Question

Find the median, quartiles, and make a histogram for the following data.

1,3,3,3,3,3,3,4,4,4,4,4,4,5,6,7,7,7,9,10,10,10,11,12,12,13,14,14,14,15,16,17,17,17,17,18,19,19,21,22,23,25,27,27,29, 32,35,35,36,45

Answer 1

Median

For median first set your data in ascending order

1,3,3,3,3,3,3,4,4,4,4,4,4,5,6,7,7,7,9,10,10,10,11,12,12,13,14,14,14,15,16,17,17,17,17,18,19,19,21,22,23,25,27,27,29, 32,35,35,36,45

No of an element in this data is even (50) so the formula is

meidan = [(n/2)th term +{(n/2)+1}th term]/2

            = [(50/2)th term +{(50/2)+1}th term]/2

            = [(25)th term +{(25)+1}ty term]/2

            =[(25)th term + (26)th term]/2

            = [12+13]/2

           =25/2

median = 12.5

Quartiles

1st quartile means 25% percentile or splits off the lowest 25% of data from the highest 75%

2nd quartile means 50% or median of the data or cuts data set in half

3rd quartile means 75% or splits off the highest 25% of data from the lowest 75%

so median is 12.5 which is between 25the term and 26th term

1,3,3,3,3,3,3,4,4,4,4,4,4,5,6,7,7,7,9,10,10,10,11,12,12

1st quartile is middel value of first 25th term which is 13th term

so 1st quartile is 4

3rd quartile

13,14,14,14,15,16,17,17,17,17,18,19,19,21,22,23,25,27,27,29, 32,35,35,36,45

3st quartile is midel value of last 25th term which is 38th term

so 3st quartile is 19

histogram