Statistics of Grouped Data
Date: 09/12/1999 at 23:47:06 From: Tony McCabe Subject: Statistics of Grouped Data I am preparing to take a statistics course after many years of being able to avoid doing stats. I am doing some preparatory work before the course starts. Can you please give me answers to the following questions? Grouped Data Income (*$1000) Midpoint(x) Number of Purchasers --------------- ----------- -------------------- 20 - 29.99 25 50 30 - 39.99 20 40 - 49.99 31 50 - 59.99 39 60 - 69.99 35 70 - 79.99 30 80 - 89.99 25 90 - 99.99 18 The above table is data from a survey of recent purchasers of superannuation plans. 1. Find the mean and standard deviation of the income of people purchasing superannuation plans. Find the mean Find the variance Find the standard deviation 2. Find the median class. 3. Choose a suitable graph and display the frequency distribution. 4. Summarize the findings.
Date: 09/13/1999 at 12:31:03 From: Doctor Mitteldorf Subject: Re: Statistics of Grouped Data Dear Tony, To start: find the mean of the distribution as follows. First, find the total number of buyers. Do this by adding up the column with the numbers from each income category. Second, find the total of all their incomes. This you can do approximately, since you have an estimate of the incomes of the people in the group. On each line, multiply the midpoint income times the number of people in the group. Add up the products. This should give a reasonable estimate of the total income. Divide total income by total buyers to give the mean income. To find the variance, you should create another column in which you are squaring the midpoint incomes before multiplying by the number of people. Add up those numbers, and divide, as before, by the total number of people to obtain the <mean squared income>. This is not the same as from the <mean income> squared - that quantity is just the number you calculated at first, multiplied by itself. In fact: you can subtract the <mean income> squared from the <mean squared income> to give the variance of the income distribution. The standard deviation is the square root of the variance. I hope that gives you a start. Dive in, try it, and report back what you think you understand. Explain as much as you feel comfortable with, and a little more. We'll try to help with a "mid-course correction" if you're not getting the ideas 100%. - Doctor Mitteldorf, The Math Forum http://mathforum.org/dr.math/
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