Question

The following number of goals were scored by a team in 10matches:2,7,0,3,5,0,9,3,8,3. find the mean, Median and mode of these scores.

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Answer 1

I) Finding Mean:

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀⠀

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$\star\:\boxed{\sf{\pink{Mean = \bigg(\dfrac{Sum\; of\; all \; observation}{Total \; number\; of \; observation}\bigg)}}}$ ⠀

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$:\implies\sf Mean = \bigg(\dfrac{2 + 7 + 0 + 3 + 5 + 0 + 9 + 3 + 8 + 3}{10} \bigg) \\\\\\:\implies\sf Mean = \cancel\dfrac{40}{10} \\\\\\:\implies{\underline{\boxed{\frak{\pink{Mean = 4 \: goals}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\; required\; mean \; is \; \bf{4}.}}}$⠀⠀⠀⠀⠀⠀

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II) Finding Median:

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Median = 0, 0, 2, 3, 3, 3, 5, 7, 8, 9.

• Number of observation, n = 10.

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Therefore,

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$\star\;\boxed{\sf{\purple{Median = \dfrac{\bigg(\dfrac{n}{2}\bigg)^{th}\; observation \: + \; \bigg(\dfrac{n}{2} + 1 \bigg)^{th} \; observation}{2}}}}$

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Therefore,

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$:\implies\sf Median = \dfrac{\bigg(\dfrac{10}{2} \bigg)^{th} \: observation \; + \; \bigg(\dfrac{10}{2} + 1 \bigg)^{th}\; observation}{2} \\\\\\:\implies\sf Median = \bigg(\dfrac{5^{th} \; observation + 6^{th} \; observation}{2} \bigg) \\\\\\:\implies\sf Median = \bigg(\dfrac{3 + 3}{2}\bigg) \\\\\\:\implies\sf Median = \bigg(\dfrac{6}{2} \bigg) \\\\\\:\implies{\underline{\boxed{\frak{\purple{ Median = 3}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\; required\; median \; is \: \bf{3 }.}}}$⠀

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III) Finding Mode:

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀⠀

• Mode is the most appearing value.⠀

Therefore, ⠀

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• 3 is the most appearing value in the given observation. ⠀

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Hence, Mode = 3

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$\therefore{\underline{\sf{Hence,\; required\; mode \;is\; \bf{3 }.}}}$

Answer 2

$\dag\: \underline{\sf{AnsWer :}}$

In the given question we are provided two things that are :

• Sum of observations = 2, 7, 0, 3, 5, 0, 9, 3, 8, 3
• Number of observation = 10

And we are asked to find mean, median and mode of the given question. So, first we will find the mean of the given data :

$:\implies\sf Mean = \dfrac{Sum \: of \: observations}{No. \: of \: observations}$

$:\implies\sf Mean = \dfrac{2 + 7 + 0 + 3 + 5 + 0 + 9 + 3 + 8 + 3}{10}$

$:\implies\sf Mean = \dfrac{40}{10}$

$:\implies \underline{ \boxed{\sf Mean = 4}}$

Here, we have find the mean of the following data so now we can find the median of the given data. In order to calculate the median first arrange the data in ascending order :

• 0, 0, 2, 3, 3, 3, 5, 7, 8, 9
• Here, No. of observation (n) = 10 (even)

$\dashrightarrow\:\:\sf Median = \dfrac{ \left(\frac{n}{2} \right)^{ \tiny{th}} observation + \left(\frac{n}{2} + 1 \right)^{ \tiny{th}} observation}{2}$

$\dashrightarrow\:\:\sf Median = \dfrac{ \left(\frac{10}{2} \right)^{ \tiny{th}} observation + \left(\frac{10}{2} + 1 \right)^{ \tiny{th}} observation}{2}$

$\dashrightarrow\:\:\sf Median = \dfrac{ \left(5 \right)^{ \tiny{th}} observation + \left(\frac{10 + 2}{2} \right)^{ \tiny{th}} observation}{2}$

$\dashrightarrow\:\:\sf Median = \dfrac{ \left(5 \right)^{ \tiny{th}} observation + \left(\frac{12}{2} \right)^{ \tiny{th}} observation}{2}$

$\dashrightarrow\:\:\sf Median = \dfrac{ \left(5 \right)^{ \tiny{th}} observation + \left(6 \right)^{ \tiny{th}} observation}{2}$

$\dashrightarrow\:\:\sf Median = \dfrac{ 3 + 3}{2}$

$\dashrightarrow\:\:\sf Median = \dfrac{6}{2}$

$\dashrightarrow\:\: \underline{ \boxed{\sf Median = 3 }}$

Hence,the median of the given data is 3 and now we can calculate the mode of the given data :

• As we know that mode is nothing but most frequently occuring number in the given data. So, from the given data we have observed that most frequently occuring number is 3 . Hence, the mode of the given data is 3.