Starter quiz
- Match each summary statistic to its definition.
- Mode⇔Most common data value ✓
- Median⇔The middle (central) piece of data when the data are in order ✓
- Mean⇔Sum of the data values divided by the number of values ✓
- Range⇔Highest data value − lowest data value ✓
- Sam collects data on how many sweets are in 9 different packs. The results are 13, 12, 11, 9, 8, 8, 10, 8, 11. The modal number of sweets is ______.
- '8' ✓
- Sam collects data on how many sweets are in 9 different packs. The results are 13, 12, 11, 9, 8, 8, 10, 8, 11. The median number of sweets is ______.
- '10' ✓
- Sam collects data on how many sweets are in 9 different packs. The results are 13, 12, 11, 9, 8, 8, 10, 8, 11. The mean number of sweets is ______.
- '10' ✓
- Sam collects data on how many sweets are in 9 different packs. The results are 13, 12, 11, 9, 8, 8, 10, 8, 11. The range in the number of sweets is ______.
- '5' ✓
- This set of data has two values missing. , 5, 6, 7, 8, , 5, 6, 8. The mean of the data is 6, the mode is 5 and the median is 6. Select the missing data values.
- 3
- 4 ✓
- 5 ✓
- 6
- 7
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Exit quiz
- Select all the types of average.
- frequency
- mean ✓
- median ✓
- mode ✓
- range
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Data has been collected and processed about the number of sweets per packet in 3 different multipacks. The company claims ‘an average of 12 sweets per pack’. Which multipack best supports the claim?- Multipack A
- Multipack B ✓
- Multipack C
- None of the multipacks
- All of the multipacks
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Izzy and Jun compare their scores in their last 10 maths tests. The tables show the summary statistics. Select the statements that are correct about their mean scores.- Izzy’s variety of scores is greater than Jun’s.
- Izzy’s middle score was lower than Jun’s.
- Izzy’s average, typical score is higher than Jun’s. ✓
- Izzy’s most common score is the higher than Jun’s.
- The total of Izzy's maths scores is higher than Jun's ✓
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- Izzy and Jun compare their scores in their last 10 maths tests. The tables show the summary statistics. Select the statement that is correct about their median scores.
- Izzy’s variety of scores is greater than Jun’s.
- Izzy’s middle score was lower than Jun’s. ✓
- Izzy’s average, typical score is higher than Jun’s.
- Izzy’s most common score is the higher than Jun’s.
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- Jacob went to the library and surveyed 10 adults in the library to find out how many books they read in a month. The mean was 2 books. Jacob says, "All adults read 2 books a month." Is he correct?
- Yes, the sample is representative of all adults.
- Yes, 2 books is a reasonable average.
- No, Jacob's sample is biased as people in the library are more likely to read. ✓
- No, Jacob needs to survey more people from the library to be sure.
- No, Jacob needs to survey people from the library on different days to be sure.
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The table of summary statistics shows the number of days of air frost each day in December over the last 10 years. Select the correct statements.- There is more variability in the number of frosty days in York.
- York is likely to be colder in December than Bristol as the average is higher. ✓
- Bristol has more frosty days than York as the range is higher.
- There is more variability in the number of frosty days in Bristol. ✓
- Bristol is likely to be colder in December than York as the range is higher.
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Worksheet
Presentation
Video
Lesson Details
Key learning points
- A statistical summary involves the mean, median, mode and range.
- Each summary gives us different insights into a data set.
- Conclusions may be affected by the way the data was collected.
Common misconception
Pupils may believe that as mean, median and mode are all averages that they are all as useful as each other for every data set.
Using non qualitative data to show that the mean and median cannot be calculated, so the mode would be the only option. Showing data sets that have the same mean value but are considerably different to each other.
Keywords
Arithmetic mean - The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.
Median - The median is the central (middle) piece of data when the data are in numerical order. It is a measure of central tendency representing the average of the values.
Mode - The mode is the most frequent value. It is a measure of central tendency representing the average of the values.
Range - The range is a measure of spread. It is found by finding the difference between the highest and lowest values.
Population - The population is the entire set of people, creatures, plants or items that make up the whole group which is being studied.