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This quiz is all about cycling to school!

Handling Data (Difficult)

In this 11-plus Maths quiz you are going to look at four important ideas: the range, the mean, the mode and the median. These numerical values will help you interpret data: especially when you have only numerical data.

Christine and some of her friends journey to school on their bicycles. You will only be given a set of numbers to work with. From these numbers, you must find numerical values. In order to get good marks in this quiz, you will need to know the meanings of the mathematical terms mentioned above. If you are not sure, or want to refresh your memory, go and get a dictionary right now and jot down the meanings. This will help you to understand what is required of you - and hopefully to get 10 out of 10!

Enjoy yourself!

1 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
What is the range of the given data?

Range = highest value - lowest value = 10 - 2 = 8

2 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
What is the mean of the given data?

6.4

Mean = (the sum of the data values) ÷ the number of data values. The sum of the data values = 9 + 2 + 4 + 5 + 6 + 9 + 10 = 45. The number of data values = 7 ∴ mean = 45 ÷ 7 = 6.429 = 6.4 (1 decimal place)

3 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
What is the mode of the given data?

odd

even

The mode is the data value that occurs most often: there are two nines

4 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
What is the median of the given data?

The median is the middle value of the data: you have to arrange the data in order BEFORE you can find it: 2, 4, 5, 6, 9, 9, 10. You have seven values, so the median is the 4^th value = 6. It is usually best to arrange the data in ascending order. DON'T make the mistake of giving the median the value of its position: in this case 4 because it is the 4^th value

5 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
How many of Christine's friends took part in the survey?

You have seven 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 45

6 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
Christine decided to include one more friend in her survey. If that friend hadn't cycled to school in the last month, how would that affect the latest month's value of the 'mean'?

It would lower the value of the 'mean'

It wouldn't affect the value of the 'mean' because the number of times she has cycled to school = 0

There isn't enough information to answer this question

It would increase the value of the 'mean'

Just because something is zero, it doesn't mean that it isn't important. Mean = (the sum of the data values) ÷ the number of data values. The sum of the data values = 0 + 9 + 2 + 4 + 5 + 6 + 9 + 10 = 45. So '0' won't affect the sum BUT the number of data values now = 8 because you have an extra person ∴ mean = 45 ÷ 8 = 5.63 = 5.6 (1 decimal place)

7 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
How many people cycled to school the same number of times?

9 repeats itself twice: so 2 people cycled to school the same number of times

8 .

The mean was 6.4: only three values > 6.4. You can't include the person who cycled 6 times because 6 < 6.4. D'oh!

9 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
Which of the following statements is correct?

The mean is always one of the data values

The mean is sometimes one of the data values

The mean is never one of the data values

The mean is never negative

A mean = 6.4 shows you that it doesn't have to be one of the data values, but it could be, e.g. the mean of the data set 1, 2, 3 is 2 which is equal to the second value

10 .

This question is based on the following data set which represents the number of times that Christine's friends cycled to school: 9, 2, 4, 5, 6, 9, 10.
Why does the data have to be ordered to calculate the median?

It makes the data set appear tidier

They don't have to be ordered

So that you know how many data values you have

If you don't order the data values, your answers will usually be different each time

Arrange the given data values in different orders: you will soon see that you get different medians most of the time, e.g. in the arrangement 6, 2, 10, 9, 9, 5, 4, the median = 9. In maths, you MUST strictly follow definitions to the letter - or you will get wrong answers!

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)