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Problems Involving the Mean

# Problems Involving the Mean

### Problems Involving the Mean

The mean can change when new values are introduced into a dataset, and we can use algebraic equations to find it.

The mean is likely to be affected when we add more values into a dataset. Forming and solving equations can help us to find values or means in this situation.

There are 9 people in a meeting room, and their heights are listed below.

$161cm, 164cm, 165cm, 167cm, 167cm, 169cm,$

$171cm, 172cm, 174cm$

1

What is the mean to 3 significant figures?

2

Another person joins the meeting

The mean height is now $167cm$. How tall is the 10th person?

3

Form an equation for the sum of all heights

$1510+x$. This is the sum of all heights with the new person included.

4

Form an equation for the mean

We know the new mean is 167, so the formula for the mean is:$\dfrac{1510 + x}{10} = 167$

5

If$\dfrac{1510 + x}{10} = 167$, what is $x$?

6

Nice!

The height of the new person is $160cm$

The temperature in London is recorded on Monday to Saturday, and the temperatures are listed below. The temperature is then recorded on Sunday, and the mean temperature changes to $20\degree C$ for the week.

How can we notate the total of the temperature across the 7 days?

There are 5 people in a room, and their weights are listed below. Another person joins the room, and the mean weight changes to 65kg. How much does this person weigh?

$58kg, 63kg, 64kg, 69kg, 76kg$

1

What is the total of the 5 original weights?

2

We can call the new person's weight $x$

The total of the original weights is $330$. Therefore, we can form an equation involving $x$.

3

How can we express the total weight of the 6 people?

4

The total weight is $330+x$

We can use this fact to form an equation for the mean.

5

What is the equation for the mean?

6

The equation for the mean is $\dfrac{x+330}{6}=65$

By rearranging this equation, we can find the weight of the new person joining the room.

7

If $\dfrac{x+330}{6}=65$, what is the value of $x$?

8

The new person weighs $60kg$

Nice!