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

Answer:

Option c - 2402

Step-by-step 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)         $x\times f$

2480                     23                 $2480\times 23=57040$  

2440                     35                 $2440\times 35=85400$  

2400                     40                 $2400\times 40=96000$  

2360                     33                 $2360\times 33=77880$  

2320                     21                  $2320\times 21=48720$  

Total                   = 152                                                 =365040

The mean of the data is given by,

$\text{Mean}=\frac{\sum xf}{\sum f}$

$\text{Mean}=\frac{365040}{152}$

$\text{Mean}=2401.578$

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

Therefore, option c is correct.