Question

Find the mean and meadian of the following 12,14,10,9,11,16​

Answer 1

Solution!!

Observations = 12, 14, 10, 9, 11, 16

The first thing which we have to do is arrange the observations in ascending order.

Observations = 9, 10, 11, 12, 14, 16

Total number of observations = 6

Let's find out the mean first.

→ Mean = (Sum of all observations) ÷ (Total number of observations)

→ Mean = (9 + 10 + 11 + 12 + 14 + 16) ÷ (6)

→ Mean = (72) ÷ (6)

Mean = 12

Now, we're gonna find the median. There are different ways to find the median. The formula to find the median of odd number of observations is different from the formula to find the median of even number of observations. In this case, the number of observations is 6. So, we will use the formula to find the median of even number of observations.

→ Median = [(n/2)th term + {(n/2) + 1}th term] ÷ 2

Here n is the total number of observations.

→ Median = [(6/2)th term + {(6/2) + 1}th term] ÷ 2

→ Median = [3rd term + 4th term] ÷ 2

→ Median = [11 + 12] ÷ 2

→ Median = 23 ÷ 2

Median = 11.5

Answer 2

Given observation

12,14,10,9,11,16

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To find

• mean
• median

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Solution

~Mean is defined as the average or central value

It is given as :-

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

$\sf{ \to sum \: of \: observations= 12+14+10+9+11+16}$

$\sf{ \to sum \: of \: the \:observations =72}$

$\sf{ \to \: No \: .of \: observation= 6}$

$\sf{ \implies \: Mean = \frac{72}{6}} \\ \\ \sf{ \implies \: \red{Mean = 12}}$

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.

$\mathtt{Ascending \: order -} \\ \mathtt \orange{9 ,10, 11, 12, 14, 16}$

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= 6, which means even

so ,

$\mathtt{ Median = \frac{\frac{6}{2}term+ \frac{6}{2}+1\:term}{2} }\\ \\\mathtt{Median =\frac{3^{rd}term+ 4^{th}term}{2}} \\ \\ \mathtt{Median =\frac{3^{rd}term+ 4^{th}term}{2}} \\ \\ \mathtt{Median = \frac{11+12}{2}} \\ \\ \mathtt{Median =\frac{ 23}{2}} \\ \\ \mathtt \color{skyblue}{Median = 11.5 }$

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