Year 7: Week 9 Thursday

The Mean – ProblemsMr J Wooler

j.wooler@bishopchalloner.bham.sch.uk

Problem solving with the mean

Click on the link below to see a video of Mr Wooler going through some examples for this topic.

tinyurl.com/Y7-Week9-Thu

Then complete the questions in the worksheet below.

Reminder – Calculating the Mean

The mean is one type of ‘average’ used in maths.

Often when you hear or read ‘the average number of…’ the value that has been calculated is the mean.

To find the mean,1. Find the total of all your data values2. Divide this total by the number of data points you have

The mean could be a fraction, decimal, or negative number.

Missing values

What if we are told the mean, but we have a value missing?Remember,

𝑀𝑒𝑎𝑛 =𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝒂𝒍𝒍 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠

𝑛𝑜. 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠

So if we are told the mean, and how many data points there are, we can work backwards to find the total.

Once we know what the total should be, we can figure out what the missing value needs to be.

Worked Example Your Turn

5, 1, 10, ? Mean = 6 6, 2, 11, ?Mean = 6

Adding or removing values

What if we are told the mean, but then we add a new piece of data to the group?

𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑀𝑒𝑎𝑛 =𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠

If I add a new data value, the total will now change, and the number of data points will increase.

I must first find the original total, then add my new data value to find the new total.

𝑵𝒆𝒘𝑀𝑒𝑎𝑛 =𝒏𝒆𝒘 𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠𝒏𝒆𝒘 𝑛𝑜. 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠

Worked Example Your Turn

Four values, mean = 65th value of 8 added.New mean = ?

Five values, mean = 66th value of 3 added.New mean = ?

Combined mean

What if I know the mean of two different groups, but then I want to know the mean of everything?

𝐺𝑟𝑜𝑢𝑝 1 𝑀𝑒𝑎𝑛 =𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝒈𝒓𝒐𝒖𝒑 𝟏 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠𝑛𝑜. 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖𝑛 𝑔𝑟𝑜𝑢𝑝 1

𝐺𝑟𝑜𝑢𝑝 2 𝑀𝑒𝑎𝑛 =𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝒈𝒓𝒐𝒖𝒑 2 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠𝑛𝑜. 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖𝑛 𝑔𝑟𝑜𝑢𝑝 2

𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝒂𝒍𝒍 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠 = 𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝒈𝒓𝒐𝒖𝒑 1 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠 + 𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝒈𝒓𝒐𝒖𝒑 2 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠

𝑡𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝒂𝒍𝒍 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠 = 𝑛𝑜. 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖𝑛 𝑔𝑟𝑜𝑢𝑝 1 + 𝑛𝑜. 𝑜𝑓 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖𝑛 𝑔𝑟𝑜𝑢𝑝 2

Using the total of all the data values, and the total number of all data points, we can find the overall mean

𝑶𝒗𝒆𝒓𝒂𝒍𝒍 𝑀𝑒𝑎𝑛 =𝑡𝑜𝑡𝑎𝑙 𝑜𝑓 𝒂𝒍𝒍 𝑑𝑎𝑡𝑎 𝑣𝑎𝑙𝑢𝑒𝑠

𝑡𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝒂𝒍𝒍 𝑑𝑎𝑡𝑎 𝑝𝑜𝑖𝑛𝑡𝑠

Worked Example Your Turn

Group 1, 10 people, mean = 7Group 2, 15 people, mean = 8Overall mean = ?

Group 1, 12 people, mean = 15Group 2, 13 people, mean = 9Overall mean = ?

f)

g)

h)

1)

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3)

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5)

Week 8 – Thursday 11th June

Task due – Thursday 18th June

The Mean – Problem Solving

Section A

(a) Work out the mean. (b) How many students scored above the mean mark?

Section B

The format of our worksheets has changed slightly. Here’s how it works.

Section A – this is for everyone. These are skills-based questions.

Section B – these are harder questions, but everyone should still give them a go.

Section C – these are challenging questions, and are optional for those who want to stretch their understanding.

Click here if you’re stuck to open some

online videos.

Section C

1) Pete has seven Shetland ponies. They have a mean height of 116cm. Pete buys an eighth pony. The height of this pony is 128cm. Find the mean height of all eight ponies.

2) The mean height of seven pupils is 123cm. One pupil of height 147cm leaves the group. Find the mean height of the remaining six pupils

3) There are 12 students in Phil’s Maths group. The mean mark in a test is 76%. In Paul’s group there are only eight students. Their mean mark is 84%. Find the overall mean for the 20 children.

4) Don delivers pint bottles of milk to two streets. For the first street of 10 houses, the mean number of bottles of milk he delivers is 3.1. For the second street of six houses, the mean number of bottles he delivers is 2.5. Find the mean number of bottles of milk he delivers per household for the two streets altogether.

5) Nigel has scored a mean of 18 runs in the last five cricket matches. His mean score must be 20 or more for him to be chosen for the school team. Find the number of runs that he must make in the next match if he is to be chosen for the school team.

Need help?

Send an email to

Mr Wooler (j.wooler@bishopchalloner.bham.sch.uk)

Mr H Sarcevic (h.sarcevic@bishopchalloner.bham.sch.uk)

Or you can tweet us @BCMathsDept