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) Number 1 up to 4 4 4 up to 7 8 7 up to 10 14 10 up to 13 9 13 up to 16 5 16 up to 19 2 What is the standard deviation (in minutes)? 17.00 6.01 3.89 8.78

Answer 1

3.89 minutes

Explanation:

Firstly, we have this in a table using the range

There are 6 ranges

We put the frequency alongside

Afterwards we calculate the midpoint of the range

For example, midpoint of range 1-4 is (1+4)/2 = 5/2 = 2.5

We multiply the midpoint by the frequency which gives another column

Then we calculate the mean, where the mean is the summation of all frequencies and their midpoints

We subtract each midpoint from the mean, square the results, then multiply each by their frequency

Lastly, we apply the standard deviation formula

Please check attachment for the tabular representation and formulas