Question

2) 15, 10, 12, 18, 12, 18, 10, 20, 25, 10, 18,
10. Find mean, median and made
of the data answer ​

Answer 1

GIVEN :-

• Data = 15, 10, 12, 18, 12, 18, 10, 20, 25, 10, 18, 10.

TO FIND :-

1. Mean .
2. Median.
3. Mode.

SOLUTION :-

Mean,

$: \implies \displaystyle \sf \: mean(average) = \frac{sum \: of \: observation}{no. \: of \: observation}$

$: \implies \displaystyle \sf \:mean(average) = \frac{15 + 10 + 12 + 18 + 12 + 18 + 10 + 20 + 25 +10 + 18 + 10}{12}$

$: \implies \displaystyle \sf \:mean(average) = \frac{178}{12}$

$: \implies \displaystyle \sf \:mean(average) = 14.833333$

$: \implies \underline{ \boxed{ \displaystyle \sf \:mean(average) = 14.8 \bar{3}}}$

__________________

Median,

For finding the median of the given observation, firstly we have to arrange the given data in ascending or descending order, so here we will arrange the given data in ascending order.

★ 10, 10, 10, 10, 12, 12, 15, 18, 18, 18, 20, 25.

$\\ \dashrightarrow\displaystyle \sf \: no \: of \: terms(n) = 12(even)$

$\dashrightarrow\displaystyle \sf \:median(even) = \dfrac{ \Bigg[ \bigg( \dfrac{ n}{2} \bigg) ^{th} term + \Bigg[\bigg\{\bigg(\dfrac{n }{2} + 1 \bigg)\bigg\} ^{th} term\Bigg]}{2}$

$\dashrightarrow\displaystyle \sf \:median(even) = \dfrac{ \Bigg[ \bigg( \dfrac{ 12}{2} \bigg) ^{th} term + \bigg(\dfrac{14}{2} \bigg) ^{th} term\Bigg]}{2}$

$\dashrightarrow\displaystyle \sf \:median(even) = \dfrac{ \Bigg[ \bigg( 6+ 7 \bigg) ^{th} term \Bigg]}{2}$

$\dashrightarrow\displaystyle \sf \:median(even) = \dfrac{ \Bigg[ \bigg( \dfrac{ 12 + 15}{2} \bigg) ^{th} term \Bigg]}{2}$

$\dashrightarrow\displaystyle \sf \:median(even) = \dfrac{ \Bigg[ \bigg(27 \bigg) \Bigg]}{2}$

$\dashrightarrow \underline{ \boxed{\displaystyle \sf \:median(even) = \Bigg[ \bigg(13.5\bigg) \Bigg]}}$

$\therefore\underline{ \displaystyle \sf Median \ of \ data \ is \ 13.5 }$

___________________

Mode,

Mode :- a number which occurred maximum times.

$\\ \sf4 \begin{cases} \sf \: 10 \\ \: 10 \\ \: 10 \: \\ \: 10\end{cases}$

$\sf2 \begin{cases} \sf \: 12 \\ \: 12 \\ \end{cases}$

$\sf1 \begin{cases} \sf \: 15\end{cases}$

$\sf3\begin{cases} \sf \: 18 \\ \: 18 \\ \: 18\end{cases}$

$\sf1 \begin{cases} \sf \: 20\end{cases}$

$\sf1 \begin{cases} \sf \:25\end{cases}$

From the above data we observe that 10 is occurred maximum 4 times

$\\ \therefore \underline{ \displaystyle \sf mode \: of \: the \: data \: is \: 10.}$

Answer 2

Answer :

• Mean = 14 . 83
• Median = 13 . 5
• Mode = 10

Explanation :

Finding Mean :

✎ The mean is the average of number.

Arranging the data in ascending order :

10 , 10 , 10 , 10 , 12 , 12 , 15 , 18 , 18 , 18 , 20 , 25

Mean ⇛ ∑ x / n

⇛10 + 10 + 10 + 10 + 12 + 12 + 15 + 18 + 18 + 18 + 20 + 25 / 12

⇛178 / 12

⇛14 . 83

Finding Median :

✎ The middle number found by ordering all data and picking out the one in the middle.

Here n = 12 { even } , median , so

⇛6 th + 7 th term / 2

⇛( 6 + 7 ) th term / 2

⇛( 12 + 15 ) th term / 2

⇛27 / 2

⇛13 . 5

Finding Mode :

✎ The mode is the value that appears most frequently in a data set.

⇛10 , 10 , 10 , 10 = 4

⇛12 , 12 = 2

⇛15 = 1

⇛18 , 18 , 18 = 3

⇛20 = 1

⇛25 = 1

⇛Mode = 10

So, It's Done !!