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1 PLC Papers Created For: Year 11 Topic Practice Paper: Cumulative Frequency and Box Plots

2 Boxplots 1 Grade 6 Objective: Interpret and construct box plots Question 1 The box plot gives information about the weights of a group of children. (a) Write down the median. kg (1) (b) Work out the interquartile range. kg (2) There are 80 children in the group. (c) Work out an estimate for the number of children who weigh 32 kg or more. (2) (Total 5 marks)

3 Question 2 The data in the table below represents the ages of a football team (a) Work out the median. years (1) (b) Work out the interquartile range. (c) Draw a boxplot to represent this data years (2) (Total 5 marks) (2) Total marks /10

4 Boxplots 2 Grade 6 Objective: Interpret and construct box plots Question 1 Dave recorded the length of time 24 pupils took to solve a puzzle. The table shows information about these times in minutes. (a) Work out the number of teachers with a travel time of 3.4 minutes or more. (2) (b) On the grid, draw a box plot to show the information in the table. (2) (Total 4 marks)

5 Question 2 Jodie measures the lengths of 120 snakes. The lengths were recorded and displayed in the boxplot below. (a) Use the boxplot to fill in the values in this summary table: (3) (b) Calculate the Inter Quartile Range (IQR). (2) (c) One of the snakes measured at 42cm was actually 44cm, what affect would this change have on the median? Decrease Stay the same Increase (1) (Total 6 marks) Total marks /10

6 Boxplots 3 Grade 6 Objective: Interpret and construct box plots Question 1 The following data represents the temperature in the first 15 days of June (Set 1) and the second 15 days of June (Set 2). Draw suitable charts to represent the data. (Total 6 marks)

7 Question 2 The boxplots below show the results of two sets of test scores from Class 1 and Class 2. (a) Make two comparisons between the two sets of data. (i) (ii) (Total 4 marks) Total marks /10

8 Boxplots 4 Grade 6 Objective: Interpret and construct box plots Question 1 The heights of 3 year olds in two towns (Mathtown and Algebraville) were measure. The data for these is found below: Compare the heights of the 3 year olds in these towns. (i) (ii) (10) Total marks /10

9 Cumulative Frequency 1 Grade 6 Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The grouped frequency table shows information about the weekly wages of 80 factory workers. (a) Complete the cumulative frequency table. (b) On the next page, draw a cumulative frequency graph for your table. (1) (2)

10 CUMULATIVE FREQUENCY WEEKLY WAGE, (c) Use your graph to find an estimate for the median. (d) Use your graph to find an estimate for the interquartile range. (1) (2) (e) Use your graph to find an estimate for the number of workers with a weekly wage of more than 530. (2) (Total 8 marks)

11 Question 2 The cumulative frequency graph shows information about the times 80 swimmers take to swim 50 metres. (a) Use the graph to find an estimate for the median time. (1) (b) Use the graph to find an estimate for the lower quartile.. (1) (Total 2 marks) Total marks /10

12 Cumulative Frequency 2 Grade 6 Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The table below shows information about the heights of 60 students. (a) On the grid, draw a cumulative frequency graph for the information in the table. (3) CUMULATIVE FREQUENCY TIME, T SECS

13 (b) Find an estimate (i) for the median,... (ii) for the interquartile range.... (Total 6 marks) (3)

14 Question 2 The table shows information about the lengths, in seconds, of 40 TV adverts. (a) Complete the cumulative frequency table for this information. (1)

15 (b) On the grid, draw a cumulative frequency graph for your table. (2) CUMULATIVE FREQUENCY TIME, T SECS (c) Use your graph to find an estimate for the median length of these TV adverts. seconds (1) (Total 4 marks) Total marks /10

16 Cumulative Frequency 3 Grade 6 Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The table below shows the times it takes a group of boys to run 150m. Boys time, secs Frequency 0 < x < x < x < x < x < x 30 2 Totals 36 The cumulative frequency graph below shows the times it takes a group of girls to run 150m CUMULATIVE FREQUENCY TIME, SECS

17 (a) Which is the quicker gender at running 150m. Explain your answer.. (1).... (5) b) Were the boys or the girls more consistent in their running speeds, explain your reasons for your answer.... (4) Total for question - 10 marks Total marks /10

18 Cumulative Frequency 4 Grade 6 Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The cumulative frequency below shows the scores of two classes (X and Y) in a maths assessment which is out of 90 marks. 30 Class X 25 Class Y CUMULATIVE FREQUENCY TEST SCORES a) (i) Which set do you think is the Higher set?. (1) (ii) Explain your answer (2)

19 b) Which class is more consistent? Explain your answer. (4) c) The pass mark for the test was 63%. How many students in total (from both classes) failed?. (3) Total marks /10

20 PLC Papers Created For: Year 11 Topic Practice Paper: Cumulative Frequency and Box Plots

21 Boxplots 1 Grade 6 SOLUTIONS Objective: Interpret and construct box plots Question 1 The box plot gives information about the weights of a group of children. (a) Write down the median. 28 A1 kg (1) (b) Work out the interquartile range = (7) M1 7 A1 kg (2) There are 80 children in the group. (c) Work out an estimate for the number of children who weigh 32 kg or more. 25% of 80 = (20) M1 20 A1 (2) (Total 5 marks) Question 2 The data in the table below represents the ages of a football team (a) Work out the median. 26 A1 years (1)

22 (b) Work out the interquartile range = 12 M1 12 A1 years (2) (c) Draw a boxplot to represent this data (2) (Total 5 marks) Total marks /10

23 Boxplots 2 Grade 6 SOLUTIONS Objective: Interpret and construct box plots Question 1 Dave recorded the length of time 24 pupils took to solve a puzzle. The table shows information about these times in minutes. (a) Work out the number of teachers with a travel time of 3.4 minutes or more. 75% of 24 = (18) M1 (b) On the grid, draw a box plot to show the information in the table. 18 A1 (2) (2) (Total 4 marks)

24 Question 2 Jodie measures the lengths of 120 snakes. The lengths were recorded and displayed in the boxplot below. (a) Use the boxplot to fill in the values in this summary table: Length, cms Minimum 24 Lower Quartile 38 Median 40 Upper quartile 46 Maximum 54 (3) (b) Calculate the Inter Quartile Range (IQR) = (8) M1 8 A1 (2) (c) One of the snakes measured at 42cm was actually 44cm, what affect would this change have on the median? Decrease Stay the same Increase (1) (Total 6 marks) Total marks /10

25 Boxplots 3 Grade 6 SOLUTIONS Objective: Interpret and construct box plots Question 1 The following data represents the temperature in the first 15 days of June (Set 1) and the second 15 days of June (Set 2). Draw suitable charts to represent the data. Set 1 Set 2 Minimum Lower Quartile Median Upper Quartile Maximum Choosing to use a boxplot Calculate summary data C1 A3 Draw boxplots A2 (Total 6 marks)

26 Question 2 The boxplots below show the results of two sets of test scores from Class 1 and Class 2. (a) Make two comparisons between the two sets of data. (i) (ii) Set 2 have scored better (Contextual answer - C1) in the test overall as the median is higher (Compare medians - C1) Set 2 scores are much more spread out (contextual answer C1, the range (or IQR) is higher in set 2 (compare IQR or Range C1) (Total 4 marks) Total marks /10

27 Boxplots 4 Grade 6 SOLUTIONS Objective: Interpret and construct box plots Question 1 The heights of 3 year olds in two towns (Mathtown and Algebraville) were measure. The data for these is found below: Mathtown Algebraville Minimum Lower Quartile Median Upper Quartile Maximum Calculate summary values for Mathtown - A3 IQR = 0.45 Median = 1.2 Range = 0.6 Write down summary values for Algebraville or draw a Boxplot for Mathtown A3 IQR = 0.6 Median = 1.2 Range = 0.6

28 Compare the heights of the 3 year olds in these towns. (i) (ii) The two towns are very similar in the spread of heights (range is the same). IQR is slightly larger in MathTown (C2) The children are taller (C1 Contextual answer) in Algebraville as all data values except median are higher (C1) (4) Total marks /10

29 Cumulative Frequency 1 Grade 6 SOLUTIONS Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The grouped frequency table shows information about the weekly wages of 80 factory workers. (a) Complete the cumulative frequency table. (b) On the next page, draw a cumulative frequency graph for your table. (1) (2)

30 CUMULATIVE FREQUENCY WEEKLY WAGE, (c) Use your graph to find an estimate for the median. 360 B1 (1) (d) Use your graph to find an estimate for the interquartile range = (155) M1 155 A1 (2) (e) Use your graph to find an estimate for the number of workers with a weekly wage of more than 530. Read off graph 73 M = (7) 7 B1 (2) (Total 8 marks)

31 Question 2 The cumulative frequency graph shows information about the times 80 swimmers take to swim 50 metres. (a) Use the graph to find an estimate for the median time. 68 A1 (1) (b) Use the graph to find an estimate for the lower quartile. 53 A1 (1) (Total 2 marks) Total marks /10

32 Cumulative Frequency 2 Grade 6 SOLUTIONS Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The table below shows information about the heights of 60 students. (a) On the grid, draw a cumulative frequency graph for the information in the table. (3) CUMULATIVE FREQUENCY HEIGHT, CMS

33 (b) Find an estimate (i) for the median, a1... (ii) for the interquartile range = (12)...M1 A1 (Total 6 marks) (3)

34 Question 2 The table shows information about the lengths, in seconds, of 40 TV adverts. (a) Complete the cumulative frequency table for this information. (1) (b) On the grid, draw a cumulative frequency graph for your table. (2)

35 CUMULATIVE FREQUENCY TIME, T SECS (c) Use your graph to find an estimate for the median length of these TV adverts. 37 B1 seconds (1) (Total 4 marks) Total marks /10

36 Cumulative Frequency 3 Grade 6 SOLUTIONS Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The table below shows the times it takes a group of boys to run 150m. Boys time, secs Frequency Boys time, secs Cumulative Frequency 0 < x < x < x < x < x < x < x < x < x < x < x < x Totals 36 The cumulative frequency graph below shows the times it takes a group of girls to run 150m CUMULATIVE FREQUENCY TIME, SECS

37 (a) Which is the quicker gender at running 150m. Explain your answer.. (1).... (5) M1 finding the cumulative frequency of the boys M1A1 Drawing the cumulative frequency curve for the boys A1 find the median for the boys 18 A1 find the median for the girls 18.5 b) Were the boys or the girls more consistent in their running speeds, explain your reasons for your answer... (4) Calculate the upper and lower quartile for boys and girls M2 Calcualate the interquartile range for boys and girls A1 Boys IQR = = 6 Girls IQR = = 7 State the more consistent due to having a smaller IQR C1 Boys Total for question 10 marks Total marks /10

38 Cumulative Frequency 4 Grade 6 SOLUTIONS Objective: Construct and interpret cumulative frequency diagrams (for grouped discrete as well as continuous data) Question 1 The cumulative frequency below shows the scores of two classes (X and Y) in a maths assessment which is out of 90 marks. 30 Class X 25 Class Y CUMULATIVE FREQUENCY TEST SCORES a) (i) Which set do you think is the Higher set? Class Y A1. (1) (ii) Explain your answer The median score in class X was 49 whilst the median score in class Y was 63 which means class Y did better B2 Finding the medians (2)

39 b) Which class is more consistent? Explain your answer. IQR class X = = (16) IQR class Y = = (18) M1A1 Class X is more consistent as the IQR is smaller and therefore lower spread... A1 Correct class C1 Reference to IQR/spread of data.. (4) c) The pass mark for the test was 63%. How many students in total (from both classes) failed? 63/100 x 90 = 57 marks B = (49) M1 32 A1. (3) Total marks /10