1. Mean
2. Median
3. Mode
Briefly explain why the mean is not a suitable average to use in order to analyse the way people voted in the last general election.
Political parties/politicians have names and so the data is non-numerical
Suggest a better measure of average that can be used.
The mode average can be used for non-numerical data
15 students were timed how long it took them to solve a maths problem. Their times, in seconds, are given below.
12 | 10 | 15 | 14 | 17 |
11 | 12 | 13 | 9 | 21 |
14 | 20 | 19 | 16 | 23 |
Find the mean and median times.
There are a fair amount of numbers so it may be wise to do the adding up in bits - we've used rows.
12 + 10 + 15 + 14 + 17 = 68
11 + 12 + 13 + 9 + 21 = 66
14 + 20 + 19 + 16 + 23 = 92
For the median, the data needs to be in order first.
Mean = 15.1 seconds (3 s.f.)
Median time = 14 seconds
Comment on the mode of the data.
The mode (or lack of) is easiest to see from the data listed in order in the median question above.
There are two modes (bi-modal) - 12 and 14 seconds
Alternatively we could say there is no mode.
A class of 24 students have a mean height of 1.56 metres.
Two new students join the class and the mean height of the class increases to 1.58 metres.
Given that the two new students are of equal height, find their height.
Start by writing down what we do know.
No. of students originally in the class; n _{1}
= 24
Mean of the original 24 students; m _{1}
= 1.56
No. after new students; n _{2}
= 24 + 2 = 26
Mean after new students; m _{2}
= 1.58
And now write down what we don't know (but need to know to answer the question).
Height of the two new students (both equal); h metres
Total of all heights before new students; T _{1
}
Total of all heights after new students; T
_{
2
}
= T _{1}
+ h + h = T _{1}
+ 2 h
Considering the formula for the mean, and the values before the new students joined, we can work out T _{1 } .
Using the mean 'formula' for the overall mean we can set up, then solve, an equation for h.
Both new students have a height of 1.82 metres