Question

construct a boxplot for the following data and comment on the shape of the distribution representing the number of

Answer 1

Answer:

Check the boxplot below,plus the comments

Step-by-step explanation:

1) Completing the question:

Construct a boxplot for the following data and comment on the shape of the distribution representing the number of games pitched by major league baseball’s earned run average (ERA) leaders for the past few years.

30 34 29 30 34 29 31 33 34 27  30 27 34 32

2) Arranging the distribution orderly to find the 2nd Quartile (Median):

27  27  29  29  30  30  30  31  32  33  34  34  34  34

Since n=14, dividing the sum of the 14th and 15th element by two:

$Md=Q_{2}=\frac{30+31}{2} =30.5$

3) Calculating the Quartiles, the Upper and the Lower one comes:

$Q_{1}=29.25\\Q_{3}=33.75$

4) Boxplotting (Check it below)

5) Notice that since the values are very close, then the box is not that tall. The difference between the Interquartile Range is not so wide what makes it shorter. Check the values on the table below.