Question

A researcher has collected the following sample data. 5 12 6 8 56 7 5 12 4. What is the median?

Answer 1

Answer:

assending order 4, 5,5,6,7,8,12,12,56

then median is 7

n+1/2 formula

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Answer 2

Median is 7 for data 5 12 6 8 56 7 5 12 4.

Given:

• sample data. 5 12 6 8 56 7 5 12 4.

To Find:

• Median

Solution:

Mean , median and Mode are measures of central Tendency

Median represent middle data

$\begin{align} & \text{Median is }\left( \frac{n+1}{2} \right)\text{th term if }n\text{ is odd} \\ & \text{Median is }\frac{1}{2}\left( \left( \frac{n}{2} \right)\text{th term +}\left( \frac{n}{2}+1 \right)\text{th term} \right)\text{ if }n\text{ is even} \\ \end{align}$

Step 1:

Arrange the Data in ascending order

4 , 5 , 5 , 6 , 7 , 8 , 12 , 12 , 56

Step 2:

Total Data points are 9 Hence median will be (9 + 1)/2 = 5th Term

Step 3:

5th Term in the data is 7

Hence, Median of the given data is 7

Additional info:

if Data is : . 5 12 6 8 5 6 7 5 12 4     ( 56 taken as 5  and 6  as 56 looks suspicious in given data)

Then arranging in ascending order

4 , 5 , 5 , 5, 6 ,  6 , 7 , 8 , 12 , 12

Total data points are 10

Median ( 6 + 6)/2 = 6