Question

The median of a set of eight numbers is 4.5. Given that seven of the numbers are 7,2,13,4,8,2 and 1, find the eight number and mode

Answer 1

Median = sum of all terms\total terms

4.5 = 7+2+13+4+8+2+x\8

36 = 36+x

x = 0

The eighth no. is 0

Answer 2

The eight number and mode is 5 and 2 respectively.

Step-by-step explanation:

We are given that The median of a set of eight numbers is 4.5.

Since median is 4.5

Data:1,2,2,4,7,8,13

So, missing value should lie after 4

So original data=1,2,2,4,x,7,8,13

No. of observations = 8 (even)

$Median = \frac{\frac{n}{2} \text{th term} + (\frac{n}{2}+1) \text{th term}}{2}$

$Median = \frac{\frac{8}{2} \text{th term} + (\frac{8}{2}+1) \text{th term}}{2}$

$Median = \frac{4 \text{th term} + 5 \text{th term}}{2}$

$4.5= \frac{4+x}{2}$

$4.5 \times 2=4+x$

$9=4+x$

$x=5$

Hence The eighth number is 5

Data : 1,2,2,4,5,7,8,13

Mode = The most occurring observations

Mode = 2

Hence the eight number and mode is 5 and 2 respectively.

#Learn more:

The median of first eight prime numbers

https://brainly.in/question/1088369