Question

Q2. The following number of goals were scored by a team in ten matches 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

Answer :

mean = 4

median = 3

mode = 3

Mean = Sum of all observations

number of observations

median refers to the value which lies in the middle of the data( when arranged in an increasing or decreasing order)

The mode of a set of observations is the observation that occurs most often.

Answer 2

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REQUIRED MEAN, MEDIAN AND MODE ARE 4, 3 & 3 RESPECTIVELY

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$\huge{\fbox{\fbox{\color{lime}{Finding Mean}}}}$

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

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$\therefore{\underline{\sf{Required\; mean \; is \; \bf{4}.}}}$

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$\huge{\fbox{\fbox{\color{lime}{Finding Median}}}}$

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Scores = 0, 0, 2, 3, 3, 3, 5, 7, 8, 9 (in increasing order)

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

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$\therefore{\underline{\sf{Required\; median \; is \: \bf{3 }.}}}$

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$\huge{\fbox{\fbox{\color{lime}{Finding Mode}}}}$

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

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Mode is the most appearing value.⠀

Therefore, 3 is the most appearing value in the given observation. ⠀

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$\therefore{\underline{\sf{Required\; mode \;is\; \bf{3 }.}}}$

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