Question

2
the data below represents the speeds,
in miles per hour, of a pitchers warm-
up pitches before a game. which box
plot best represents this data?
{87, 92, 93, 88, 88, 93, 90,
93, 86, 90, 94, 95, 90, 92}
a)
tickled pink
b)
overjoyed
c)
honored
d)
surprised

Explanation:

Step1: Sort the data

Sort the data set \(\{87, 92, 93, 88, 88, 93, 90, 93, 86, 90, 94, 95, 90, 92\}\) in ascending order: \(\{86,87,88,88,90,90,90,92,92,93,93,93,94,95\}\)

Step2: Find the minimum, maximum, median, Q1 and Q3

• Minimum (\(min\)): \(86\)
• Maximum (\(max\)): \(95\)
• Number of data points \(n = 14\). The median (\(Q2\)) is the average of the 7th and 8th values. \(\frac{90 + 92}{2}=91\)
• For \(Q1\) (lower - quartile), consider the first \(n/2=7\) values \(\{86,87,88,88,90,90,90\}\). \(Q1 = 88\)
• For \(Q3\) (upper - quartile), consider the last \(n/2 = 7\) values \(\{92,93,93,93,94,95\}\). \(Q3=93\)

Now, check the box - plots:

• The box - plot should have a minimum at \(86\), \(Q1 = 88\), median \(Q2 = 91\), \(Q3 = 93\) and maximum at \(95\)

Answer:

A.