Question

What is the median, first quartile third quartile and interquartile of 38 46 55 56 558 59 61 65 67 75

Answer 1

Answer:

Median = 58.5

Q1 = 55

Q3 = 65

Interquartile = 10

Step-by-step explanation:

first let’s correct the data set :

It’s 38 46 55 56 58 59 61 65 67 75  not   38 46 55 56 558 59 61 65 67 75

Data set : 38 46 55 56 58 59 61 65 67 75

Median:

After we put Our data set from Smallest to largest

we define the median as the middle number of the data set but our set consists of an even number which is 10

In this case the median is the average of the two middle numbers which are the 5th and 6th numbers

38 46 55 56 [58 59] 61 65 67 75

Then

Median = (58+59)/2 = 117/2 = 58.5

quartile 1 : It’s just the median of the lower set of numbers which means it’s the median of : 38 46 55 56 58

Then Q1 = 55 because it’s the middle number.

quartile 3 : It’s just the median of the upper set of numbers which means it’s the median of : 59 61 65 67 75

Then Q3 = 65  (Easy to spot)

Interquartile = Q3 - Q1 = 65 - 55 = 10