Question

Hi, I need help with this question. Please explain in details how you got the answer with steps shown for each part so I can understand it thank you.

The Department of Energy provides fuel economy ratings for all cars and light trucks sold in the United States. Here are the estimated miles per gallon for city driving for 30 cars classified as midsize, arranged in increasing order. 11 12 12 12 13 13 13 14 14 14 15 15 16 16 16 17 17 17 17 17 18 18 18 18 19 20 24 25 36 46 (a) Give the five-number summary of this distribution. minimum 11 21 median 16.5 23 maximum 46 15 i6ade 18

Answer 1

Solution :

=> The first quartile Q1 = 14

Given data 11,12,12,12,13,13,13,14,14,14,15,15,16,16,16,17,17,17,17,17,18,18,18,18,19,20,24,25,36,46

=> The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

11 12 12 12 13 13 13 14 14 14 15 15 16 16 16 17 17 17 17 17 18 18 18 18 19 20 24 25 36 46   

=> So, the bottom half is

11 12 12 12 13 13 13 14 14 14 15 15 16 16 16   

=> The median of these numbers is 14.

=> The first quartile Q1 = 14