Question

Find the mean, median and mode of the following marks of 15 students on
screening test (out of 20): 2,5, 3,3,0, 18, 5, 7, 11, 15, 1, 13, 0,8,0​

Answer 1

I) Finding Mean:

Mean = 0, 0, 0, 1, 2, 3, 3, 5, 5, 7, 8, 11, 13, 15, 18.

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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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Therefore,

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$:\implies\sf Mean = \bigg(\dfrac{ 0 + 0 + 0 + 1 + 2 + 3 + 3 + 5 + 5 + 7 + 8 + 11 + 13 + 15 + 18}{15}\bigg) \\\\\\:\implies\sf Mean = \bigg(\dfrac{91}{15}\bigg) \\\\\\:\implies{\underline{\boxed{\frak{\pink{Mean = 6.04}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\; required\; mean \; is \; \bf{ 6.04}.}}}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

II) Finding Mode:

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

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

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Therefore,

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• n = 15 (Number of observation)

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$:\implies\sf Median = \bigg(\dfrac{15 + 1}{2}\bigg) \\\\\\:\implies\sf Median = \bigg(\dfrac{16}{2} \bigg) \\\\\\:\implies\sf Median = 8th \; term \\\\\\:\implies{\underline{\boxed{\frak{\purple{ Median = 5}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence,\; required\; median \; is \: \bf{5 }.}}}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

III) Finding Mode:

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

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• Mode is the most appearing value.

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Therefore,

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• 0 is the most appearing value in the given observation.

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Hence, Mode = 0.

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$\therefore{\underline{\sf{Hence,\; required\; mode \;is\; \bf{0 }.}}}$

Answer 2

Answer:

Given :-

Observation

2,5, 3,3,0, 18, 5, 7, 11, 15, 1, 13, 0,8,0

To Find :-

• Mean
• Median
• Mode

Solution :-

As we know that

Mean = Sum of observation/Total no. of Observation

Mean = 2 + 5 + 3 + 3 + 0 + 18 + 5 + 7 + 11 + 15 + 1 + 13 +0 8 + 0/15

Mean = 91/15

Mean = 6.04

Now,

Median = n + 1/2

Median = 15 + 1/2

Median = 16/2

Median = 8th term

Now,

0 appears most (3) times.

Mode = 0

Conclusion :-

$\fbox{Mean = 6.04}$

$\fbox{Median = 5}$

$\fbox{Mode = 0}$