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Standard Deviation, Variance, Mean, Median and Mode : Statistics Application Problem

Q1. For the set of numbers given: 9, 8, 7, 27, 16, 3, 1, 9, 4 and 16
(a) the mean (b) the median (c) the mode
(d) the variance from 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 data elements 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 ...

Solution Summary

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