Question

question 15 (multiple choice, 10 points)(21-108-042)the table shows the number of goals made by two hockey players during the seasons gamesplayer a2 3 1 3 2 2 1 3 6player b1, 4, 0, 1, 2, 4, 5, 5, 11which measure of variability is best for the data, and which player is more consistent?player a is the most consistent, with an iqr of 1.5player b is the most consistent, with an iqr of 3.5player a is the most consistent, with a standard deviation of 1.4player b is the most consistent, with a standard deviation of 2.9

Explanation:

Step1: Identify outlier presence

Player B has an outlier (11), so IQR is better.

Step2: Sort Player A's data

Sorted Player A: $1, 1, 2, 2, 2, 3, 3, 8$

Step3: Calculate Player A's IQR

Q1 = $\frac{1+2}{2}=1.5$, Q3 = $\frac{3+3}{2}=3$
IQR = $3 - 1.5 = 1.5$

Step4: Sort Player B's data

Sorted Player B: $1, 1, 2, 4, 4, 5, 5, 11$

Step5: Calculate Player B's IQR

Q1 = $\frac{1+2}{2}=1.5$, Q3 = $\frac{5+5}{2}=5$
IQR = $5 - 1.5 = 3.5$

Step6: Compare consistency

Lower IQR = more consistent. Player A has smaller IQR.

Answer:

Player A is the most consistent, with an IQR of 1.5