Michael's copy of Complete a frequency table and find the measures of central tendency

Error

There was an error loading the page.

Contributors

History

○

Michael Proudman 6 years, 5 months ago

Created this as a copy of Complete a frequency table and find the measures of central tendency.

Name	Status	Author	Last Modified
Complete a frequency table and find the measures of central tendency	Ready to use	Stanislav Duris	15/02/2021 10:10
Statistics - Frequency Tables, Measures of central tendency and Spread	draft	Paul Hancock	26/07/2018 01:45
Measures of central tendency from frequency tables	Needs to be tested	Lauren Frances Desoysa	02/10/2018 13:07
Nazim's copy of Complete a frequency table and find the measures of central tendency	draft	Nazim Khan	15/11/2018 03:45
Michael's copy of Complete a frequency table and find the measures of central tendency	draft	Michael Proudman	07/12/2021 09:49
Michael's copy of Complete a frequency table and find the measures of central tendency	draft	Michael Proudman	07/12/2021 09:49
Complete a frequency table and find the measures of central tendency	draft	Xiaodan Leng	10/07/2019 23:58
Probability: two-way table 2 - conditional	Ready to use	Ruth Hand	16/01/2023 14:32

There are 26 other versions that do you not have access to.

Question statement

30 random students were asked about the number of siblings they have. These are their responses:

$\var{a[0]}$	$\var{a[1]}$	$\var{a[2]}$	$\var{a[3]}$	$\var{a[4]}$	$\var{a[5]}$	$\var{a[6]}$	$\var{a[7]}$	$\var{a[8]}$	$\var{a[9]}$
$\var{a[10]}$	$\var{a[11]}$	$\var{a[12]}$	$\var{a[13]}$	$\var{a[14]}$	$\var{a[15]}$	$\var{a[16]}$	$\var{a[17]}$	$\var{a[18]}$	$\var{a[19]}$
$\var{a[20]}$	$\var{a[21]}$	$\var{a[22]}$	$\var{a[23]}$	$\var{a[24]}$	$\var{a[25]}$	$\var{a[26]}$	$\var{a[27]}$	$\var{a[28]}$	$\var{a[29]}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	list	List of 30 items
mean	number	1.6666666667
median	number	2
m	list	[ 2 ]
mode	integer	2
freq	list	[ 7, 7, 8, 5, 3, 0, 0 ]
as	list	The variable name `as` is reserved.

			Name	Type	Generated Value

a1	list	List of 30 items
modea1	list	[ 2 ]
a2	list	List of 30 items
modea2	list	[ 0 ]
a3	list	List of 30 items
modea3	list	[ 1 ]

Automatically regenerate variables?

Name

Data type

Value

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

JME function reference

Description

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`

[ 3, 3, 2, 2, 0, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 4, 2, 0, 0, 2, 0, 3, 1, 0, 0, 2, 4, 4, 0, 1 ]

← Depends on:

a1
a2
a3
modea1
modea2

→ Used by:

as
freq
m
mean
median

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Complete the following frequency table:

Number of siblings	Frequency
$0$	Gap 0.
$1$	Gap 1.
$2$	Gap 2.
$3$	Gap 3.
$4$	Gap 4.
$5$	Gap 5.
$6$	Gap 6.
Total	$30$

Advice

a)

Organising the data in a frequency table helps to make mistakes less likely when calculating statistics from our data, summarising the responses all in one place with fewer numbers.

Each row of the frequency column gives the number of students with the corresponding number of siblings.

Number of siblings	Frequency
$0$	$\var{freq[0]}$
$1$	$\var{freq[1]}$
$2$	$\var{freq[2]}$
$3$	$\var{freq[3]}$
$4$	$\var{freq[4]}$
$5$	$\var{freq[5]}$
$6$	$\var{freq[6]}$
Total	$30$

Always remember to check whether your frequency column adds up to the total (here, it is $30$) to make sure you have not left out any responses.

b)

Mean

The mean number of siblings is the total number of siblings, $\sum x$, divided by the number of students in the sample, $n$.

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

The total number of students $n$ is $30$.

Therefore the mean is

\begin{align}
\bar{x} &= \frac{\sum x}{n} \\
&= \frac{\var{sum(a)}}{30} \\
&= \var{mean} \text{.}
\end{align}

Rounding the answer to 2 decimal places, we get $\var{precround(mean, 2)}$.

Mode

The mode is the value with the highest frequency. Here, the mode is $\var{mode}$ siblings, with frequency $\var{freq[mode]}$.

Median

The median is the "middle" value in the sample, when arranged in numerical order.

Since $n = 30$, we have two middle values in this data (15^th and 16^th place). We can count from the top of the table until we locate rows where these middle values lie, as the numbers in the table are already sorted by order.

Here, both $15$^th and $16$^th value lie in the row $\var{as[14]}$.Here, the $15$^th value lies in the row $\var{as[14]}$ while the $16$^th value lies in the row $\var{as[15]}$.

As $15$^th value $= 16$^th value $= \var{as[14]}$, the median is $\var{as[14]}$.As $15$^th value $= \var{as[14]}$ and $16$^th value $= \var{as[15]}$, we need to find their mean.

\[ \displaystyle \begin{align} \frac{\var{as[14]} + \var{as[15]}}{2} &= \frac{\var{as[14] + as[15]}}{2} \\&= \var{median} \text{.} \end{align}\]

This is the median for this data.

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?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is not used in any exams.

Loading...

Error

Michael's copy of Complete a frequency table and find the measures of central tendency

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

a)

b)

Mean

Mode

Median

Loading...

Error

Michael's copy of Complete a frequency table and find the measures of central tendency

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

Mean

Mode

Median

Generated value: `list`