New
New
Year 8

Analysing different statistical representations

I can use the different statistical representations to compare two sets of data.

New
New
Year 8

Analysing different statistical representations

I can use the different statistical representations to compare two sets of data.

Lesson details

Key learning points

  1. Statistical summaries can be compared to graphical representations of data.
  2. Statistical summaries can be used to produce a sketch of what the graphical representation could be.
  3. Different statistical representations can help form a more complete picture.

Common misconception

The mean and median will always be close to the most frequent values (or peaks) in a dataset.

The mean and median may be at the lower or lowest frequency parts of a distribution. This is especially likely if the data is bimodal.

Keywords

  • Statistical summary - A statistical summary sums up the features of a data set. It may contain the averages (mean, median, mode). It may also contain the range.

  • Central tendency - is a summary measure that attempts to describe a whole dataset with a single value that represents the middle or centre of its distribution.

  • Spread - The spread/dispersion of data values describes how far apart the pieces of data are.

Sketching graphs can be a quick way of visualising the distribution of a dataset without accurately producing a graph. However, the x-axis must still be scaled correctly, otherwise distributions will be inaccurately skewed.
Teacher tip

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).

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6 Questions

Q1.
In which of these statistical graphs can the frequency of the data set be seen from the graph alone?
Correct answer: bar chart
line graph
pictogram
Correct answer: pie chart
Correct answer: scatter graph
Q2.
Which of these statistical graphs is best at showing the change in the value of something over time?
bar chart
Correct answer: line graph
pictogram
pie chart
scatter graph
Q3.
Which of the following statements is true when describing the mode of these four bar charts?
An image in a quiz
Data set A is bimodal.
Correct answer: Data set B is bimodal.
Correct answer: At least one data set is trimodal.
The highest modal frequency is 13.
Correct answer: The highest modal frequency is 14.
Q4.
Match the statements that summarise these bar charts to the value that end each sentence.
An image in a quiz
Correct Answer:The range of data set C is,13

13

Correct Answer:The range of data set D is,9

9

Correct Answer:The median of A, B, and C is,5

5

Correct Answer:The mode of data set D is,4

4

Q5.
How much larger is the mode of this dot plot compared to its mean?
An image in a quiz
Correct Answer: 2, two
Q6.
How much larger is the mean of this dot plot compared to its mode? Give your answer rounded to 1 decimal place.
An image in a quiz
Correct Answer: 0.6, 0.62, 0.615

6 Questions

Q1.
Which of these statements is valid when comparing the height of Alex in year 6 to the "average" height of other year 6s at his primary school?
An image in a quiz
Correct answer: Alex is taller than average because he is taller than the modal height.
Alex is taller than average because he is taller than the mean height.
Correct answer: Alex is shorter than average because he is shorter than the median height.
Correct answer: Alex is around average height because his height is close to frequent heights.
Alex is shorter than average because the maximum height is 150 cm
Q2.
Select the data sets which match the following statistical summary: a range of 14
An image in a quiz
Correct answer: dataset A
Correct answer: dataset B
dataset C
dataset D
Q3.
Which of these is a representative median of the data set that has following statistical summary: a mode at 54, a range of 14, a mean of approximately 50?
An image in a quiz
44
Correct answer: 51
54
58
Q4.
Sam asks 55 people how many times per month they visit the supermarket. Sam loses some of the data, but represents the rest on a bar chart. How many people's data did Sam lose? people
An image in a quiz
Correct Answer: 11, eleven
Q5.
Here is an incomplete bar chart for a data set. The range of the data set is 12 days. What is the maximum number of days per month that the people surveyed visited the supermarket? days
An image in a quiz
Correct Answer: 13, thirteen
Q6.
This bar chart has missing bars. 50 people were surveyed. The range is 7. The frequency of 11 days is 3 greater than the frequency of 10 days. Work out the frequency for 10 days.
An image in a quiz
Correct Answer: 5, 5 times, 5 times per month, five