Question

41;39;48;52;46;62;54;40;96;52;98;40;42;52;60 find mean, median ,mode​

Answer 1

Solution:

Given Data:

41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52 and 60.

To Find:

=> Mean

=> Median

=> Mode

Firstly,

What is Mean?

• Mean is the sum of the values of all the observations divided by the total number of observations.

What is Mode?

• The value of a data set that occurs most often is known as the mode of the data.

What is Median?

• The median of data is a value of the middle observation, when data is arranged in ascending and descending order.

So, Mean of following data is,

=> Mean = (41+39+48+52+46+62+54+40+96+52+98+40+42+52+60)/15

$\sf{\implies Mean=\dfrac{822}{15}}$

$\large{\boxed{\boxed{\purple{\sf{\implies Mean = 54.8}}}}}$

As, we know mode is value that occurs most.

So,

$\large{\boxed{\boxed{\orange{\sf{\implies Mode = 52}}}}}$

Now, we will find the median of following data,

So, firstly we arrange following data into ascending order.

=> 39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98.

So,

$\sf{\implies Median = \dfrac{(n+1)}{2}}$

$\sf{\implies \dfrac{15+1}{2}}$

$\sf{\implies \dfrac{16}{2}}$

$\sf{\implies 8th\;Observation}$

=> Median of this is 8th observation, Means 52 is the median.

$\large{\boxed{\boxed{\pink{\sf{\implies Median = 52}}}}}$

Answer 2

$\huge{\mathfrak{\green{S}}}{\mathfrak{o}}{\mathfrak{\orange{l}}}{\mathfrak{\red{u}}}{\mathfrak{\pink{t}}}{\mathfrak{\blue{i}}}{\mathfrak{\purple{o}}}{\mathfrak{\gray{n}}}$

Mean = 54.8

Mode = 52

Median = 52

$\mathrm{\gray{To \: Find}}$

Mean, Mode and Median

$\mathrm{\gray{Solution}}$

We know that mean is

$\boxed{\bf{Mean = \frac{Sum \: of \:observations}{Total \: number \:of \\:observations}}}$

_______________[Put Values]

$\sf{Mean = \frac{41 + 39 + 48 + 52 + 46 + 62 + 54 + 40 + 96 + 52 + 98 + 40 + 42 + 52 + 60}{15}}$

Mean = 822/15

Mean = 54.8

$\huge{\boxed{\pink{Mean = 54.8}}}$

We know that the number which repeats highest time is mode

$\huge{\boxed{\pink{Mode = 52}}}$

To find median we will arrange data in descending order.

98, 96, 62, 60, 54, 52, 52, 52, 48, 46, 42, 41 ,40, 39

$\huge{\boxed{\bf{Median = \frac{n + 1}{2}}}}$

Here is number of observations.

$\implies{Median = \frac{15 + 1}{2}}$

$\implies{Median = \frac{{\cancel16}}{{\cancel2}}}$

$\bf{Median = 8^{th} term}$

So,

$\huge{\boxed{\pink{Median = 52}}}$