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Data Representation Techniques

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Data Representation Techniques

Read each question carefully. Use the data shown to answer. When asked to draw a graph, label both axes and give it a clear title.

Choosing a representation

1.Match each representation to its most suitable purpose.

Bar graph
Pie chart
Line graph
Dot plot
Frequency table

Show how a whole is divided into parts
Organise categories or values alongside their counts
Display individual numerical values and their frequency
Compare amounts in separate categories
Show how a measure changes over time

2.A weather station records the air temperature at regular intervals from morning to evening. Which display is the best choice for showing how the temperature changes?

Bar graph
Pie chart
Line graph
Frequency table

Category data

At a marae visit, a group recorded which activity visitors most wanted to try. The counts are shown below.

Activity

Votes

Weaving

Poi

Kapa haka

Carving

3.Which activity received the greatest number of votes?

4.How many more votes did weaving receive than carving?

5.How many votes were recorded altogether?

6.Why is a graph with separate bars a useful way to display the activity votes?

Parts of a whole

Visitors chose one way to travel to a community event. The data lists the percentage choosing each option.

The data represents the same four travel choices: walk 35%, car 25%, bus 30%, bicycle 10%.

7.What percentage of visitors chose to walk?

8.Which travel option was chosen by the smallest share of visitors?

9.If 200 visitors took part, how many chose the bus?

10.Select both statements that describe a useful feature of this display.

It shows how categories make up a whole.
It is designed to show change from day to day.
It can make proportions or percentages easy to compare.
It shows every individual observation as a separate dot.

Change over time

Tane recorded the temperature at the same outdoor site once each day for a week.

Day

Temperature (°C)

Monday

Tuesday

Wednesday

Thursday

Friday

11.What was the highest temperature recorded?

12.On which day was the lowest temperature recorded?

13.What was the greatest temperature decrease between consecutive days?

14.Describe the overall pattern in the temperatures from Monday to Friday.

Use the values in the temperature table to draw a graph showing the changes over time. Put the days on the horizontal axis and temperature in °C on the vertical axis. Include a suitable scale, plotted points, connecting lines and a title.

Frequency tables and dot plots

A group asked families how many reusable drink bottles each household had.

Bottles per household

Number of households

15.How many households had exactly two bottles?

16.What number of bottles occurred most often?

17.How many households were included in the survey?

18.Explain one way a dot plot could make this set of results easier to understand.

Use the household counts in the frequency table to draw a dot plot. Label the horizontal axis with bottle counts and stack one dot per household above each count.

Choose and evaluate displays

19.A school wants to compare the number of students in each year level. Which display is the best fit?

Bar graph
Pie chart
Line graph

20.A team measures the height of a seedling at the end of each week for six weeks. Which display would best show its growth over time?

Bar graph
Pie chart
Line graph

21.A group wants to show what proportions of an event budget are spent on food, transport and equipment. Which display would best show the shares of the total?

Bar graph
Pie chart
Line graph

22.Suggest a numerical question that could be asked in a class survey, name a suitable way to display its results, and explain why that display would work well.

23.A report claims that 9 out of 10 visitors enjoyed an activity. Name two questions you would ask before deciding whether this result is reliable.

24.Write one useful idea about choosing or reading a data display that you will remember.