Relative Frequency

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Elliott Fletcher

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Christian Lawson-Perfect	said	Ready to use	7 years, 8 months ago
Elliott Fletcher	said	Needs to be tested	7 years, 8 months ago
Vicky Hall	said	Has some problems	7 years, 8 months ago

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Christian Lawson-Perfect 7 years, 8 months ago

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Christian Lawson-Perfect 7 years, 8 months ago

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Elliott Fletcher 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Vicky Hall 7 years, 8 months ago

Gave some feedback: Has some problems

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Vicky Hall commented 7 years, 8 months ago

In part b), I would use metric units of measurement rather than imperial. Perhaps reword the question to say: the relative frequency of a student being taller than $y\mathrm{cm}$ is known to be $x$ . The final row of the table in part c) slightly out of sync with the other rows.

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Elliott Fletcher 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Elliott Fletcher 7 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Relative Frequency	Ready to use	Elliott Fletcher	20/11/2019 14:41
Hugh's copy of Relative Frequency	draft	Hugh O'Donnell	16/01/2018 13:47
Relative Frequency	draft	Chris Graham	08/08/2018 10:16
Relative Frequency	Needs to be tested	Lauren Frances Desoysa	21/08/2018 14:58
Michael's copy of Relative Frequency	draft	Michael Proudman	07/12/2021 09:49

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Question statement

The relative frequency of an outcome is the frequency of the outcome divided by the number of trials.

Give any introductory information the student needs.

			Name	Type	Generated Value

no_people	integer	110
free_range	integer	16
no_students	integer	20
rel_freq	number	0.65
dog	integer	27
cat	integer	43
hamster	integer	17
parrot	integer	29
n	integer	116

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(50..150 #10)

JME function reference

Description

Number of people asked in part a)

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

Can an exam override the value of this variable?

Generated value: `integer`

110

This variable doesn't seem to be used anywhere.

Advice

The relative frequency of an outcome is the frequency of the outcome divided by the number of trials.

a)

We are told that $\var{no_people}$ people were asked whether they preferred to buy free-range eggs or caged eggs in supermarkets and that $\var{free_range}$ of these people said that they preferred to buy free-range eggs.

To calculate the relative frequency of people who prefer buying free-range eggs we need the number of trials and the frequency of people who said that they preferred buying free-range eggs.

So, the number of trials in this situation is the number of people who were asked the question, which is $\var{no_people}$ .

The frequency of people who said that they preferred to buy free-range eggs is $\var{free_range}$ .

Therefore, the relative frequency of people who prefer buying free-range eggs is

$\frac{\var{free_range}}{\var{no_people}} = \var{dpformat({free_range/no_people}, 2)} \; (\text{rounded to $2$ decimal places}).$

b)

We are told that the relative frequency of a student being taller than $150$ cm is $\var{rel_freq}$ .

Here, we must use the formula for relative frequency in reverse in order to estimate the number of students in the class who are taller than $150$ cm.

As we are using relative frequency to calculate this number, our answer may not be completely accurate, therefore our answer will be an estimate of the actual number.

If we let $n$ denote the number of students in the class who are taller than $150$ cm and if there are $\var{no_students}$ students in the class then

$\begin{align} \frac{n}{\var{no_students}} &= \var{rel_freq}\\ n &= \var{rel_freq} \times \var{no_students}\\ &= \var{{rel_freq}*{no_students}}. \end{align}$

As $n$ represents a number of people we must round our value of $n$ to the nearest integer.

So, the estimated number of students in the class who are taller than $150$ cm is $\var{dpformat({rel_freq}*{no_students},0)}$ .

c)

Using the frequency table given in the question, we can calculate the sample size of the survey by adding together the frequencies of each of the different types of pets.

So, the sample size of the survey is

$\var{dog}+\var{cat}+\var{hamster}+\var{parrot} = \var{{dog}+{cat}+{hamster}+{parrot}}.$

ii)

To calculate the relative frequency of a person having a dog as a pet, we divide the frequency of people in the survey who had a dog as a pet by the sample size of the survey.

So, the relative frequency is

$\frac{\var{dog}}{\var{n}} = \var{dpformat({dog/n}, 2)} \; (\text{rounded to $2$ decimal places}).$

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Vicky Hall 7 years, 8 months ago

Vicky Hall commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Number entry

Advanced settings

a)

b)

c)

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Relative Frequency

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Elliott Fletcher 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Vicky Hall 7 years, 8 months ago

Vicky Hall commented 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

a)

b)

c)

Generated value: `integer`