Worksheets for GCSE Mathematics. Representing Data. Mr Black's Maths Resources for Teachers GCSE 1-9. Handling Data

Transcription

1 Worksheets for GCSE Mathematics Representing Data Mr Black's Maths Resources for Teachers GCSE 1-9 Handling Data

2 Representing Data Worksheets Contents Differentiated Independent Learning Worksheets Pictograms Bar Charts Dual & Compound Bar Charts Drawing Pie Charts Interpreting Pie Charts Stem & Leaf Diagrams Frequency Polygons Time Series Cumulative Frequency Graphs Cumulative Frequency Graphs & Box Plots Interpreting Box and Whisker Diagrams Drawing Histograms Interpreting Histograms Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Solutions Pictograms Bar Charts Dual & Compound Bar Charts Drawing Pie Charts Interpreting Pie Charts Stem & Leaf Diagrams Frequency Polygons Time Series Cumulative Frequency Graphs Cumulative Frequency Graphs & Box Plots Interpreting Box and Whisker Diagrams Drawing Histograms Interpreting Histograms Page 16 Page 17 Page 18 Page 19 Page 20 Page 21 Page 22 Page 23 Page 24 Page 26 Page 27 Page 28 Page 300 2

3 Pictograms Q1. This pictogram shows the favourite sports in Year 7. Football d) e) f) Which is the most popular sport? Which is the least popular sport? How many people have basketball as their favourite sport? How many people chose golf? How many more people prefer football to tennis? How many people were included in the survey? Basketball Tennis Golf Key: = 4 students Q2. d) e) f) This pictogram shows the favourite musical instrument of Year 8 students. Which is the most popular instrument? Which is the least popular instrument? How many people have piano as their favourite instrument? How many people chose harp? How many more people prefer guitar to violin? How many people were included in the survey? Guitar Drums Piano Harp Violin Key: = 8 students Q3. Class 9U took part in a survey. Their results are shown in the four frequency tables. Use a pictogram with your own key to represent each set of data. d) 3

4 Q1. d) e) Here are the results of a survey about the favourite pets for students in Year 8. Which is the most popular pet? Which is the least popular pet? How many people prefer Hamster s over Rabbits? How many more people prefer Dogs to Cats? How many people were included in the survey? Bar Charts Q2. d) e) Here are the results of a survey about the favourite subjects for students in Year 7. Which is the most popular subject? Which is the least popular subject? How many people prefer Science over Geography? How many more people prefer Maths to English? How many people were included in the survey? Q3. Year 9 were surveyed. Their results are shown in the four frequency tables. Represent the data using bar charts. Q4. Simon does a survey about peoples favourite sport. Here are her results. Other, Running, Hockey, Hockey, Hockey, Rugby, Tennis, Rugby, Rugby, Rugby, Football, Hockey, Football, Rugby, Hockey, Tennis, Running, Other, Hockey, Football, Hockey, Tennis, Football, Running, Tennis, Hockey, Running, Rugby, Rugby, Hockey, Rugby, Tennis, Running, Rugby, Running, Tennis, Hockey, Tennis, Other, Football, Football, Rugby, Football, Other, Other, Other Organise the data into a tally chart. Represent the data using a bar chart. i) Which sport is the most popular? ii) Which sport is the least popular? iii) How many more people prefer Hockey to Football? 4

5 Q1. d) Boys in primary and secondary school were asked to name their favourite subject. This dual bar chart shows the results. Which subject is most popular at primary school? Which subject is least popular at secondary school? Which subject became most popular from primary to secondary? Which subject became less popular at secondary after primary school? Compound & Dual Bar Charts Q2. d) e) Students in year 7 and 8 were each asked whether they were for or against wearing school uniform. The compound bar chart shows the results. How many students in year 7 are for uniforms? How many students in year 8 are against? How many students in year 7 are against uniforms? In total, how many students are for uniforms? In total, how many students are against uniforms? Q3. a ) A group of students were asked how they travelled to and from school. The table below shows the results. A group of students were surveyed about their favourite snack. The table below shows the results. Create a dual bar chart to represent the data. Create a dual bar chart to represent the data. Q4. A survey was carried out to determine how people s preferred film genre changed over time. The results are shown. Represent the data using a compound bar chart. Describe how people s favourite movie genre changes as they get older. 5

6 Drawing Pie Charts Q1. A survey of 18 people is carried out to understand information about their working life. The results are shown below. Create a pie chart for each set of data. d) Q2. A survey was carried out to find the favourite pet for students in year 9. The results are shown below. Create a pie chart to represent the data. Q3. A coffee shop carried out a survey to determine the most popular type of drink. The results are shown in this bar chart. Favourite Drink Survey Other Tea Drink Espresso Cappuccino Americano Latte Frequency Create a pie chart to represent the same set of data. Which representation, bar chart or pie chart, do you think is the best? Explain why. 6

7 Interpreting Pie Charts Q1. Match pie charts A, B, C and D to the correct data set. Q2. The pie chart on the right shows the proportion of student s favourite subject in a high school. What fraction of the students prefer Maths? 24 people took part in the survey. Calculate how many students chose each of the subjects. Q3. Elliot asked pupils in his school to name their favourite pizza topping. The pie chart shows his results. What fraction of people said chicken was their favourite topping? 18 students said vegetable was their favourite topping. How many people took part in the survey overall? How many more people prefer pineapple to ham? Q4. Simon and Jane carried out a survey to compare the makes of cars on two streets. The results are shown in the pie charts. Simon says half the cars on North Street are either Mercedes or Renault. Is he correct? Do the pie charts tell you which street has the most Renaults? Explain your answer. Based on the pie charts, what can you tell about the two neighbourhoods? 7

8 Stem & Leaf Diagrams Q1. Organise these data into the Stem and Leaf diagram Q2. Organise these data into the Stem and Leaf diagram Q3. Organise these data into the Stem and Leaf diagram Calculate the modal average. Calculate the range of the data. Q4. Organise these data into the Stem and Leaf diagram Calculate the modal average. Calculate the median average. Calculate the range of the data

9 Q1. d) A group of people were asked how long they had to wait for a train, What is the modal waiting time? How many people waited between 20 and 25 minutes? How many less people waited between 5 to 10 minutes than 10 to 15? How many people were included in the survey? Frequency Diagrams and Polygons Q2. The table shows the waiting time for 60 customers at a local Doctor s surgery. Draw a frequency diagram to represent the data. Q3. Participants in an after school P.E. class were asked to balance on one leg for as long as possible. The frequency table shows the results. Draw a frequency polygon to represent the data. Q4. Marisa recorded the number of hours of bright sunshine each day in for a period of time during a 34 day period. The frequency polygon shows her results. In which season is she likely to have carried out her survey? How many days fell in the class for 2 to 2.5 hours? What is the modal class for this data? 9

10 Time Series Q1. Describe the trend shown by each time series graph. Q2. The number of people absent from work were recorded. Week 1 Week 2 Week 3 M T W Th F M T W Th F M T W Th F Plot the data on a time series graph and draw a trend line by eye Sales ( oo's) Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Time d) On which day is the absence greatest? On which day is the absence the least? Suggest a reason for the difference in absenteeism between the two days. Q3. The table shows the quarterly sales figures for a small company over the past 3 ½ years. Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Sales ( 00's) Plot these figures as a time series graph. Plot a trend line and describe the overall trend shown. Use the trend line to predict the sales figure for the third quarter in the third year. 10

11 Q1. Cumulative Frequency A group of 40 students took an exam. Their results are recorded in the table below. d) Complete the cumulative frequency table. Plot the cumulative frequency graph. How many students scored above 45 marks? How many students scored less than 16 marks? Q2. The weights of 80 people between the age of are recorded in the table below. d) e) f) Complete the cumulative frequency table. Plot the cumulative frequency graph. How many people weigh over 62 kg. How many people weigh less than 35 kg? How many people weigh between 35 and 62 kg? How many people weigh between 41 and 76 kg? Q3. The heights of 36 boys and girls aged 12 years old are shown in the cumulative frequency graphs below. Write the median average height for each of the boys and girls. How many boys are between 1.25 and 1.55 meters tall? How many girls are taller than 1.45 meters? d) How many boys are taller than 1.45 meters? e) Comment on the difference in height between the boys and girls based on your findings. 11

12 Cumulative Frequency Graphs & Box Plots Q1. The following cumulative frequency graph shows the time taken in seconds for a group of 44 children and adults to complete a puzzle. Use the cumulative frequency graphs to draw a box plot showing the median and interquartile range for the: i) adults ii) children. Write a statement to compare the two sets of time taken including the median and interquartile range. Q2. The tables below show the waiting time at two different doctor s surgeries. The shortest waiting time at surgery A was 4 minutes and the longest time was 23 minutes. The shortest waiting time at surgery B was 2 minutes and the longest time was 18 minutes. d) Construct a cumulative frequency table for i) Surgery A ii) Surgery B Draw, on a single pair of axes a the cumulative frequency curve for i) Surgery A ii) Surgery B Draw a box and whisker diagram for each of the surgeries to show the key statistical data. Make a comparison of the two surgeries waiting times. 12

13 Q1. The lengths of two types of plants are recorded. The box plots show their results. What is the median average for: i) Plant A ii) Plant B What is the interquartile range for: i) Plant A ii) Plant B Compare the two distributions by commenting on the median and IQR. Interpreting Box Plots Q2. A group of students take a science and mathematics exam. The box plots show their results. What is the median average for: i) Mathematics ii) Science What is the interquartile range for: i) Mathematics ii) Science Compare the two distributions by commenting on the median and IQR. Q3. A groups of students sit an exam. Their results are analyzed by gender. The box plot below shows the results for the girls. The results for the boys are given as: Minimum Percentage = 32% Lower Quartile = 43% Median = 54% Upper Quartile = 59% Maximum Percentage = 75% Draw the box plot to represent the boys performance. Compare the two distributions by commenting on the median and interquartile range. 13

14 Drawing Histograms Q1. Draw histograms for these grouped frequency distributions. Speed, s (km/h) 20 s < s < s < s < 28 Frequency Time, t (seconds) 1 t < 4 4 t < 6 6 t < 7 7 t < 10 Frequency Length, L (cm) 0 L < L < L < L < L < 100 Frequency Q2. Eric works in a customer service centre. The table shows some information about the length of time, t, minutes of the calls he had. Draw a histogram to show this information. Q3. Sophie works in a cable production factory. She records the lengths of each of 100 cables that she makes one day. Sophie drew an incorrect histogram to represent the data. Explain what Sophie has done wrong. Draw a correct histogram to represent the data. 14

15 Interpreting Histograms Q1. This frequency table shows the time taken for 320 people to run 200 m. Estimate how many people ran between 60 and 70 seconds. Estimate how many people ran between 80 and 90 seconds. Estimate how many people took more than 78 seconds to complete 200 m. Q2. This histogram shows the heights for a group of students. Construct a frequency table for this data to show how many students are included in each class interval. Q3. A survey was carried out to find the speeds of cars passing a particular point on the M6. The histogram illustrates the results of the survey. Work out an estimate for the mean average speed of the cars on this part of the M6. 15

16 Solutions Pictograms Q1. Football Golf 8 d) 6 e) 2 f) 44 Q2. Guitar Harp 32 d) 18 e) 14 f) 136 Q3. Check students work using their key as a reference. 16

17 Bar Charts Q1. Dog Other 3 d) 4 e) 40 Q2. Maths Geography 2 d) 3 e) 44 Q3. Q4. i) Hockey and Rugby ii) Other iii) 3 17

18 Solutions Compound & Dual Bar Charts Q1. Maths History Maths d) English, History, P.E. Q d) 32 e) 28 Q3. Q4. As people get older they prefer action and comedy genres. Younger viewers tend to prefer animated movies. 18

19 Solutions Drawing Pie Charts d) Q2. Q3. 19

20 Solutions Interpreting Pie Charts Q1. A -> 4, B -> 1, C -> 3, D -> 2 Q2. Maths = 1 3 P.E. = 4, Maths = 8, Music= 8, French = 6, Drama = 5 Q3. Chicken = people 9 people Q4. Yes, = 180 No, population sizes not known. North Street is likely to be more effluent o to the makes of cars. 20

21 Stem & Leaf Diagrams Solutions Q1. Q2. Q3. Q4. Mode = 7.7 Median = 6.2 Range =

22 Frequency Diagrams and Polygons Solutions Q minutes 5 minutes 14 people d) 55 people Q2. Q3. Q4. Winter 6 days hours 22

23 Solutions Time Series Q1. A -> Downward trend, B -> Upward trend, C -> Level trend Q2. Monday Wednesday d) People could have been ill over the past weekend and are likely to have recovered by Wednesday. Q3. a,

24 Solutions Q1. Cumulative Frequency 34 people d) 6 people Q2. 24

25 Cumulative Frequency 40 people. d) 4 people. e) 36 people. f) 60 people. Q3. Girls median = 1.34 m; Boys Median = 1.52 m 14 boys 29 Girls d) 12 Boys e) Boys are generally taller than girls. 25

26 Q1. Cumulative Frequency Graphs & Box Plots Children take approximately 4 seconds longer to complete the puzzle than adults. However, adults are consistent due to the larger interquartile range. Q2. d) Surgery A has the longer average waiting time. Surgery B is less consistent since it has a larger interquartile range. 26

27 Solutions Interpreting Box Plots Q1. i) 14 cm ii) 11 cm i) 16 cm ii) 7 cm The median shows plant A, on average is 3 cm taller than plant B. The interquartile range shows plant B is more consistent. Q2. i) 40 marks ii) 37 marks i) 9 marks ii) 12 marks The median students scored 3 marks higher in the mathematics exam than science. The interquartile range shows students were more consistent in mathematics than science. Q3. Boys and girls tend to have a similar percentage in the exam as shown by the median averages. However, the boys were more consistent in the exam than girls since they have a lower interquartile range. 27

28 Solutions Drawing Histograms Q1 28

29 Q2. Drawing Histograms Q3. Sophie plotted frequency rather than frequency density. 29

30 Solutions Interpreting Histograms Q1. 40 people 87 people 160 people Q2. Q3. Mean Estimate = 99 km/h 30