Probability & Statistics

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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.

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

$171cm, 172cm, 174cm$

What is the mean to 3 significant figures?

Another person joins the meeting

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

Form an equation for the sum of all heights

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

Form an equation for the mean

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

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

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?

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

What is the total of the 5 original weights?

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

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

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

The total weight is $330+x$

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

What is the equation for the mean?

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.

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

The new person weighs $60kg$

Nice!