# Transcript: Calculating ticket sales mean quiz

Remember, in order to find the mean, Hayden and Bo have determined the middle value of each range to help them calculate the weighted average.

Their new table shows that:

The middle value for the 11 to 15 age range is 13.

The middle value for the 16 to 20 age range is 18.

The middle value for the 21 to 25 age range is 23.

The middle value for the 26 to 30 age range is 33.

The middle value for the 31 to 35 age range is 38.

The middle value for the 36 to 40 age range is 43.

The middle value for the 41 to 45 age range is 43.

The middle value for the 46 to 50 age range is 48.

The middle value for the 51 to 55 age range is 53.

The middle value for the over 55 age range is 58.

We know Bo has begun calculating the weighted average for the first two age ranges. He adds a fourth column to the table to represent this data. In the first row of the fourth column, it shows that the weighted value of the 11 to 15 age range is 4498, which Bo got by multiplying the middle value (13) by the number of tickets sold (346). In the second row, it shows that the weighted value of the 16 to 20 age group is 7020 (18 times 390).

## Question 1:

Knowing that the weighted average can be found by multiplying the middle value of the age range by the number of tickets sold to that age range, help Bo and Hayden complete the table.

Part 1: What is the weighted value of the 21 to 25 age range, if the middle value is 23 and the number of tickets sold is 219?

Part 2: What is the weighted value of the 26 to 30 age range, if the middle value is 28 and the number of tickets sold is 240?

Part 3: What is the weighted value of the 31 to 35 age range, if the middle value is 33 and the number of tickets sold is 119?

Part 4: What is the weighted value of the 36 to 40 age range, if the middle value is 38 and the number of tickets sold is 129?

Part 5: What is the weighted value of the 41 to 45 age range, if the middle value is 43 and the number of tickets sold is 22?

Part 6: What is the weighted value of the 46 to 50 age range, if the middle value is 48 and the number of tickets sold is 42?

Part 7: What is the weighted value of the 51 to 55 age range, if the middle value is 53 and the number of tickets sold is 24?

Part 8: What is the weighted value of the over 55 age range, if the middle value is 58 and the number of tickets sold is 31?

Part 9: Once you have worked out all of the individual weighted values, add them together to determine what the total is.

## Question 2:

Which age range represents an estimate of the **mean** ticket sales so far?

a) 16 to 20;

b) 21 to 25;

c) 26 to 30 or;

d) 31 to 35.

### Hint:

To find the mean, divide the total of the weighted value column by the total number of tickets sold.

## Answers:

**Question 1:**

Part 1 – The weighted value is 5037.

Part 2 – The weighted value is 6720.

Part 3 – The weighted value is 3927.

Part 4 – The weighted value is 4902.

Part 5 – The weighted value is 946.

Part 6 – The weighted value is 2016.

Part 7 – The weighted value is 1272.

Part 8 – The weighted value is 1798.

Part 9 – The sum total of weighted values is 38,136.

**Question 2:**

b) 21 to 25.