Question

Find the mean, median, mode and range of the given data:
4, 5, 4, 3, 4, 6, 4, 5

Answer 1

Answer:

hope it's helpful to you

Answer 2

~Mean is defined as the average or central value

It is given as :-

${\underline{\boxed{\sf{\color{orange}{\bull \:mean=\frac{sum\:of \:observations}{no\:.of\: observation}}}}}}$

$\sf{ \to sum \: of \: observations= 4+5+4+3+4+6+ 4+5}$

$\sf{ \to sum \: of \: the \:observations =35}$

$\sf{ \to\:No\: .of \:observation= 8}$

$\sf{ \implies \: Mean = \frac{35}{8}} \\ \\\sf{ \implies \: \red{Mean=4.375}}$

✏️Therfore mean is 4.375

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Now, let us find the median of the given data.

~Median is defined as a value of a variable which divides the data into two equal parts.

~the first most important step to obtain the median is that data should be arranged in an ascending or descending order.

$\mathtt{ \bull\:Ascending\:order} \\\pink{3,4,4,4,4,5,5,6}$

Condition for individual series:-

⇝If the value of N is odd then simply the value of median is:-

$\mathtt{ \to \frac{(N+1)}{2}^{th}term}$

⇝If the value of N is even, then the formula is :-

$\mathtt{Median = \frac{[ size\:of \:\frac{N}{2} \: term+\: size\: of\: (\frac{N}{2}+ 1)^{th}\:term]}{2}}$

Here the n= 8, which means even.

⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀

$\sf{ \implies Median = \frac{\frac{8}{2}+ (\frac{8}{2}+1)}{2}}\\ \\ \sf{ \implies \frac{4^{th}term+5^{th}term}{2}}\\ \\ \sf{ \implies \frac{4+4}{2}}\\ \\ \sf{\implies \frac{8}{2} }\\ \\ \sf{\implies \red{4^{th} term}}$

⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀

✏️So 4th term is the median of the given data and 6th term is 4.

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Now let us find the mode of the given data.

⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀

~The observation Which has the highest frequency in data is called Mode.

⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀

Data️️️️️ ⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀Frequency

3⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀1

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4⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀4

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5⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀⠀⠀⠀⠀️️️️️️⠀️️️️️️2

_______________________

6⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀⠀⠀⠀⠀️️️️️️⠀️️️️️️1

_______________________

⠀⠀⠀⠀️️️️️️⠀️️️️️️⠀

We observe that 4 has the highest frequency.

✏️So 4 is the mode of the given data.

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Now let us find Range of the data

~Range is calculated by subtracting the smallest observations from the highest observation.

• Highest observation= 6
• Lowest observation= 3

$\sf{ \implies Range =6-3 } \\ \\ \sf{ \implies \pink{ Range=3}}$

Therefore the Range of the given data is 3.

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