069. Summarising Numerical Data
Learning Intentions
- To understand that numerical data can be summarised as a single number by finding its range, mean, median or mode
- Solve the range of a set of numerical data
- find the mean, median and mode of a set of numerical data
Pre-requisite Summary
- Understand that numerical data consists of numbers that can be counted or measured
- Be able to order a set of numbers from smallest to largest
- Recall addition facts and be able to find a total
- Understand division as sharing a total equally
- Know how to Identify the largest and smallest values in a data set
- Understand that some data values may repeat
- Be able to count how many values are in a data set
- Know that different summary measures Describe different features of the data
Worked Examples
Worked Example 1
A set of numerical data is:
a) Find the range.
b) Find the mode.
c) Explain what each summary tells you about the data.
Worked Example 2
A set of numerical data is:
a) Find the mean.
b) Find the median.
c) Explain how the mean and median are different.
Worked Example 3
A set of numerical data is:
a) Order the data if needed.
b) Find the median.
c) Find the mode.
Worked Example 4
A set of numerical data is:
a) Find the range.
b) Find the mean.
c) Find the median.
Worked Example 5
A set of numerical data is:
a) Find the range.
b) Find the mean.
c) Find the median and mode.
Worked Example 6
The test scores are:
a) Find the range.
b) Find the mean, median and mode.
c) Decide which value is the most frequent.
Problems
Problem 1
A set of numerical data is:
a) Find the range.
b) Find the mode.
c) Explain what each summary tells you about the data.
Problem 2
A set of numerical data is:
a) Find the mean.
b) Find the median.
c) Explain how the mean and median are different.
Problem 3
A set of numerical data is:
a) Order the data if needed.
b) Find the median.
c) Find the mode.
Problem 4
A set of numerical data is:
a) Find the range.
b) Find the mean.
c) Find the median.
Problem 5
A set of numerical data is:
a) Find the range.
b) Find the mean.
c) Find the median and mode.
Problem 6
The test scores are:
a) Find the range.
b) Find the mean, median and mode.
c) Decide which value is the most frequent.
Exercises
Understanding and Fluency
Exercise 1.
Find the range of each data set:
a)
b)
c)
Exercise 2.
Find the mode of each data set:
a)
b)
c)
Exercise 3.
Find the mean of each data set:
a)
b)
c)
Exercise 4.
Find the median of each data set:
a)
b)
c)
Exercise 5.
Find the range, mean, median and mode of each data set:
a)
b)
c)
Exercise 6.
Find the range, mean, median and mode of each data set:
a)
b)
c)
Exercise 7.
For each data set, first order the values, then find the median:
a)
b)
c)
Exercise 8.
Mixed practice:
a) Find the range of
b) Find the mean of
c) Find the median of
d) Find the mode of
Reasoning
Exercise 9.
Explain why the range is found by subtracting the smallest value from the largest value.
Exercise 10.
A student says the mode of
Exercise 11.
Explain why the data should be ordered before finding the median.
Exercise 12.
A student adds the values in a data set and forgets to divide by the number of values when finding the mean. Explain why this is incorrect.
Exercise 13.
Explain the difference between the mean and the median.
Exercise 14.
A student says every data set must have exactly one mode. Explain why this is incorrect.
Problem-solving
Exercise 15.
The numbers of books read by students in a week are:
Exercise 16.
The daily temperatures for one week are:
Exercise 17.
The scores in a quiz are:
Exercise 18.
The numbers of goals scored by a team in six games are:
Exercise 19.
The times in minutes taken to finish a task are:
Exercise 20.
A class recorded the numbers of pets owned by students:
Potential Misunderstandings
- Students may confuse the range with the largest value rather than the difference between the largest and smallest values
- Students may think the mode is always the biggest number rather than the most frequent value
- Students may forget to order the data before finding the median
- Students may Choose the middle position incorrectly when there is an even number of values
- Students may forget that the mean requires dividing the total by the number of data values
- Students may think every data set has a mode
- Students may confuse the median with the mean because both describe a central value
- Students may make arithmetic errors when adding the data or dividing to find the mean