What is the Calculation for Mean and Standard Deviation with Grouped Data?

[pinkpolkadots]

Homework Statement

For this set of data find the mean and standard deviation

Temp...# of days
90-94...1
85-89...3
80-84...6
75-79...12
70-74...7
65-69...1


2. The attempt at a solution

I don't know how to find the mean or standard deviation when the data is divided into ranges like this.
Can this be solved on the calculator?
Any help is appreciated.

 

[HallsofIvy]

That depends on what you mean by "solved on the calculator". Many calculators now have built in functions to find means and standard deviations of lists of numbers, but I don't know any that have functions for means and standard deviations of grouped data.

One problem is that "70- 74... 7" could mean all 7 numbers are 70 or all 74 or spread between 70 and 74. You've lost data by grouping like that so can't get an exact value. One thing you could do is take a midpoint: assume all data in "70- 74" is actually 72. Do that for each group and enter all 30 numbers as a list. Then use the calculator function on that list.

Here's how you would do it "by hand". To find the mean enter the mid-number times the number of data points in that group: 92(1)+ 87(3)+82(6)+ 77(12)+ 72(7)+67(1) and divide that sum by 30. To find the standard deviation, multiply the square of each mid-number by the number of data points.

 

[pinkpolkadots]

Thanks!