Simon's copy of Averages (frequency table)

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Simon Thomas 6 years ago

Created this as a copy of Averages (frequency table).

Name	Status	Author	Last Modified
Averages (frequency table)	Ready to use	Julie Crowley	07/10/2016 21:41
Gemiddelde en mediaan met tabel	draft	Johan Maertens	11/12/2023 13:09
Simon's copy of Averages (frequency table)	draft	Simon Thomas	27/03/2019 09:30
Averages (frequency table)	Ready to use	Yvonne Wancke	03/05/2023 13:02
PRAC Averages (frequency table)	Ready to use	Yvonne Wancke	16/02/2021 17:28
Averages (frequency table) EXAM	Ready to use	Yvonne Wancke	12/01/2023 10:05
S2 EXAM Averages freq table	Ready to use	Yvonne Wancke	09/05/2023 10:44

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Question statement

Calculate the mean, the median and the mode for the following frequency table:

Class	0	1	2	3	4	5
Frequency	{f1}	{f2}	{f3}	{f4}	{f5}	{f6}

Give any introductory information the student needs.

			Name	Type	Generated Value

f1	integer	14
f2	integer	15
f3	integer	13
f4	integer	13
f5	integer	9
f6	integer	1

			Name	Type	Generated Value

cf2	integer	29
cf3	integer	42
cf4	integer	55
cf5	integer	64
tot	integer	65

			Name	Type	Generated Value

a1	integer	1
a2	integer	1
a3	integer	0
a4	integer	0
a5	integer	0
mp5	rational	65/2
median	integer	2

			Name	Type	Generated Value

			sfx	integer	121
			mn	rational	121/65

			Name	Type	Generated Value

			a	integer	1
			b	integer	5

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Advice

(a)

To find the mean use the formula $\frac{\Sigma fx}{\Sigma f}$

In other words

multiply each value by its corresponding frequency: Work out $0\times\var{f1}, 1\times \var{f2}, 2\times\var{f3}$ etc.
add up all of these: $(0\times\var{f1})+(1\times \var{f2})+(2\times\var{f3})+(3\times\var{f4}) +(4\times\var{f5})+(5\times\var{f6})=\var{sfx}$
divide by the sum of all the frequencies: Divide by $\var{f1}+\var{f2}+\var{f3}+\var{f4}+\var{f5}+\var{f6} = \var{f1+f2+f3+f4+f5+f6}$

In other words $\frac{(0\times\var{f1})+(1\times \var{f2})+(2\times\var{f3})+(3\times\var{f4}) +(4\times\var{f5})+(5\times\var{f6})}{\var{f1}+\var{f2}+\var{f3}+\var{f4}+\var{f5}+\var{f6}}$

$=\frac{\var{sfx}}{\var{tot}}=\var{precround(sfx/(tot),2)}$

(b)

The median is the "middle" value.

In a frequency table, the observations are already arranged in an ascending order. We can obtain the median by looking for the value in the middle position.

First add up the frequencies to find $n$ .

Case 1. When the sum of the frequencies is odd, then the median is the value at the $\frac{n+1}{2}^{th}$ position.
Case 2. When the sum of the frequencies is even, then the median is the mean of values at the positions $\frac{n}{2}^{th}$ and $\frac{n+2}{2}^{th}$ .

We need to add up the frequencies until we reach this value and then the class we land in is the median.

In our example, $n=\var{f1}+\var{f2}+\var{f3}+\var{f4}+\var{f5}+\var{f6}=\var{tot}$

Since $n$ is odd, the median is the value at the $\frac{n+1}{2}=\frac{\var{tot}+1}{2}^{th}$ position, i.e. value number $\var{(tot+1)/2}$

From our table, we can calculate the following cumulative frequencies:

Class	0	1	2	3	4	5
Frequency	{f1}	{f2}	{f3}	{f4}	{f5}	{f6}
Cum Freq	{f1}	{cf2}	{cf3}	{cf4}	{cf5}	{tot}

And by looking at our cumulative frequencies we can see that value number $\var{(tot+1)/2}$ occurs in class $\var{median}$ , which is therefore our median class.

(c)

The mode is the number which occurs most often. In other words the class with the highest frequency.

In this example, the mode is 1, since {f2} is the highest frequency.

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Simon's copy of Averages (frequency table)

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Taxonomy: mathcentre

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Simon Thomas 6 years ago

Error in variable testing condition

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Generated value: integer

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Generated value: `integer`