Q1. For the set of numbers given: 9, 8, 7, 27, 16, 3, 1, 9, 4 and 16

determine:

(a) the mean(b) the median(c) the mode

(d) the variancefrom the mean and from it calculate the standard deviation.

All calculations must be shown for (a), (b) and (c) and a hand drawn table consisting of manipulated dataelements and calculations to produce the answer for (d).

Q2. A machine produces rods with a nominal diameter of 10 mm. The distribution of a sample of 150 rods is given below. The diameters are correct to 0.01 mm

diameter (mm) 9.76- 9.82- 9.88- 9.94- 10.00- 10.06- 10.12-

9.81 9.87 9.93 9.99 10.05 10.11 10.17

No. of rods 1 22 30 45 34 16 2

(a) Calculate the mean and the standard deviation. You will find it convenient to copy the above results into a table and do your work in a tabular form.

(b) When the machine is functioning correctly the company expects a mean of 10.00 mm and a standard deviation of 0.05 mm. The machine is overhauled when the variability (i.e. the SD) deviates from the norm by 50% or more. What do your results suggest to the company?

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Question 1. Solution.

(a) The mean is

(b) The mode is 9

Since among those 10 numbers, 9 occurs twice. So, the mode is 9.

(c) The median is 8.5

If you put all 10 numbers in order, we have

1, 3, 4,7, 8,9,9,16,16, 27

The …

Standard Deviation, Variance, Mean, Median and Mode are investigated.