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Year 10
Foundation

Comparing various representations of data sets

I can use measures of central tendency and spread to compare two data sets in context.

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New
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Year 10
Foundation

Comparing various representations of data sets

I can use measures of central tendency and spread to compare two data sets in context.

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Lesson details

Key learning points

  1. Data can be hard to compare when presented in differing formats.
  2. Being able to convert/interpret differing representations is useful.
  3. It is important to identify the most efficient form for the data to be in to compare it.

Keywords

  • Bar chart - A bar chart (bar graph) is a graph consisting of bars visually representing the frequency of objects or groups.

  • Pie chart - A pie chart (pie graph) is a circular graph where sectors represent different groups proportionally.

  • Stem and leaf diagram - A stem and leaf diagram is a systematic way to visually organise and represent numerical data.

Common misconception

The mode is the most useful average as it can be calculated from bar charts, pie charts and frequency tables.

Although it is often the easiest of the averages to calculate, this does not make it the most useful.

Pupils could curate their own data set (perhaps by surveying their peers) and then produce as many different charts as possible. Which chart best displays their data and why?
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Licence

This content is © Oak National Academy Limited (2024), licensed on

Open Government Licence version 3.0
except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
A statistical summary sums up the features of a __________ .
data cycle
Correct answer: data set
datum
graph
Q2.
When using spreadsheet software, which command would calculate the mean for a column of numerical data?
=average(A1:J1)
average(B1:B10)
=mean(A1:J1)
Correct answer: =average(B1:B10)
Q3.
When using spreadsheet software, which command would calculate the range for a column of numerical data?
max(A1:A10)-min(A1:A10)
=range(A1:J1)
Correct answer: =max(B1:B10)-min(B1:B10)
=range(B1:B10)
Q4.
When using spreadsheet software, which command would calculate the median for a row of numerical data?
=median(A1:A10)
=middle(A1:A10)
Correct answer: =median(A1:J1)
=middle(A1:J1)
Q5.
When using spreadsheet software, what symbol represents multiplication?
Correct answer: *
x
$$x$$
Q6.
When using spreadsheet software, what is the correct way to input, and calculate, $$\frac{2\times3}{5}$$ ?
Correct answer: = 2 * 3 / 5
= 2 x 3 / 5
= 2 x 3 \ 5
= 2 * 3 \ 5

Exit quiz

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6 Questions

Q1.
Both the pie chart and bar chart represent the same data set of: modes of transport to work. What percentage of people took the bus to work?
An image in a quiz
Less than 25%
Exactly 25%
Correct answer: More than 25%
Exactly 50%
More than 50%
Q2.
Both the pie chart and bar chart represent the same data set of: modes of transport to work. Calculate the percentage of people who travelled by car. Give your answer to 1 d.p.
An image in a quiz
Correct Answer: 19.1, 19.1%
Q3.
True or false? A pie chart can be used to complete an incomplete stem and leaf diagram.
True. Pie charts help identify which groups the missing data points belong to.
True. Pie charts give the exact missing values.
False. Pie charts do not share any information with stem and leaf diagrams.
Correct answer: False. Pie charts give no information about the value of a missing data point.
Q4.
Calculate the median for this data set represented as a frequency table.
An image in a quiz
Correct Answer: 2 goals, 2
Q5.
Calculate the mean for this data set represented as a frequency table. Give your answer to 1 d.p.
An image in a quiz
Correct Answer: 1.5 goals, 1.5
Q6.
A newspaper reporter is writing an article about your hockey team's performance. Which average(s) would you use to help describe your average number of goals scored per match?
An image in a quiz
Mean
Correct answer: Median
Correct answer: Mode
Range