Question

a set of numbers consist of 3 times 1/3's, 5 times 1/2's, 8 times 1/4's, 3 times 2/3's. find the median.

Answer 1

Answer:

The median is $\frac{1}{3}$.

Step-by-step explanation:

The median is a measure of central tendency. It is middle value of the data set when arranged in ascending or descending order.

The data set provided arranged in ascending order is:

$\frac{1}{4} ,\frac{1}{4} , \frac{1}{4} , \frac{1}{4}, \frac{1}{4} , \frac{1}{4} , \frac{1}{4} ,\frac{1}{4} ,\frac{1}{3}, \frac{1}{3},\frac{1}{3}, \frac{1}{2} , \frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{2}{3},\frac{2}{3},\frac{2}{3}$

There are total n = 19 values.

So the median of the data set is the $(\frac{n+1}{2})^{th}$ observation.

The median observation is:

$Median=(\frac{n+1}{2})^{th}\\=(\frac{19+1}{2})^{th}\\=10^{th} observation$

The median is the 10th observation, i.e. $\frac{1}{3}$

Answer 2

Median of the data set is  $\frac{1}{3}$.

Step-by-step explanation:

A set of numbers consists the numbers :

$3times=\frac{1}{3}, \frac{1}{3}, \frac{1}{3},5times=\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2},\frac{1}{2},8times=\frac{1}{4},\frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4},3times=\frac{2}{3}, \frac{2}{3}, \frac{2}{3}$

Now first we arrange the data in ascending order to find median.

$\frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{4}, \frac{1}{3},\frac{1}{3}, \frac{1}{3},\frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{2}{3}, \frac{2}{3}, \frac{2}{3}$

Total number of values of the given data is 19. The median is the middle number of the data.

Median = $\frac{1}{3}$

Median of the data set is  $\frac{1}{3}$.

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