Question

Find the mean , median, and mode for the following : 3,4,3,6,3,2,4,3,8,​

Answer 1

Answer :-

• Mean of the given data = 4.
• Median of the given data = 3.
• Mode of the given data = 3.

To find :-

• The mean, median and mode for the given data :- 3, 4, 3, 6, 3, 2, 4, 3, 8.

Step-by-step explanation :-

• Let's find the mean, median and mode of the given data!

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Finding the mean :-

We know that :-

$\underline{\boxed{\sf Mean = \dfrac{Sum \: of \: all \: observations}{Number \: of \: observations}}}$

Here,

• Sum of all observations = 3 + 4 + 3 + 6 + 3 + 2 + 4 + 3 + 8.

• Number of observations = 9.

Hence,

$\rm Mean = \dfrac{3 + 4 + 3 + 6 + 3 + 2 + 4 + 3 + 8}{9}$

Adding all the numbers,

$\rm Mean = \cancel{\dfrac{36}{9}}$

Dividing 36 by 9,

$\overline{\boxed{\rm Mean = 4}}$

Therefore,

• Mean of the given data is 4.

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Finding the median :-

• Here, the number of observations is 9, which is odd.

We know that :-

$\underline{\boxed{\sf Median = \dfrac{n + 1}{2} \: th \: observation, if \: n \: is \: odd}}$

Where,

• n = Number of observations.

Hence,

$\rm Median = \dfrac{9 + 1}{2}\: th \: observation$

Adding 1 to 9,

$\rm Median = \cancel{\dfrac{10}{2}} \: th \: observation$

Dividing 10 by 2,

$\overline{\boxed{\rm Median = 5th \: observation}}$

Arranging the data in ascending order,

• 2, 3, 3, 3, 3, 4, 4, 6, 8.

Here,

• The 5th observation is 3.

Therefore,

• Median of the given data is 3.

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Finding the mode :-

We know that :-

• The number that has the highest frequency in the data, is it's mode.

Here,

• 3 occurs more times than any other number and it's frequency is 4.

Therefore,

• Mode of the given data is 3.

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