Question

create a box plot of devoirys transportation costs for two weeks. her expenses were: {13, 18, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 18, 19}. use the box plot of transportation costs to answer the questions. were there any clear outliers in devoirys transportation costs? the inter - quartile range (iqr) of a data set is the difference between the upper and lower quartiles. what is the iqr for devoirys transportation costs?

Explanation:

Step1: Arrange data in ascending order

{13, 13, 14, 15, 16, 17, 18, 18, 19, 19, 20, 21, 22}

Step2: Find the median (Q2)

There are 13 data - points. The median is the 7th value. So, Median (Q2)=18.

Step3: Find the lower half of data

The lower half is {13, 13, 14, 15, 16, 17}. The median of the lower half (Q1) is the average of the 3rd and 4th values. $Q1=\frac{14 + 15}{2}=14.5$.

Step4: Find the upper half of data

The upper half is {18, 19, 19, 20, 21, 22}. The median of the upper half (Q3) is the average of the 3rd and 4th values. $Q3=\frac{19+20}{2}=19.5$.

Step5: Calculate the inter - quartile range (IQR)

$IQR = Q3 - Q1=19.5−14.5 = 5$.

Answer:

5