Application of Number
Level 2
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Mean, Median, Mode and Range Problems - Tutorial 5
So far we have looked at how to work out the mean, median, mode and range. We will now look at some problems.
| Summary |
To find the mean:
add up all of the numbers and then divide by the number of numbers |
To find the median:
put the numbers in order and then find the middle number if the middle is 2 numbers, then find the mean of these two numbers |
To find the mode:
put the numbers in order and then find the most popular number |
To find the range:
find the largest and smallest numbers and then take the smallest away from the largest. |
E.g. 1
Two music shops both sell chart CDs. Below are the prices of the top 10 CDs in each shop.
Shop A - £13.99, £13.99, £13.99, £13.99, £9.99, £13.99, £13.99, £9.99, £13.99, £13.99
Shop B - £13.99, £13.99, £12.99, £12.99, £12.99, £12.99, £12.99, £12.99, £12.99, £12.99
| Mean |
Shop A
Add the numbers -
13.99+13.99+13.99+13.99+9.99+13.99+13.99+9.99+13.99+13.99=131.90
Divide by the number of numbers -
131.90 ÷ 10 = 13.19
Mean is £13.19
Shop B
Add the numbers -
13.99+13.99+12.99+12.99+12.99+12.99+12.99+12.99+12.99+12.99=131.90
Divide by the number of numbers -
131.90 ÷ 10 = 13.19
Mean is £13.19
Both shops have the same mean. So on average the price is the same.
| Range |
Shop A
Largest is £13.99
Smallest is £9.99
Range is £13.99 - £9.99 = £3.00
Shop B
Largest is £13.99
Smallest is £12.99
Range is £13.99 - £12.99 = £1.00
So both shops sell CDs at the same mean price, but the range of Shop A is larger than Shop B. This means that the price is more variable. So you could pay more than the average or a lot less than the average. With Shop B, you will pay roughly the same price each time, because the range is small and so the price doesn't vary much.
Question 1
A survey of Fish and Chip shops took place. Ten bags of chips were bought from each shop. The number of chips in each bag was counted. The results are below. Work out the mean and the range for each shop. Then explain which shop you would go to if they both tasted the same and cost the same.
Fryers Plaice - 46, 50, 54, 48, 52, 40, 60, 50, 58, 42
Batter Fish and Chips - 46, 50, 48, 49, 47, 48, 50, 48, 48, 46
Question 2
The house prices of two different housing estates were surveyed. The results are below. Which estate is the best? Find the mean and the range to help you decide.
Estate A - £80,000, £85,000, £90,000, £87,000, £83,000, £86,000, £84,000
Estate B - £120,000, £130,000, £40,000, £150,000, £50,000, £110,000
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