NC SP Difference between mean and median (10+)

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Ed questions to share :

Adelle Colbourn

said

Ready to use

4 years, 11 months ago

History

○

Adelle Colbourn 4 years, 5 months ago

Published this.

○

Adelle Colbourn 4 years, 11 months ago

Gave some feedback: Ready to use

○

Adelle Colbourn 5 years, 3 months ago

Created this.

There is only one version of this question that you have access to.

There are 2 other versions that do you not have access to.

Question statement

A random sample of 10 residents from Sydney were asked how many times they had watched a movie at a cinema last year.

Here are their responses:

$\var{a[0]}$

$\var{a[1]}$

$\var{a[2]}$

$\var{a[3]}$

$\var{a[4]}$

$\var{a[5]}$

$\var{a[6]}$

$\var{a[7]}$

$\var{a[8]}$

$\var{a[9]}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	list	List of 10 items
a_s	list	List of 10 items
mean	number	2.8
median	number	2.5

			Name	Type	Generated Value

modea1	list	[ 3 ]
modea2	list	[ 2, 6, 8 ]
a1	list	List of 10 items
a2	list	List of 10 items
a3	list	List of 10 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))

JME function reference

Description

The final list.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 0, 6, 3, 3, 1, 2, 8, 3, 2, 0 ]

← Depends on:

a1
a2
a3
modea1
modea2

→ Used by:

a_s
mean
median

Statement
Advice

Advice

The mean is the sum of all the responses ($\sum x$) divided by the number of responses ($n$).

Here, $n = 10$.

\begin{align}
\sum x &= \var{a[0]} + \var{a[1]} +\var{a[2]} +\var{a[3]} +\var{a[4]} +\var{a[5]} +\var{a[6]} +\var{a[7]} +\var{a[8]} +\var{a[9]} \\
&= \var{sum(a)} \text{.}
\end{align}

Therefore we calculate the mean

\begin{align}
\overline{x} &= \frac{\sum x}{n} \\[0.5em]
&= \frac{\var{sum(a)}}{10} \\[0.5em]
&= \var{mean} \text{.}
\end{align}

The median is the middle value. We need to sort the list in order:

\[ \var{a_s[0]}, \quad \var{a_s[1]}, \quad \var{a_s[2]}, \quad \var{a_s[3]}, \quad \var{a_s[4]}, \quad \var{a_s[5]}, \quad \var{a_s[6]}, \quad \var{a_s[7]}, \quad \var{a_s[8]}, \quad \var{a_s[9]}\]

There is an even number of responses, so there are two numbers in the middle (5^th and 6^th place). To find the median, we need to find the mean of these two numbers $\var{a_s[4]}$ and $\var{a_s[5]}$:

\begin{align}
\frac{\var{a_s[4]} + \var{a_s[5]}}{2} &= \frac{\var{a_s[4] + a_s[5]}}{2} \\
&= \var{median} \text{.}
\end{align}

To find the difference between the mean and the median, we subtract the two values:

Since we require a positive number, we subtract the median from the mean.

mean - median = {mean} - {median} = {mean-median}

Finally, check that we have answered to one decimal place.

The difference between the mean and the median is {abs(precround({mean-median},1))}.

Since we require a positive number, we subtract the mean from the median.

median - mean = {median} - {mean} = {median - mean}

Finally, check that we have answered to one decimal place.

The difference between the mean and the median is {abs(precround({mean-median},1))}.

However, the mean and the median are equal.

Therefore the difference between the mean and the median is 0.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Timed Practice Quiz by Adelle Colbourn in Ed questions to share.
Untimed Practice questions by Adelle Colbourn in Ed questions to share.
Practice questions from menu by Adelle Colbourn in Ed questions to share.
Timed Practice Quiz v2 by Adelle Colbourn in Odds and Ends.
Timed Practice Quiz v3 by Adelle Colbourn in Odds and Ends.
Education Discipline Page questions OLD by Adelle Colbourn in Ed questions to share.
Lantite (Numeracy) 75 minute practice quiz by Ben Brawn in LANTITE (Numeracy).

Loading...

Error

NC SP Difference between mean and median (10+)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Adelle Colbourn 4 years, 5 months ago

Adelle Colbourn 4 years, 11 months ago

Adelle Colbourn 5 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Number entry

Advanced settings

Loading...

Error

NC SP Difference between mean and median (10+)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Adelle Colbourn 4 years, 5 months ago

Adelle Colbourn 4 years, 11 months ago

Adelle Colbourn 5 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Number entry

Advanced settings

Generated value: `list`