MA 1135 Lecture 04 - Intro to Mean and Median
Thursday, January 29, 2015.
Objectives: Define mean and median, and compute using Excel.
Go over homework.
Mean and Median
One of the things we do in statistics is to find a few numbers that represent a large set of numbers, which I’ll
call a data set. The first two of these representative numbers that we’ll discuss are the mean and median.
Mean. The mean of a finite data set is essentially the same as what we typically call an average. We
compute it by adding all the numbers in the data set together, and then dividing by the number of numbers
in the set. For example, consider the following set of numbers.
3, 6, 9, 3, 10, 4, 5, 1, 1
There are 9 numbers in this data set, so the mean is
(1)
mean =
3 + 6 + 9 + 3 + 10 + 4 + 5 + 1 + 1
42
=
= 4.6666 . . . = 4.67
9
9
You can round to two decimal places in this class, unless I tell you otherwise.
Median. The median is the middle number in the data set. You can find it by sorting the data set from
smallest to largest, and then choosing the middle number. If there are two middle numbers, then the median
is halfway between the two middle numbers. For example, ordering the data set above yields
1, 1, 3, 3, 4, 5, 6, 9, 10
The middle number is the 4, so that’s the median. We generally expect that the mean and median will be
approximately the same, but that’s not always true.
Using Excel to compute means. Computing means and medians is pretty easy using a spreadsheet. I’ve
put our data set in a spreadsheet as shown below, and started the calculation by using B11: =SUM(B2:B10).
I highlighted the data set in yellow with the button with the picture of a paint can in the menu bar. Doing
something like this can help organize your spreadsheet.
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MA 1135 Lecture 04 - Intro to Mean and Median
From here, you can compute the mean by dividing by 9. Use either
B12: =B11/9
or all in one step, like
B12: =SUM(B2:B10)/9
There’s an Excel function that does this also
B12: =AVERAGE(B2:B10)
Using Excel to compute medians. I’ve copied the data set to Column E.
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MA 1135 Lecture 04 - Intro to Mean and Median
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One way of finding the median is to sort the data set, so the numbers are in ascending order. To do this,
highlight the cells in the data set, and click on the button circled. I’ve also circled the median.
Another way is to use
B13: =MEDIAN(B2:B10)
which finds the median for you.
MA 1135 Lecture 04 - Intro to Mean and Median
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Homework 04
1.
Play with the data set in the last spreadsheet (that is, change the numbers in the data set) to do the
following. Write down the numbers that you ended up with. There are lots of different answers.
a.
Make the mean and median equal to each other.
b.
Make the mean twice as large as the median.
c.
Make the mean equal to 0.
d.
Make the mean equal to 100.
2.
Find the mean and median for the three data sets in the spreadsheet below.
3.
Find a data set that has a median of 5 and mean of 50. List out the numbers in the data set.
MA 1135 Lecture 04 - Intro to Mean and Median
4.
Can the mean be larger than the largest number in a data set?
5.
Can the mean be equal to the largest number in the data set?
Answers on next page.
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MA 1135 Lecture 04 - Intro to Mean and Median
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HW
1a) Any set that is symmetric about the mean will do this. You could pick any number, like 20, to be the
mean. Then pick the other numbers in pairs like 17 and 23 which are 3 bigger and smaller than 20.
b) Start with any set. By changing the largest number, you can change the mean, but the median will stay
the same. Choose a really big number for the largest number and play with that.
c) You’ll need negative numbers to offset your positive numbers. Make sure everything adds up to zero.
d) You can take your numbers from Part c, and then add 100 to every number.
2) 3, 0, and −5.5
3) There are lots of answers. One easy example { 1, 5, 144 }.
4) No. The mean will always be between the largest and smallest numbers (unless all the numbers are the
same, in which case, the smallest number, the largest number, and the mean will all be equal).
5) Only if all the numbers are the same.