the population from which the samples were taken? (a) 2367 (b) 2398 (c) 2402 (d) 2419

Answer 1

Option c - 2402

Explanation:

Given : Samples of aluminum-alloy channels were tested for stiffness. The following frequency distribution was obtained.

To find : What is the approximate mean of the population from which the samples were taken?

Solution :

The distribution is assumed to be normal as

Stiffness(x) Frequency(f)
`x* f`

2480 23
`2480* 23=57040`

2440 35
`2440* 35=85400`

2400 40
`2400* 40=96000`

2360 33
`2360* 33=77880`

2320 21
`2320* 21=48720`

Total = 152 =365040

The mean of the data is given by,

`\text{Mean}=(\sum xf)/(\sum f)`

`\text{Mean}=(365040)/(152)`

`\text{Mean}=2401.578`

Approximately, the approximate mean of the population from which the samples were taken is 2402.

Therefore, option c is correct.