New
New
Year 10
•
Higher
Calculating the mean from a grouped frequency table
I can calculate the mean from a grouped frequency table.
New
New
Year 10
•
Higher
Calculating the mean from a grouped frequency table
I can calculate the mean from a grouped frequency table.
Lesson details
Key learning points
- The mean is a measure of central tendency.
- The mean can only be estimated with a grouped frequency table.
- Calculating this from a grouped frequency table may be easier when the data is very large.
Common misconception
That estimation is guessing.
Estimation is a process with each step being logical. In this case the estimation is necessary because some of the detail is lost in a grouped frequency table.
Keywords
Frequency - The frequency is the number of times an event occurs; or the number of individuals (people, animals etc.) with some specific property.
Interval - An interval is all the values between two points. e.g. 4 < x ≤ 10
Why the midpoint? Effectively we are using an estimate for the mean of the data within each interval. Get pupils to investigate what estimate would be most sensible for this mean. Randomly generate data within an interval multiple times, and with differing frequencies. Find the means and discuss.
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).
Video
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Starter quiz
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6 Questions
Q1.
The sum of the 10 data points in a data set is 180. The mean of this data set is .
Correct Answer: 18
18
Q2.
Match each summary statistic to its value for a data set of: 1, 3, 6, 10, 13, 15, 15.
Correct Answer:mean,9
mean -
9
Correct Answer:median,10
median -
10
Correct Answer:mode,15
mode -
15
Correct Answer:range,14
range -
14
Q3.
In total, many people are there in this data set?
4
8
9
Correct answer: 25
25
72
Q4.
The table shows the number of pets owned by some volunteers at an animal rescue centre. Calculate the mean number of pets.
2.44...
Correct answer: 5.5
5.5
44
80.66...
242
Q5.
This grouped frequency table shows the length of grass in different people’s gardens. What does the highlighted row of this grouped frequency table mean?
15 people had grass 20 cm long, and 15 people had grass 40 cm long.
15 people had grass 20 cm long.
Correct answer: 15 people had grass between 20 cm and 40 cm long.
15 people had grass between 20 cm and 40 cm long.
30 people had grass 15 cm long.
Q6.
The average expected range of this data set is .
Correct Answer: 580
580
Exit quiz
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6 Questions
Q1.
What is the midpoint of this interval?
2
3
30
Correct answer: 35
35
39
Q2.
An estimate for the total number of litres used by the 10 people who each used between 40 and 60 litres is litres.
Correct Answer: 500, 500 litres
500, 500 litres
Q3.
Which of these statements are correct?
$$a$$ has an estimated value of 405
Correct answer: $$a$$ has an estimated value of 2000
$$a$$ has an estimated value of 2000
Correct answer: $$b$$ has an estimated value of 7500
$$b$$ has an estimated value of 7500
$$b$$ has an estimated value of 75000
Estimates of $$a$$ and $$b$$ cannot be found
Q4.
A supermarket manager records the total number of shoppers each day for a month. The table shows her results.
The estimate for the total number of shoppers in this data set is shoppers.
Correct Answer: 5950, 5950 shoppers
5950, 5950 shoppers
Q5.
Both $$a$$ and $$b$$ are the totals of their columns. Which of these statements are correct?
$$a$$ = 3
Correct answer: $$a$$ = 62
$$a$$ = 62
$$b$$ = 3
$$b$$ = 170
Correct answer: $$b$$ = 2520
$$b$$ = 2520
Q6.
The table shows some pupils' marks in an exam. The estimated mean score to the nearest integer is marks.
Correct Answer: 54, 54 marks
54, 54 marks