1 2.1–2.6 Mode, median, mean and using the three types of average · 2017. 7. 12. · 1 2.8–2.9 Modal class interval, median and mean of grouped data 21A 1 The students in Year

�1 2.1–2.6 Mode, median, mean and using the three types of average

17A

1 Mai collects y pieces of data, Jack collects 3y pieces of data and Vishnu collects x pieces of data. Write down the number of pieces of data collected altogether.

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2 Nadir enters a mathematics competition. He is asked to divide 33.6 by –1.2. What answer should he get?

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3 Work out the value of each of the following.

a 42 b 23

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c 32 × 4 d √49

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e 2 × 42 + 6 f 2 × 22 + (3 + 4)

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4 Here are the prices of 7 toys bought as Christmas presents.

£7.00 £9.20 £6.50 £5.40 £6.50 £12.30 £9.10

a Write down the mode b Write down the median price

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c Work out the mean price

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5 Write down the advantages and disadvantages of using the mode as an average.

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6 Write down the advantages and disadvantages of using the median as an average.

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7 Write down the advantages and disadvantages of using the mean as an average.

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Guided practice worksheet Questions are targeted at the grades indicated

Remember BIDMAS:Brackets IndicesDivision MultiplicationAddition Subtraction


17B

Guided practice worksheet

8 Ten boys write down the number of computer games they own. The results are:

5 5 7 5 5 8 8 7 10 40

a Write down the mode ..........................................................

b Write down the median number of games ..........................................................

c Work out the mean number of games ..........................................................

d Which of the three averages best describes the number of games the boys have? .................................................

e Two more boys have 8 and 12 games respectively. How will this affect the mean, the mode and the median numbers of games?

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9 The mean of � ve numbers is 7.8.

Four of the numbers are 8, 9, 5 and 6. Work out the fifth number.

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1 0 Five friends go shopping. The mean amount they spend is £6.20.

Jack spends £6 Jean spends £5 Suha spends £3 Patrick spends £7 Maddie spends £x

a How much does their fifth friend, Maddie, spend?

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b A sixth friend spends £6.20. How will this affect the mean amount they spend? ........................................................

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1 1 Work these out.

a 2.72 b 133 c √22.09 d 3√3375

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1 2 Mia and her friends are going to a fancy dress party.Here is a list of what each person spent on clothes.£12.65, £8.25, £2.60, £14.20, £12.70

a Estimate the total amount of money they spent.

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b Work out exactly the total amount of money they spent.

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c Use your answer to b to find the mean amount of money spent.

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1 3 a Estimate the value of 3.9 + √34

5.25

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b Find the correct value of 3.9 + √34

5.25

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D



17C

1 4 There are 40 students studying Biology at Amesbury College.

28 are male and the others are female.

All the students did a Biology exam.

The overall mean mark was 62.3. The mean mark for males was 56.

Work out the mean mark for the females.

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D

�1 2.7 Using frequency tables to � nd averages

19A

1 The frequency table shows the number of eggs in the nests of 20 pairs of sparrows.

Number of eggs 5 6 7 8 9

Frequency 1 2 3 8 6

a Write down the mode.

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b Work out the median number of eggs.

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c Work out the mean number of eggs.

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2 The frequency table shows the number of siblings the members of a school class have.

Number of siblings 0 1 2 3 4 5

Frequency 4 8 7 4 3 2


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b Work out the median number of siblings.

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c Work out the mean number of siblings.

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D

Add an extra row to the table to help with your calculations.

Questions are targeted at the grades indicated

�1 2.7 Using frequency tables to � nd averages

19B


Two more people join the class. They have 1 and 4 siblings respectively.

d Write down what effect this will have on:

i the mode

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ii the median

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iii the mean.

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3 The frequency table shows the actual weekly wages of 40 factory employees.

Weekly wage (£s) 240 250 300 500 600 800

Frequency 11 6 7 2 6 8


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b Work out the median weekly wage.

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c Work out the mean weekly wage.

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Nassim says ‘I think that the mean best represents the weekly wage of employees in this factory.’

d Discuss whether or not you agree or disagree with Nassim.

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D

�1 2.8–2.9 Modal class interval, median and mean of grouped data

21A

1 The students in Year 7 take a spelling test. The grouped frequency table shows the marks that they achieved.

Mark 6–8 9–11 12–14 15–17 18–20

Frequency 4 9 10 15 12

a Write down the modal class.

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b Write down the class in which the median lies.

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c Work out the mean mark.

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2 West� eld School has three rugby teams. The grouped frequency table gives information about the weights of the forwards in the three rugby teams.

Weight (w kg) 85–89 90–94 95–99 100–104

Frequency 2 3 14 5


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C

Add extra rows to the table to help with your calculations.


�1 2.8–2.9 Modal class interval, median and mean of grouped data

21B


c Work out the mean weight.

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3 The grouped frequency table shows the weights of 60 babies born in Handlaw Hospital one week in May.

Weight (w kg) Frequency

1.5 � w � 2.0 2

2.0 � w � 2.5 12

2.5 � w � 3.0 14

3.0 � w � 3.5 16

3.5 � w � 4.0 11

4.0 � w � 4.5 5


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c Work out the mean weight.

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C

�1 2.10 Range, quartiles and interquartile range

23A

1 The weights, to the nearest kg, of the girls in a hockey team are:

49 53 47 56 51 55 45 58 57 46 37

a Write these weights in ascending order.

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b Write down the median weight Q2.

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c Write down the range of the weights. ..........................................................

d Write down the lower quartile Q1.

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e Write down the upper quartile Q3.

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f Find the interquartile range IQR. ..........................................................

2 Rosso keeps a weekly record of the number of ducks on the village pond for several weeks. The numbers he collects are as follows:

12 11 14 13 16 28 36 31 24 12 14

a Write down Q2.

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b Write down the range of the number of ducks.

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c Write down Q1 and Q3.

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d Find the IQR. ..........................................................


B


�1 2.10 Range, quartiles and interquartile range

23B


3 Here are the ages of a group of 21 people on a school coach outing.

9 8 8 9 9 10 8 10 10 9 42

8 9 9 8 8 53 11 11 12 11

a Write down Q2.

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b Write down the range of the ages. ..........................................................

c Write down Q1 and Q3.

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d Find the IQR. ..........................................................

4 Zak has to do a stock-take of the number of gold� sh at a garden centre. They are kept in several different aquariums. He counts the number of � sh in each aquarium. The results are as follows:

14 8 5 16 9 9 9 9 19 7 5

a Write down the mode. ..........................................................

b Work out the mean.

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c Write down the median Q2.

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d Write down Q1 and Q3.

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e Find the IQR. ..........................................................

f Find the range. ..........................................................

B

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1 2.1–2.6 Mode, median, mean and using the three types of average · 2017. 7. 12. · 1 2.8–2.9 Modal class interval, median and mean of grouped data 21A 1 The students in Year