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Find the 5 number summary for the data shownx2.72.97.27.58.511.215.418.3

Sagot :

2.7 ,2.9, 7.2, 7.5, 8.5, 11.2,15.4, 18.3

The minimum is the smallest number in the data : 2.7

The maximum is the largest number in the data : 18.3

Next, we find the median, which is the middle number in the data when arranged from smallest to largest. There are 8 numbers, so we will average the middle 2 numbers

2.7 ,2.9, 7.2, 7.5, 8.5, 11.2,15.4, 18.3

The middle is between the 4th and 5th numbers

( 7.5 + 8.5) / 2 = 16/2 = 8

The median(Q2) is 8

To find Q1 ( the 1st quartile), we take the numbers below the mean

2.7 ,2.9, 7.2, 7.5,

and find the median of these numbers

There are 4 numbers so the middle is between the 2nd and 3rd numbers

2.7 , 2.9, 7.2, 7.5,

(2.9+7.2) /2 =5.05

Q1 = 5.05

We will do the same process for Q3, which is the third quartile. We will use the numbers above the median

8.5, 11.2,15.4, 18.3

( 11.2 + 15.4) /2 =13.3

Q3 = 13.3