 A box of paperclips says 'average contents 100'. But how many are really in there?

# Handling Data 2 (Difficult)

Welcome to this, our second difficult quiz on handling data. If you played the first one, you’ll be familiar with four things associated with data handling: the range, the mean, the mode and the median. These four ideas are used to work out averages.

The range of a set of data is the difference between its highest and lowest values. The mean is worked out by adding all the values together, then dividing by the number of values. The mode is the value which appears most often. Finally, the median is the middle value of the data, if it is arranged from lowest to highest.

As you can see, there are several ways to work out the average value in a set of data. This means that, depending on the method you use, your results might be very different!

So, now we know all about averages, it’s time to put your knowledge to the test. Good luck!

1.
Which of the following statements is correct?
The median is the value which appears most often
The mode is the middle value if the data is arranged from smallest to largest
The median is the middle value if the data is arranged from smallest to largest
The mode might not appear in the set of data
Median sounds a bit like medium - that's one way to remember that the median is the medium, or middle, value
2.
Sarah counted the number of vehicles which passed her school over the course of one hour. She did this every day for a week and got these results: 180, 164, 212, 197, 207, 222, 146.
What is the mean of the given data?
1,328
197
189.7
Impossible to work out
Mean = (the sum of the data values) ÷ the number of data values. The sum of the data values = 180 + 164 + 212 + 197 + 207 + 222 + 146 = 1,328. The number of data values = 7 ∴ mean = 1,328 ÷ 7 = 189.7 (1 decimal place)
3.
From the following set of data, which average is highest: the mean, the median or the mode?
75, 48, 82, 65, 70, 68, 75.
The mean
The median
The mode
They are all the same
The mean is worked out by adding all the values and dividing the result by 7: 75 + 48 + 82 + 65 + 70 + 68 + 75 = 483. 483 ÷ 7 = 69.
The median is 70 as this is the middle value if arranged from lowest to highest.
The mode is 75, as this appears most often. This is higher than 70 and 69.
4.
Steven asked some of his classmates how many brothers or sisters they had. Here’s his results: 2, 3, 0, 0, 1, 0, 2, 0, 1, 3, 5, 0, 1, 2, 0.
How many of Steven’s classmates took part in the survey?
14
15
16
20
You have 15 data values: each value corresponds to one person. DON'T make the mistake of calling the sum of the data values the number of people: it is NOT 20
5.
From the following set of data, which average is lowest: the mean, the median or the mode?
18, 21, 22, 19, 20, 21, 21.
The mean
The median
The mode
They are all the same
The mode is 21, as this appears most often. The median is also 21, as the middle value is 21 if arranged from lowest to highest. The mean is worked out by adding all the values and dividing the result by 7: 18 + 21 + 22 + 19 + 20 + 21 + 21 = 142. 142 ÷ 7 = 20.3 (to one decimal place), which is the lowest.
6.
A poll was taken, asking 8 people how many pets they had. Here are the results: 0, 7, 3, 1, 0, 2, 0, 1.
What is the range of the given data?
8
0
7
6
Range = highest value - lowest value = 7 - 0 = 7
7.
Michael asked 10 of his friends how many times they had been to watch a live football match. Here are his results: 40, 27, 18, 36, 0, 7, 16, 0, 2, 12.
What is the mode of the given data?
14
15.8
12
0
The mode is the data value that occurs most often: there are two zeros so that is the mode.
8.
Charlotte wanted to find out the average height of her friends. She collected these results: 143 cm, 139 cm, 145 cm, 149 cm, 144 cm.
The mean of these results was 144 cm. She then measured one more friend, Clare, and the mean rose to 145 cm. How tall was Clare?
150 cm
148 cm
151 cm
145 cm
Originally there were five pieces of data, with a mean of 144: 144 x 5 = 720.
Adding one extra piece of data means that there are now six of them. 6 x 145 = 870.
To find Clare's height just subtract 720 from 870: 870 - 720 = 150. Clare is 150 cm tall.
9.
Which of the following statements is false?
The mode is always one of the values in a set of data
The mode always appears more than any other value
The median always appears in the set of data
The mean always includes a fraction or a decimal
The mean can SOMETIMES include a fration or a decimal (the mean of 2 and 3 is 2.5 for example), but not always (the mean of 1 and 3 is 2).
10.
Jane wanted to know how old the men in her family were when they began shaving. She asked 9 of them and got these results: 15, 16, 17, 18, 16, 15, 17, 19, 20.
What is the median of the given data?
18
16
17
18
The median is the middle value of the data: you have to arrange the data in order BEFORE you can find it: 15, 15, 16, 16, 17, 17, 18, 19, 20.. You have nine values, so the median is the 5th value = 17. It is usually best to arrange the data in ascending order.
Author:  Frank Evans