How do find the median of this?

X Frequency cumulative fr.
1 3 3
2 8 11
3 5 16
4 3 19
5 1 20
#Ef#=20

1 Answer
smendyka
Feb 21, 2018

See a solution process below:

Explanation:

To find the median:

1) Put all the numbers in numerical order.

The numbers are already in numerical order 1 through 5 and there are 20 observations.

2) If there is an odd number of results, the median is the middle number.

There are an even number of results so we can skipped this step.

3) If there is an even number of results, the median will be the mean of the two central numbers.

There are an even number of results, 20 to be specific. The two central numbers then would be the 10th and 11th number which are both 2. Therefore the median is #2#.

We can show this by writing out the numbers based on the frequency of each #X#:

1 #1#
2 #1#
3 #1#
4 #2#
5 #2#
6 #2#
7 #2#
8 #2#
9 #2#
10 #"color(red)(2)#
11 #color(red)(2)#
12 #3#
13 #3#
14 #3#
15 #3#
16 #3#
17 #4#
18 #4#
19 #4#
20 #5#

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