Question

which statements are true. select all the correct statements.
wayne county little league has a higher lower quartile than howard county little league.
howard county little league has 50% of its data above 150 pitches and wayne county little league has 25% of its data above 150 pitches.
howard county little league has a larger range the wayne county little league
wayne county little league has 50% of its data above 150 pitches and howard little league has 25% of its data above 150 pitches.
the inner quartile range for wayne county is smaller than the inner quartile range for howard county.

Explanation:

To solve this, we analyze box - and - whisker plots (implied by quartile and range references):

Step 1: Recall Box - and - Whisker Plot Concepts

• The lower quartile ($Q_1$) is the 25th percentile.
• The median (middle line in the box) is the 50th percentile.
• The upper quartile ($Q_3$) is the 75th percentile.
• The range is calculated as $max - min$.
• The inter - quartile range (IQR) is $Q_3 - Q_1$.

Step 2: Analyze Each Statement

1. Statement 1: Wayne County Little League has a higher lower quartile than Howard County Little League

• In a box - and - whisker plot, the left end of the box is $Q_1$ (lower quartile). If Wayne County's box starts to the right of Howard County's, then Wayne County has a higher $Q_1$. So this statement can be true.

1. Statement 2: Howard County Little League has 50% of its data above 150 pitches and Wayne County Little League has 25% of its data above 150 pitches

• The median (50th percentile) divides the data into two halves (50% above, 50% below). The upper quartile (75th percentile) means 25% of the data is above it. If 150 is the median for Howard County, then 50% of Howard's data is above 150. If 150 is the upper quartile for Wayne County, then 25% of Wayne's data is above 150. So this statement can be true.

1. Statement 3: Howard County Little League has a larger range than Wayne County Little League

• The range is $max - min$. If Howard County's whiskers (from min to max) span a wider range than Wayne County's, then its range is larger. But from the context of typical box - plot analysis and the other statements, this is likely false.

1. Statement 4: Wayne County Little League has 50% of its data above 150 pitches and Howard Little League has 25% of its data above 150 pitches

• This is the reverse of the correct relationship (based on median and upper quartile). So this statement is false.

1. Statement 5: The Inner Quartile Range for Wayne County is smaller than the Inner Quartile Range for Howard County

• The IQR is $Q_3 - Q_1$. If Wayne County's box is narrower than Howard County's box, then its IQR is smaller. So this statement can be true.

Step 3: Identify True Statements

After analyzing each statement using box - and - whisker plot concepts:

• The true statements are:
• Wayne County Little League has a higher lower quartile than Howard County Little League.
• Howard County Little League has 50% of its data above 150 pitches and Wayne County Little League has 25% of its data above 150 pitches.
• The Inner Quartile Range for Wayne County is smaller than the Inner Quartile Range for Howard County.

Answer:

• Wayne County Little League has a higher lower quartile than Howard County Little League.
• Howard County Little League has 50% of its data above 150 pitches and Wayne County Little League has 25% of its data above 150 pitches.
• The Inner Quartile Range for Wayne County is smaller than the Inner Quartile Range for Howard County.