Question

Calculate the mean, median, mode, range, and 5 Number Summary of the following data set: 5,6,8,4,7,5,4,2,5,6,5,2,1,4

Answer 1

Answer:

mean = 4.57, median = 5 , mode = 5, range =7 ,

five number summary: Minimum value= 1 , First Quartile = 4, Median = 5

Third Quartile  = 6, Maximum value = 8

Step-by-step explanation:

First arrange the data in ascending order.

1,2,2,4,4,4,5,5,5,5,6,6,7,8

Mean = sum of all numbers / total numbers

         = 1+2+2+4+4+4+5+5+5+5+6+6+7+8 / 14

         = 64 / 14

         = 4.57

Median:

Since the given data is even number so, we can find median by taking mean of 2 middle numbers.

so the middle numbers are 7th and 8th  data i.e, 5 and 5

Median =(5+5)/2

           = 5

Mode:

The most repetitive number in the data set is mode

So Mode = 5

Range:

Range can be found by subtracting smallest number from largest number in the data set.

Smallest number  = 1, Largest number = 8

Range= Largest number - Smallest number

        = 8-1 = 7

Five no Summary

Minimum value= 1

First Quartile ( 25 % mark )= 4

Median = 5

Third Quartile (75 % mark) = 6

Maximum value = 8

First quartile can be found by : consider the data on left of the median and find median among them

Third quartile can be found by:  consider the data on right of the median and find median among them