Question

The table shown below provides statistical data on the bowling scores for David and Elise.

Bowling Score Data
David
145
Interquartile Range 30
Mean
Elise
120
20
David claims that his scores were more consistent than Elise's scores. Which statement is
MOST likely true about David's claim?
t
David claims that his scores were more consistent than Elise's scores. Which statement is
MOST likely true about David's claim?
David's claim is correct because his mean score is greater than Elise's mean score.
David's claim is correct because the interquartile range for his scores is greater than the interquartile range
for Elise's scores.
David's claim is incorrect because his mean score is greater than Elise's mean score.
David's claim is incorrect because the interquartile range for his scores is greater than the interquartile

Answer 1

Explanation:

Let's set David's score to D, and Aaron's score to A. If so, we get the equation that satisfies the constraints:

D = 3*A-5, D + A = 215

Set D in terms of A:

D = 215 - A

Input it into the equation:

215 - A = 3*A - 5 -> add 5 and A to both sides to set numbers to the left and variables to the right

215 + 5 = 3* A + A ->

220 = 4A -> divide by 4

220/4 = A ->

55 = A -> substitute A into D + A = 215

D + 55 = 215 -> subtract 55 from both sides

D = 215 - 55 = 160

So, out final answer is:

D = 160, A = 55

Answer 2

A statement that is most likely true about David's claim is that: D. David's claim is incorrect because the interquartile range for his scores is greater than the interquartile.

In Mathematics and Statistics, IQR is an abbreviation for interquartile range and it is a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) of a data set is the difference between third quartile (
`Q_3`) and the first quartile (
`Q_1`):

Interquartile range (IQR) of data set = third quartile - first quartile

Additionally, interquartile range is used for measuring the reliability or consistency of a data set, the lower the interquartile range, the more reliable and consistent the data set would be.

In this context, Elise is more consistent because he has a lower interquartile range in comparison woth David, so David's claim is incorrect.