Question

Q11. 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

Median is 4.5

Explanation:

Median

Median is a value that is in the middle position of data. In order to find median, there are several ways, from counting to middle position to a median formula.

However, in this scenario, we will not be requiring formulas to find median - we can count to middle position instead. The formulas should be recommended if you are trying to find a median with a lot of data.

Note: Before counting for a middle position of data, make sure that the data is all sorted.

Mean

Mean (Average) is a total sum of all data divided by total number of data. Mean value is useful when we want to consider numerical data all together in one - an example is if you have the data of students’ scores and you want to find how well your class do, the mean value should answer your doubts.

Since mean is total sum divided by total number, we can express the words mathematically as:

`\displaystyle{\bar x = (\sum x)/(N)}`

The
`\displaystyle \bar x` (x bar) denotes mean value.

`\displaystyle{\sum}` (sigma) denotes the sum so
`\displaystyle{\sum x}` denotes the sum of data.

N denotes the number of data.

Solution

To our problem, we are given with the mean value equal to 4.5 and here’s also our given data below:

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

We will be sorting the data later since we lack one element which is x. We can apply the mean value formula to solve for the variable x:

`\displaystyle{4.5 = (5+7+7+8+x+5+4+3+1+2)/(10)}`

Solve the equation for x:

`\displaystyle{4.5 \cdot 10= (5+7+7+8+x+5+4+3+1+2)/(10) \cdot 10}\\\\\displaystyle{45=5+7+7+8+x+5+4+3+1+2}\\\\\displaystyle{45=42+x}\\\\\displaystyle{45-42=x}\\\\\displaystyle{3=x}`

Now we know the missing data which is 3, so by substituting x = 3 in the data, we will have:

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

Then sort the data from least to greatest:

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

When you count for middle position, you’ll see that the middle position is between 4 and 5.

The number that is middle between 4 and 5 can only be one number which is 4.5

Therefore, our median to this data is 4.5