◄UNIT 13:Calculating the circumference of a circle and the volume of cuboids and cubesUNIT 15:Probability►

UNIT 14:Statistics

  • UNIT 14:Statistics

    14.1 Continuous and Discrete Quantitative data

    Activity 14.1
    1. Question: What type of data are your heights?
    Materials: Tape measure or ruler.

    Steps:b

    (i) In groups, measure your heights. Record your results in the table
    below.

    (ii) Observe the values you record.

    n

    (a) Name the type of data you collect. Discuss your answer.
    (b) Does your data have various values that include decimals?
    2. Now, form a question to collect data for
    • distance to school compound.
    • time taken to get to school.

    Follow the same process you used in (1).

    Activity 14.2
    1. Question: How many brothers and sisters do you have?
    Steps:
    (i) In groups, make a chart below. State and record your number of

    sisters and brothers.

    n

    (ii) Observe the values you record. Do they take various values? Do
    your values include decimals? Explain your answers.
    2. Now, follow the same steps and form questions to collect data on:
    – Shoe sizes worn by adults.

    – Shoe sizes worn by children.

    Task
    Discuss the differences in the type of data from Activity 14.1 and 14.2.
    Show a summary of the type of data you collected.
    Tip:
    • Data with numerical values is called quantitative data.
    • The values for numerical data can be whole numbers only. Such data
    is discrete.
    • The values for numerical data can take any number including decimals.

    Such data is continuous.

    Example 14.1
    From Activity 14.1 and 14.2, state the type of quantitative data you
    collected.
    Solution
    (a) Discrete quantitative data include: number of brothers or sisters
    you have and shoe size worn by different people.
    (b) Continuous quantitative data include: distance from home to school,
    time taken to get to school and heights of pupils in class.

    (c) Discuss and name other discrete and continuous quantitative data.

    Practice Activity 14.1

    1. The following data was collected by a group of pupils.

    h

    (i) What type of data was collected?
    (ii) Is the data discrete or continuous? Explain your answer.
    2. A class collected numerical data on the following.
    (a) Shoe sizes worn by pupils in school.
    (b) Time taken to run twice round the field.
    (c) Distance from home to school for group members.
    (d) Number of parents for different pupils in a class.

    Draw a table and group the data accordingly. Discuss your answers.

    b

    3. Shyaka and Filonne collected the following data

    b

    b
    In each case, identify the type of quantitative data?

    Explain your answer.

    14.2 Representing data using bar charts
    Activity 14.3
    Represent the data you collect in Activity 14.1 and 14.2 using a bar chart.
    Explain your bar chart.

    Tell cases where you can represent data using bar graphs.

    Example 14.2

    The table below contains data about the number of cars in a car park.

    s

    Represent the data in a bar chart.
    Solution
    Steps:
    • Draw horizontal and vertical axes. Label them as shown.
    • Choose a good scale to allow you to plot the data easily.
    • Mark the length of bars as per the number of cars for each colour.

    Draw them.

    e

    Practice Activity 14.2
    1. The table below contains data for heights of family members.
    j
    Represent the data using a bar chart.

    2. The table below contains data for shoe sizes for different people.

    t

    Represent the data using a bar chart.
    3. The table below contains data about the number of books each pupil

    has.

    g

    Represent the data using bar chart.

    4. What type of data are those in questions 2 and 3?

    14.3 Interpreting bar charts
    Activity 14.4

    Study the bar chart below.

    m

    (a) What is the bar chart about? Explain.
    (b) Read the height of:
    (i) Dad            (ii) Mum          (iii) Boy            (iv) Girl

    Tip: In interpreting bar charts
    (i) Read the lengths of bars and the information they represent. Check
    the vertical axis.
    (ii) State the information represented by each bar. Check the horizontal axis.

    Example 14.3
    From Activity 14.4, answer the following.
    (a) What information is shown by the bar chart?
    (b) Who is the tallest?
    (c) Who is 150 cm tall?
    (d) How is bar chart important to you?

    Solution
    (a) On the vertical axis, we have height (in cm).
    On the horizontal axis, we have family members.
    The information shown is the heights of family members.
    (b) Dad is the tallest. His height is 180 cm.
    (c) Starting from vertical axis, at 150 cm put a ruler. Draw a dotted line
    to see which bar is at 150 cm.
    The bar representing the Girl is at 150 cm. The girl is 150 cm tall.

    Practice Activity 14.3

    1. Look at the bar graph below.

    v

    (a) How many pupils measured their heights?
    (b) What information is shown on the graph?
    (c) Who is the shortest?
    (d) How many metres tall is the tallest pupil?
    (e) Which pupils were the same height?

    2. Study the bar chart below.

    s

    (a) What is the bar chart about?
    (b) How many pupils did the mathematics activity?
    (c) What is the highest score?
    (d) Who scored the lowest mark?
    (e) Which pupils scored the same mark?
    (f) Who scored the highest mark?
    (g) How many more marks did Ruth score than Rosy?
    heart What score did Seth get?

    14.4 Representing data using line graphs
    Activity 14.5
    Materials: Metre rule or tape measure.
    • Measure the length of your shadow at the following times. Record
    your findings in the following table.
    z
    • Represent your data using a line graph. Discuss your steps.

    Where can you use line graphs to represent data in daily life?

    Tip: To draw a line graph;
    (i) Choose a suitable scale for all values.
    (ii) Draw axes and label them.
    (iii) Plot points on the graph.

    (iv) Join the points using straight line.

    Example 14.4

    Below is data for the distance covered by a cyclist at different times.

    h

    Represent the data using a line graph.

    t

    Practice Activity 14.4
    1. Study the data in the table below. It shows the distance travelled by a
    motoris
    e
    Represent the data using a line graph.
    2. The data below is the amount of water used by a family after every two
    hours.

    e

    (a) Represent the data using a line graph.
    (b) Why was the amount of water the same from 11 a.m to 1 p.m?
    Explain your answer.
    3. A pupil did a number of competence exams. She got the following
    marks at different times.
    n
    Represent the data using a line graph.
    Was the pupil improving in performance or not? Explain your answer.
    4. A farmer planted a crop. She measured its height after every two
    months. She recorded the data below.
    /
    Represent the data using a line graph. Discuss your steps to draw an

    accurate line.

    14.5 Interpreting line graphs
    Activity 14.6
    Look at the line graph below. It represents data for distance covered by

    an athlete.

    n

    (i) What is the line graph about?
    (ii) How many seconds does the athlete take to cover 100 m? Explain
    the steps you used to find the answer.
    Example 14.5
    Study the graph in Activity 14.6. Answer these questions:
    (a) What distance does the athlete cover in 4 seconds?
    (b) How long does it take the athlete to cover 75 m?
    (c) Find the distance the athlete covered in 8 seconds.
    (d) How is line graph important to you?
    Solution
    (a) Put the ruler vertically at 4 seconds. It cuts the line at 25 m.
    (b) Put the ruler horizontally at 75 m. It cuts the line at 12 seconds.

    (c) In 8 seconds, the athlete covered 50 m.

    Practice Activity 14.5

    1. Look at the graph below.

    x

    (a) What is the graph about?
    (b) What is the mass of the child at birth?
    (c) Read the mass of the child at 3rd month.
    (d) At what month is the mass of the child 7 kg?
    (e) What is the change in the child’s mass from the 3rd to the 4th month?
    2. A motorist started a journey from town A to B. The data is represented

    in the graph below.

    d

    (i) How far is town A from B?
    (ii) What time did the motorist start the journey?
    (iii) What time did the motorist start to rest?
    (iv) What distance did the motorist cover from 11.00 a.m to
    11.30 a.m?

    (v) Find the time taken to reach town B after resting.

    Revision Activity 14

    1. In a school the following data was recorded.

    m

    (a) Name the type of quantitative data above. Explain.
    (b) Represent the data using a bar chart. What do you notice?
    (c) From your bar graph;
    (i) Which class had the highest number of pupils?
    (ii) Which two classes had the same number of pupils?
    2. In a cross-country race, a top athlete was involved. The time and

    distance covered are represented below.

    d

    (a) What was the distance ran by the athlete?
    (b) At what time did the athlete complete the race?
    (c) At what time did the race begin? Explain your answer.
    (d) How much distance had the athlete completed at 7.00 a.m?
    (e) At what time had the athlete run 10 km? Discuss the steps
    to your answer. What are the importance of interpreting line
    graphs?
    3. The amount of rainfall was recorded for a certain town.
    b
    (a) What type of quantitative data was collected?
    (b) Represent the data using a line graph.

    (c) From your graph, which month had the highest rainfall? Explain.

    Word list
    Quantitative data                          Continuous quantitative data
    Discrete quantitative data            Record                   Collect data
    Represent data                            Interpret data          Bar graph
    Line graph

    Task
    Do the following.
    (i) Read each word aloud to your friend.
    (ii) Write the meaning of each of the words above. Discuss with your friend.

    (iii) Write sentences using each of the words above. Read with your friend.

    ◄UNIT 13:Calculating the circumference of a circle and the volume of cuboids and cubesUNIT 15:Probability►