Question

Find median of the following data:
\[43\],\[63\],\[86\],\[50\],\[59\],\[74\],\[32\],\[78\],\[89\],\[45\],\[54\]

Answer 1

Hint: In this question, we have to find the median of the given set of data. First we will arrange the given data in either ascending order or descending order. Then we will find the number of terms. And use the formula to find the median.
Formula Used:
When the number of terms ( \[n\] ) is odd, then median is given by
$Median={\left\{ {\dfrac{{n + 1}}{2}} \right\}^{th}}$ term.
When the number of terms ( \[n\] ) is even, then median is given by
$Median=\dfrac{{\left\{ {{{\dfrac{n}{2}}^{th}}term + {{\left( {1 + \left( {\dfrac{n}{2}} \right)} \right)}^{th}}term} \right\}}}{2}$

Complete step-by-step answer:
This question is based on the calculation of median. Median is a measure of Central tendency to find the middle value of any given data. This middle value represents the whole set of data.
Consider the given question, we have to find the median
First we arrange the given data into either ascending or descending order.
Hence, arranging the data into ascending order, we get
\[32\],\[43\],\[45\],\[50\],\[54\],\[59\],\[63\],\[74\],\[78\],\[86\] ,\[89\]
Now, the number of terms ( \[n\] ) \[ = \] which is odd.
Hence, when \[n\] odd median is given by Median \[ = \]\[{\left\{ {\dfrac{{n + 1}}{2}} \right\}^{th}}\] term.
Putting, \[n\] \[ = \]\[11\] we have,
Median \[ = \]\[{\left\{ {\dfrac{{11 + 1}}{2}} \right\}^{th}} = {\left\{ {\dfrac{{12}}{2}} \right\}^{th}} = {\left\{ 6 \right\}^{th}}\] term.
Now from the arranged data, \[{6^{th}}\] term \[ = \] \[59\]
Hence, we have $median=59$
Hence, the median of given data is \[59\].
So, the correct answer is “ \[59\] ”.

Note: In statistics, Central tendency is an average central value which represents the whole set of data.
Mean, median and mode is used to find central tendency.
Mean is the average of data, while median is the middle most value when arranged in an order and mode is the value which is repeated most often.
Ascending order is the arrangement of data in an increasing order. Whereas descending order is the arrangement of data in decreasing order.