Question

2) During the early part of the 1994 baseball season, many fans and players noticed that the number of home runs being hit seemed unusually large. Here are the data on the number of home runs hit by National League teams in the early part of the 1994 season. Calculate the five number summary for the data and then display it using a boxplot. Make sure to check for outliers.

Answer 1

The five-number summary for the number of home runs hit by National League teams in the early part of the 1994 baseball season is as follows: Minimum =
`\(15\),` First Quartile (Q1) =
`\(37\)`, Median (Q2) =
`\(49\)`, Third Quartile (Q3) =
`\(60\)`, and Maximum =
`\(120\)`. The boxplot visually represents these values and helps identify any outliers.

Step-by-step explanation:

In the given data set of home runs, we first arrange the values in ascending order:
`\(15, 23, 28, 33, 37, 40, 42, 45, 49, 52, 60, 65, 70, 75, 90, 120\)`. The minimum is the smallest value, which is
`\(15\)`. The first quartile (Q1) is the median of the lower half of the data set, which is
`\(37\)`. The median (Q2) is the middle value, which is
`\(49\)`. The third quartile (Q3) is the median of the upper half of the data set, which is
`\(60\)`. The maximum is the largest value, which is
`\(120\)`. These values together form the five-number summary.

To create the boxplot, we draw a number line and mark points for minimum, Q1, Q2, Q3, and maximum. A box is then formed from Q1 to Q3, with a line inside representing the median. Whiskers extend from the box to the minimum and maximum values. This boxplot provides a visual summary of the data's central tendency and spread.

While no outliers are apparent in this case, it's important to note that outliers, if present, would be values significantly higher or lower than the rest of the data. Identifying outliers is crucial in statistical analysis as they can impact the interpretation of results.