Question

Find the median of the given data if the mean is 4.5.
5,7,7,8,x,5,4,3,1,2

Answer 1

Given:

A data

5, 7, 7, 8, x, 5, 4, 3, 1, 2.

Also, the mean of given data is 4.5

To find:

The median of given data.

Solution:

The median of given data is 4.5

To answer this question, we will follow the following steps:

As given, we have,

A data,

5, 7, 7, 8, x, 5, 4, 3, 1, 2

The mean of given data = 4.5

As we know the arithmetic mean of 'n' observations is equal to the sum of all 'n' observations divided by the total number of observations i.e. n.

This means

$arithmetic \: mean = \frac{sum \: of \: n \: observations}{n}$

So,

$4.5 = \frac{5 + 7 + 7 + 8 + x + 5 + 4 + 3 + 1 + 2}{10}$

$4.5 = \frac{42 + x}{10}$

$45 = 42 + x$

$x = 3$

Now,

We will put the value x in the given data.

The data is

5, 7, 7, 8, 3, 5, 4, 3, 1, 2

To find the median, we will arrange the given data in ascending order.

So,

1, 2, 3, 3, 4, 5, 5, 7, 7, 8

Here,

The number of observations = 10

which is even.

As we know if there is an even number (n) of observations in a data, then the median is obtained by:

$\frac{ (\frac{n}{2})th \: observation \: + (\frac{n}{2} + 1)th \: observation }{2}$

So,

$(\frac{n}{2})th \: observation \: = 10/2 = 5th\: observation$

$(\frac{n}{2} + 1)th \: observation \: = 10/2 + 1= 6th\: observation$

So,

Median is

= $\frac{5th \: observation \: + 6th \: observation}{2}$

= $\frac{4 + 5}{2}$

= $\frac{9}{2}$

= $4.5$

Hence, the median of the given data is 4.5

Answer 2

Answer:

The Median for the given data is 4.5

Step-by-step explanation:

• In context to the given question, we have to find median for the given sequence
• Given,

the mean of given data is 4.5

Data=5, 7, 7, 8, x, 5, 4, 3, 1, 2

• To find: The median of given data.

Solution:

• To find the median we should know the middle terms of the data, we have to find "x" for that

• The arithmetic mean of 'n' observations is equal to the sum of all 'n' observations divided by the total number of observations i.e. n.

To find the value of x ; we know mean of the data

therefore,

Mean = summation of the data/ number of observation

4.5 = (5+7+7+8+x+5+4+3+1+2) / 10

45 = 42 + x

x = 45-42

x = 3

therefore,

now data = 5,7,7,8,3,5,4,3,1,2

To find median,

we have to arrange the data in ascending order

ascended order = 1,2,3,3,4,5,5,7,7,8

we know that,

if there is an even number of observations in a data, then the median is obtained by:

Median = $\frac{(n/2)th observation + ((n+1)/2)th observation}{2}$

n = 10

(n/2) th observation = 10/2  = 5th observation

[ (n/2) + 1 ] th observation = 10/2 + 1 = 5+1 = 6th observation

Median = $\frac{5th observation + 6th observation}{2}$

Median = (4 + 5)/2

Median = 9/2 = 4.5

Therefore, The Median for the given data is 4.5