Posted by **mary** on Friday, April 27, 2007 at 3:26am.

the following data represents the percentages of family income allocated to groceries for a sample of 50 shoppers:

percentage of family income #of shoppers

10-19 6

20-29 14

30-39 16

40-49 11

50-59 3

1.calculate the value of mean

1.1 meadian percentage of family income spent on groceries

1.12 determine the standard deviation and comment on the spread

If you are expected to do this by hand, start by calculating the mean. (The median is the "middle" of the distribution.) For grouped data, the mean can be calculated using the following formula:

mean = (Efx)/n

...where n represents the total frequencies (50 in this case), x represents the midpoint of each class interval (which is found by adding the lowest and the highest number in the interval together and dividing by 2), and E represents the sum of each midpoint times each frequency f. It might be helpful to set up a table of midpoints for each interval, then multiply each midpoint by its respective frequency (number in each interval), then add those numbers to get a total. Then divide the total by n.

Standard deviation is the square root of the variance. For grouped data, the variance can be calculated using the following formula:

variance = Ef(x - mean)^2/(n-1)

...where E represents sum of frequency f times (x-mean)^2, and n = 50. (x represents the midpoint of each class interval.)

Again it might be helpful to set up tables with the following headings:

x - mean ...... (x - mean)^2 ..... f(x - mean)^2

Add up the last column for a total, then divide by 49 (which is n-1 or 50-1 = 49). When you are finished calculating the variance, take the square root of the variance and you will have your standard deviation for this group of data.

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Hope this will help get you started on these problems,

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