Question

Each person who applies for an assembly job at Robert’s Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. Length of Time (in minutes)Number1 up to 444 up to 787 up to 101410 up to 13913 up to 16516 up to 192 What is the standard deviation (in minutes)?

Answer 1

The value of standard deviation is 3.894 minutes.

Explanation:

Consider the provided table:

Complete the table as shown:

Length of time f class mid pt(x) f·x x² f·x²

1-4 4 2.5 10 6.25 25

4-7 8 5.5 44 30.25 242

7-10 14 8.5 119 72.25 1011.5

10-13 9 11.5 103.5 132.25 1190.25

13-16 5 14.5 72.5 210.25 1051.25

16-19 2 17.5 35 306.25 612.5

n=42 ∑f·x=384 ∑f·x²=4132.5

Now use the formula to calculate standard deviation.

`s=\sqrt{(n[\sum(f\cdot x^2)]-[\sum(f\cdot x)]^2)/(n(n-1))}`

Substitute the respective values in the above formula and solve for s.

`s=\sqrt{(42(4132.5)-(384)^2)/(42(41))}`

`s=\sqrt{(173565-147456)/(1722)}\\s=\sqrt{(26109)/(1722)}\\s=√(15.16)\\s\approx3.894`

Hence, the value of standard deviation is 3.894 minutes.