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Year 10
Foundation

Checking understanding of statistical problems

I can evaluate different statistical measures to draw conclusions about a data set.

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New
New
Year 10
Foundation

Checking understanding of statistical problems

I can evaluate different statistical measures to draw conclusions about a data set.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A statistical summary involves the mean, median, mode and range.
  2. Each summary gives us different insights into a data set.
  3. 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.

If you feel your pupils need some practice with calculating the summary statistics you could get them to work them out before revealing them on the slide deck.
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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Starter quiz

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6 Questions

Q1.
Match each summary statistic to its definition.
Correct Answer:Mode,Most common data value

Most common data value

Correct Answer:Median,The middle (central) piece of data when the data are in order

The middle (central) piece of data when the data are in order

Correct Answer:Mean,Sum of the data values divided by the number of values

Sum of the data values divided by the number of values

Correct Answer:Range,Highest data value − lowest data value

Highest data value − lowest data value

Q2.
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 .
Correct Answer: 8, eight, 8 sweets, eight sweets
Q3.
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 .
Correct Answer: 10, 10 sweets, ten sweets , ten
Q4.
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 .
Correct Answer: 10, 10 sweets, ten, ten sweets
Q5.
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 .
Correct Answer: 5, five, 5 sweets, five sweets
Q6.
This set of data has two values missing. $$\square$$, 5, 6, 7, 8, $$\square$$, 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
Correct answer: 4
Correct answer: 5
6
7

Exit quiz

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6 Questions

Q1.
Select all the types of average.
frequency
Correct answer: mean
Correct answer: median
Correct answer: mode
range
Q2.
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?
An image in a quiz
Multipack A
Correct answer: Multipack B
Multipack C
None of the multipacks
All of the multipacks
Q3.
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.
An image in a quiz
Izzy’s variety of scores is greater than Jun’s.
Izzy’s middle score was lower than Jun’s.
Correct answer: Izzy’s average, typical score is higher than Jun’s.
Izzy’s most common score is the higher than Jun’s.
Correct answer: The total of Izzy's maths scores is higher than Jun's
Q4.
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.
An image in a quiz
Izzy’s variety of scores is greater than Jun’s.
Correct answer: 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.
Q5.
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.
Correct answer: 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.
Q6.
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.
An image in a quiz
There is more variability in the number of frosty days in York.
Correct answer: 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.
Correct answer: 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.