A family at the cinema
Jason asked his friends how many times they had visited the cinema this year.

Handling Data 3 (Difficult)

Calculating the average value from a set of data is an important part of data handling, and you need to be familiar with it if you want to do well in your Eleven Plus maths exam. If you have played the first two quizzes in this section, then it shouldn’t be a problem. This third quiz gives you another opportunity to revise!

Here are some terms you need to know about averages:

  • Range is the difference between the highest and lowest values in a set of data
  • Mean is the average when you add all the values together, then divide by the number of values
  • Median is the average when you line up the data in ascending order and choose the middle value
  • Mode is the average worked out by choosing the value which appears most often in a set of data

That may sound a little complicated, but it’s quite easy really – once you know what you are doing, that is! Do you? Well, it’s time to find out by playing the quiz. Take your time and be sure to work out your answers properly. Good luck!

1.
This question is based on the following data set which represents the number of times that Jason’s friends had visited the cinema this year: 12, 1, 4, 6, 3, 5, 8.
How many of Jason’s friends took part in the survey?
7
39
12
24
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 39
2.
This question is based on the following data set which represents the number of times that Jason’s friends had visited the cinema this year: 12, 1, 4, 6, 3, 5, 8.
What is the range of the given data?
11
8
12
2
Range = highest value - lowest value = 12 - 1 = 11
3.
This question is based on the following data set which represents the number of times that Jason’s friends had visited the cinema this year: 12, 1, 4, 6, 3, 5, 8.
What is the mean of the given data?
5
5.6
6
5.7
Mean = (the sum of the data values) ÷ the number of data values. The sum of the data values = 12 + 1 + 4 + 6 + 3 + 5 + 8 = 39. The number of data values = 7 ∴ mean = 39 ÷ 7 = 5.571 = 5.6 (1 decimal place)
4.
This question is based on the following data set which represents the number of times that Jason’s friends had visited the cinema this year: 12, 1, 4, 6, 3, 5, 8.
What is the median of the given data?
3
4
5
6
The median is the middle value of the data: you have to arrange the data in order BEFORE you can find it: 1, 3, 4, 5, 6, 8, 12. You have seven values, so the median is the 4th value = 5. 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 4th value
5.
This question is based on the following data set which represents the number of times that Jason’s friends had visited the cinema this year: 12, 1, 4, 6, 3, 5, 8.
How many people went to the cinema the same number of times?
12
8
6
0
None of the numbers occurs more than once, so nobody went to the cinema the same number of times
6.
Which of the following statements is correct?
The mode is always one of the data values
The mode is never one of the data values
The mode is sometimes one of the data values
The mode is the middle number in a set of data
The mode is the number which appears most often, so it is always one of the data values
7.
This question is based on the following data set which represents the number of times that Jason’s friends had visited the cinema this year: 12, 1, 4, 6, 3, 5, 8.
How many people went to the cinema more times than the mean number of times?
5
4
3
2
The mean is 5.6: only three values > 5.6. You can't include the person who went to the cinema 5 times because 5 < 5.6. D'oh!
8.
This question is based on the following data set which represents the number of times that Jason’s friends had visited the cinema this year: 12, 1, 4, 6, 3, 5, 8.
What is the mode of the given data?
5
5.5
6
There isn't a mode
The mode is the data value that occurs most often: in this set of data, there isn't a mode as each value occurs only once
9.
This question is based on the following data set which represents the number of times that Jason’s friends had visited the cinema this year: 12, 1, 4, 6, 3, 5, 8.
Jason decided to include one more friend in his survey. If that friend hadn't been to the cinema this year, how would that affect the value of the 'mean'?
It would increase the value of the 'mean'
It would lower the value of the 'mean'
It wouldn't affect the value of the 'mean'
There isn't enough information to answer this question
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 + 12 + 1 + 4 + 6 + 3 + 5 + 8 = 39. So '0' won't affect the sum BUT the number of data values now = 8 because you have an extra person ∴ mean = 39 ÷ 8 = 4.875 = 4.9 (1 decimal place)
10.
Why does data have to be ordered to calculate the mode?
So that you know how many data values you have
So that you can find the'middle' value
To make calculating the answer easier
It doesn't have to be ordered
The mode is the value which appears most often - you can usually spot this at a glance, without orderinfg the data - but you do have to order the data if you want to find the median value
Author:  Frank Evans

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