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

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

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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 provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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