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Name: ___________________________ Fluency 1 Data representing the number of pets that a
year 8 class has is shown below: 0, 1, 3, 2, 1, 0, 1, 2, 0, 1, 2, 0 What is the mean number of pets the students have?
Answer: Mean ;
�̅� = ∑"#= $%&%'%(%&%$%&%(%$%&%(%$
&(
= 1.08
2 Data representing the number of pets that a year 8 class has is shown below: 0, 1, 3, 2, 1, 0, 1, 2, 0, 1, 2, 0 What is the mean number of pets the students have, including that new student with 14 pets?
Answer: Mean ;
�̅� = ∑"#= $%&%'%(%&%$%&%(%$%&%(%$%&)
&'
= 2.07
That confirms our answer to earlier in the other worksheet, that including the new student with 14 pets would Increase the mean.
3 Data representing the number of texts our year 8 class receives on their phone for the day could look like; 20, 14, 33, 42, 31, 29, 40, 28, 37 What is the mean number of texts the students receive?
Answer: Mean ;
�̅� = ∑"#= ($%&)%''%)(%'&%(*%)$%(+%',
*
= 30.44
4 Data representing the number of texts our yr 8 class receives on their phone for the day could look like; 20, 14, 33, 42, 31, 29, 40, 28, 37 What is the mean number of texts the students receive, if we include Mr Finney’s outlier of 2?
Answer: Mean ;
�̅� = ∑"#= ($%&)%''%)(%'&%(*%)$%(+%',%(
&$
= 27.6
That confirms our answer earlier in the other worksheet, that including Mr Finney’s texts would Decrease the mean. *** Notice how I show my full working EVERY time!
5 Data representing the number of pets that a year 8 class has is shown below: 0, 1, 3, 2, 1, 0, 1, 2, 0, 1, 2, 0 What is the mean, median and Range of pets the students have?
1st, put the data into order; 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3 Mean; �̅� = ∑"
#= $%$%$%$%&%&%&%&%(%(%(%'
&(= 1.08
Median, use your fingers to find the Middle number – 1 Range; 𝑥-." − 𝑥-/# = 3 − 0 = 3
6 Data representing the number of pets that a year 8 class has is shown below: 0, 1, 3, 2, 1, 0, 1, 2, 0, 1, 2, 0 What is the mean, median and range of pets the students have, if we include that outlier of the new student with 14 pets?
1st, put the data into order; 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 14 Mean;
�̅� = ∑"#= $%$%$%$%&%&%&%&%(%(%(%'%&)
&'
= 2.07
Median, use your fingers to find the Middle number – 1 Range; 𝑥-." − 𝑥-/# = 14 − 0 = 14
7 Have you noticed that maths is about Repetition J
8 Data representing the number of texts our year 8 class receives on their phone for the day could look like; 20, 14, 33, 42, 31, 29, 40, 28, 37 What is the mean, median and range of texts the students receive?
1st, put the data into order; 14, 20, 28, 29, 31, 33, 37, 40, 42 Mean;
�̅� = ∑"#= &)%($%(+%(*%'&%''%',%)$%)(
*
= 30.44
Median, use your fingers to find the Middle number – 31 Range; 𝑥-." − 𝑥-/# = 42 − 14 = 28
9 Data representing the number of texts our yr 8 class receives on their phone for the day could look like; 20, 14, 33, 42, 31, 29, 40, 28, 37 What is the mean, median and Range of texts the students receive, if we include Mr Finney’s outlier of 2?
1st, put the data into order; 2, 14, 20, 28, 29, 31, 33, 37, 40, 42 Mean;
�̅� = ∑"#= (%&)%($%(+%(*%'&%''%',%)$%)(
&$
= 27.6
Median, use your fingers to find the Middle number = 30 Range; 𝑥-." − 𝑥-/# = 42 − 2 = 40
10 Use the frequency distribution table below to answer the following questions.
(a) How many data results were collected? (b) Which score had the highest
frequency?
(c) Which score(s) had the lowest
frequency?
Answers:
(a) Total = 6 + 12 + 9 + 7 + 6 Total = 40
(b) 12 (c) 11 and 15
11 Find the mean of each set of scores. (a) 1.3, 2.4, 5.6, 7.9, 1.2 (b) 7, 6, 5, 10, 2, 4, 8
12 A survey of the number of cars owned by each family in a suburban street gave the following data. 2, 3, 1, 2, 2, 3, 1, 2, 1, 3, 4, 2, 4, 3, 1. (a) What is the mean? (b) Calculate the Median. (c) Determine the mode. (d) Find the Range of the data.
Answers: First, put the data in order: 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4. (a)
13 Terry obtained the following test results. The scores are out of 10. 7, 8, 9, 5, 7, 6, 8, 4, 8, 7, 7 Determine the Mean, Median, Mode and Range.
Answers: First, put the data in order: 4, 5, 6, 7, 7, 7, 7, 8, 8, 8, 9.
𝑀𝑒𝑎𝑛 = �̅� =∑𝑥𝑛
=4 + 5 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 9
11
= 6.91
𝑀𝑒𝑑𝑖𝑎𝑛 =𝑛 + 12 =
11 + 12 = 6𝑡ℎ𝑛𝑢𝑚𝑏𝑒𝑟
Median is 7
Mode = most common = 7
𝑅𝑎𝑛𝑔𝑒 = 𝑥-." − 𝑥-/# = 9 − 4 = 5
14 Twenty young people were picked at random and surveyed to find the number of colours they have in their hair. Here are the raw data collected: 1, 3, 4, 2, 1, 2, 2, 2, 1, 1, 2, 2, 3, 3, 1, 2, 3, 1, 1, 2. (a) Organise the data into a frequency
distribution table.
(b) How many people have 1 colour in their hair?
(c) Which score has the highest
frequency?
Answers: (a)
(b) 7 people (c) 2 colours
15 Are the following statements true or false? The mode of: (a) 1, 2, 3, 4, 4, 5 is 5 (b) 12, 11, 17, 16, 11, 12, 11 is 11.
temperature for the week? (b) What was the mean average temperature?
Answers: (a) Mode = most common = 31oC (b)
𝑀𝑒𝑎𝑛 = �̅� =∑𝑥𝑛
=33 + 31 + 30 + 27 + 32 + 31 + 29
7
= 30.43
20 What is the median temperature for the data in the last question?
Answer: Must put the data into order, then because it’s a small set of data, just use your fingers to find the Middle number; 27, 29, 30, 31, 31, 32, 33 Median temperature is 31°C.
Temperature over the weekDay 1 2 3 4 5 6 7Temp (°C) 33 31 30 27 32 31 29
21 *** Dot Plots are NOT required and won’t be in our test, but they are easy to work out, so its good practice for you to do one. The dotplot below shows the number of games won (out of a possible 20) by the local soccer club over the last 20 seasons.
Find the Mean, Median, Mode and Range of the data.
= 73.2 With 22 values, choose the average of the 11th and 12th values. Median = 78 Class 8B: Total = 1336
Mean =
= 60.7 With 22 values, choose the average of the 11th and 12th values.
Median =
= 62.5 (c) Class 8A: range = 91 – 34 = 57
Class 8B: range = 88 – 23 = 65
26
Are the following statements true or false? (a) There are 30 pieces of data. (b) The most common frequency is 5. (c) The score with a frequency of 15 is 6.
Answers: (a) Total = 3 + 0 + 7 + 11 + 2 + 15
Total = 38 (False) Total (b) False … the most common frequency is 15 (c) True