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
find the range of a set of numerical data
find the mean, median and mode of a set of numerical data

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

A set of numerical data is: $4, 7, 7, 9, 12$
a) Find the range.
b) Find the mode.
c) Explain what each summary tells you about the data.

A set of numerical data is: $6, 8, 10, 12, 14$
a) Find the mean.
b) Find the median.
c) Explain how the mean and median are different.

A set of numerical data is: $3, 5, 5, 6, 9, 11$
a) Order the data if needed.
b) Find the median.
c) Find the mode.

A set of numerical data is: $2, 4, 6, 8, 10, 12$
a) Find the range.
b) Find the mean.
c) Find the median.

A set of numerical data is: $7, 9, 9, 10, 12, 12, 12, 15$
a) Find the range.
b) Find the mean.
c) Find the median and mode.

The test scores are: $11, 13, 15, 15, 16, 18, 20$
a) Find the range.
b) Find the mean, median and mode.
c) Decide which value is the most frequent.

A set of numerical data is: $5, 8, 8, 10, 13$
a) Find the range.
b) Find the mode.
c) Explain what each summary tells you about the data.

A set of numerical data is: $4, 6, 8, 10, 12$
a) Find the mean.
b) Find the median.
c) Explain how the mean and median are different.

A set of numerical data is: $2, 4, 4, 7, 9, 10$
a) Order the data if needed.
b) Find the median.
c) Find the mode.

A set of numerical data is: $1, 3, 5, 7, 9, 11$
a) Find the range.
b) Find the mean.
c) Find the median.

A set of numerical data is: $6, 8, 8, 9, 11, 11, 11, 14$
a) Find the range.
b) Find the mean.
c) Find the median and mode.

The test scores are: $10, 12, 14, 14, 17, 19, 21$
a) Find the range.
b) Find the mean, median and mode.
c) Decide which value is the most frequent.

Find the range of each data set:
a) $3, 6, 8, 10, 12$
b) $5, 5, 7, 9, 14$
c) $11, 13, 15, 18, 20$
Find the mode of each data set:
a) $4, 6, 6, 7, 9$
b) $2, 3, 3, 3, 8$
c) $10, 12, 12, 15, 15, 15$
Find the mean of each data set:
a) $2, 4, 6, 8, 10$
b) $5, 7, 9, 11, 13$
c) $6, 8, 8, 10, 13$
Find the median of each data set:
a) $1, 3, 5, 7, 9$
b) $4, 6, 8, 10, 12, 14$
c) $2, 4, 4, 7, 9, 10$
Find the range, mean, median and mode of each data set:
a) $3, 5, 5, 6, 9$
b) $4, 6, 8, 8, 10, 12$
c) $7, 7, 9, 10, 10, 10, 13$
Find the range, mean, median and mode of each data set:
a) $2, 5, 7, 7, 8, 10$
b) $6, 8, 9, 9, 11, 14$
c) $1, 4, 4, 4, 6, 8, 9$
For each data set, first order the values, then find the median:
a) $9, 4, 7, 7, 2$
b) $12, 6, 10, 8, 14, 4$
c) $5, 3, 9, 3, 11, 7$
Mixed practice:
a) Find the range of $8, 11, 13, 17, 20$
b) Find the mean of $4, 6, 8, 10, 12$
c) Find the median of $2, 3, 5, 7, 9, 11$
d) Find the mode of $6, 6, 7, 8, 8, 8, 9$

Explain why the range is found by subtracting the smallest value from the largest value.
A student says the mode of $3, 4, 5, 6$ is $6$ because it is the largest value. Explain the mistake.
Explain why the data should be ordered before finding the median.
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.
Explain the difference between the mean and the median.
A student says every data set must have exactly one mode. Explain why this is incorrect.

The numbers of books read by students in a week are: $1, 2, 2, 3, 5, 7$ . Find the range, mean, median and mode.
The daily temperatures for one week are: $18, 20, 20, 21, 23, 24, 26$ . Find the range, mean, median and mode.
The scores in a quiz are: $6, 8, 8, 9, 10, 10, 10, 12$ . Find the range, mean, median and mode.
The numbers of goals scored by a team in six games are: $0, 1, 2, 2, 4, 5$ . Find the range, mean, median and mode.
The times in minutes taken to finish a task are: $12, 15, 15, 18, 20, 24$ . Find the range, mean, median and mode.
A class recorded the numbers of pets owned by students: $0, 1, 1, 2, 2, 2, 4, 5$ . Find the range, mean, median and mode.

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