# Find the Median

In this worksheet, students find the median from a small data set.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics, Analysing Data

Difficulty level:

### QUESTION 1 of 10

When you have a whole load of information, it can be quite difficult to deal with.

For example, If I asked whether Boys were taller than Girls, you would have to do something to the data to be able to answer the question.

To do this we take averages.

What is an average?

An average is just one piece of information that represents all the other information in a data set.

What are the averages?

There are three averages. Mean, Median and Mode.

Each one has advantages and disadvantages, in this worksheet we are going to look at finding the median

How do we find the mean?

To find the mean, we put all the data in order and find out what is in the middle.

Example 1: Find the median of 2,3,5,6,1,2,3,4,5,4,6

Step 1: Put all the data in order

1,2,2,3,3,4,4,5,5,6,6

Step 2: Find the number in the middle

To do this, the easiest way is to cross of one from each end until we get to the middle.

1,2,2,3,3,4,4,5,5,6,6

This means the median is 4

Example 2: Find the median of 51,28,42,31,43,57

Step 1: Put all the data in order

28,31,42,43,51,57

Step 2: Find the number in the middle

If we do what we did before, we don't get a number in the middle, we get two!

28,31,42,43,51,57

If this happens, we find out the number half way between these two numbers in the middle/

Our median here is 42.5

The median is the number in...

Find the median for 7,6,2,3,1,9,5,4,8

Which of these two numbers is the median for the data set...

4,12,7,6,10,5,11,8,14,3,2,9

8

7.5

Which number is in the median for 10,6,0,5,7,13,11,14

7

10

8.5

The median for 7,4,3,8,2,6,5,2,9,8,3 is 6.

Use this to find the median for 17,14,13,18,12,16,15,12,19,18,13

The median for 7,4,3,8,2,6,5,2,9,8,3 is 6.

Use this to find the median for 14,8,6,16,4,12,10,4,18,16,6

If I want to increase the median of 3,4,5,6 and 7, I have to add a number that is ....

The median of 1,2,4,6,8,7,9,5,4,11 is 5

Use this to match the data sets with their medians

## Column B

0.2, 1, 2, 3, 4, 3.5, 4.5, 2.5, 2, 5.5
10
2,4,8,12,16,14,18,10,8,22
2
11,12,14,16,18,17,19,15,14,21
15
-2,-1,1,3,5,4,6,2,1,8
2.5

5 walkers in a group are 38,28,30,42 and 37.

What is their median age?

5 walkers in a group are 38,28,30,42 and 37.

If a new member who is 37 joins, what happens to the median?

It increases

It decreases

It stays the same

• Question 1

The median is the number in...

EDDIE SAYS
Think about the words - median sounds like middle. It's vital to remember that these need to be in order. It doesn't matter if it is ascending or descending as the middle will be the same. (most people order ascending as it's easier.)
• Question 2

Find the median for 7,6,2,3,1,9,5,4,8

5
EDDIE SAYS
If we put them in order, we get 1,2,3,4,5,6,7,8,9. Remember to cross them out from each end until you get to the middle
• Question 3

Which of these two numbers is the median for the data set...

4,12,7,6,10,5,11,8,14,3,2,9

7.5
EDDIE SAYS
The common error most people have when doing this question is forgetting to order the numbers. If we order them, we get 2,3,4,5,6,7,8,9,10,11,12,14 Crossing one of from each side gives 7 and 8 in the middle. Can you remember how to get the median from this?
• Question 4

Which number is in the median for 10,6,0,5,7,13,11,14

8.5
EDDIE SAYS
This one's a little bit different again. If we sort them and cross off, we get 7 and 10 in the middle. The easiest way to find what's half-way is to add them together and half the number.
• Question 5

The median for 7,4,3,8,2,6,5,2,9,8,3 is 6.

Use this to find the median for 17,14,13,18,12,16,15,12,19,18,13

EDDIE SAYS
Did you notice all the numbers had just gone up by 10? What will this do to the median?
• Question 6

The median for 7,4,3,8,2,6,5,2,9,8,3 is 6.

Use this to find the median for 14,8,6,16,4,12,10,4,18,16,6

12
EDDIE SAYS
All I've done here is double all the numbers. What will this do to the order? What does that mean for the middle number?
• Question 7

If I want to increase the median of 3,4,5,6 and 7, I have to add a number that is ....

EDDIE SAYS
If I want the median to be higher, I have to shift the median to the right of the list. The only way I can do this is if I add numbers too the right hand side of the list.
• Question 8

The median of 1,2,4,6,8,7,9,5,4,11 is 5

Use this to match the data sets with their medians

## Column B

0.2, 1, 2, 3, 4, 3.5, 4.5, 2.5, 2...
2.5
2,4,8,12,16,14,18,10,8,22
10
11,12,14,16,18,17,19,15,14,21
15
-2,-1,1,3,5,4,6,2,1,8
2
EDDIE SAYS
Remember with these, you need to spot the links between these and the original data set Hint: One of them is doubled, one is halved, one has something added and one has something subtracted.
• Question 9

5 walkers in a group are 38,28,30,42 and 37.

What is their median age?

37
EDDIE SAYS
Just because it\'s a worded question, we don\'t do it any different. We still order them and find the middle value.
• Question 10

5 walkers in a group are 38,28,30,42 and 37.

If a new member who is 37 joins, what happens to the median?

It stays the same
EDDIE SAYS
The original median is 37 (we found that out in Q9) If we put the new member in, we have two numbers in the middle (37 and 37). What\'s halfway between 37 and 37? It\'s still 37
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