Analysing different statistical representations | Maths

Starter quiz

In which of these statistical graphs can the frequency of the data set be seen from the graph alone?
- bar chart ✓
- line graph
- pictogram
- pie chart ✓
- scatter graph ✓
Which of these statistical graphs is best at showing the change in the value of something over time?
- bar chart
- line graph ✓
- pictogram
- pie chart
- scatter graph
Which of the following statements is true when describing the mode of these four bar charts?
- Data set A is bimodal.
- Data set B is bimodal. ✓
- At least one data set is trimodal. ✓
- The highest modal frequency is 13.
- The highest modal frequency is 14. ✓
Match the statements that summarise these bar charts to the value that end each sentence.
- The range of data set C is
  
  ⇔
  
  13 ✓
- The range of data set D is
  
  ⇔
  
  9 ✓
- The median of A, B, and C is
  
  ⇔
  
  5 ✓
- The mode of data set D is
  
  ⇔
  
  4 ✓
How much larger is the mode of this dot plot compared to its mean? ______
- '2' ✓
How much larger is the mean of this dot plot compared to its mode? Give your answer rounded to 1 decimal place. ______
- '0.6' ✓

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?
- 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.
- Alex is shorter than average because he is shorter than the median height. ✓
- 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
Select the data sets which match the following statistical summary: a range of 14
- dataset A ✓
- dataset B ✓
- dataset C
- dataset D
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?
- 44
- 51 ✓
- 54
- 58
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
- '11' ✓
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
- '13' ✓
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.
- '5' ✓

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

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.

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.