The table below shows the distribution of the number of goals scored by a soccer team in each of its 15 games last season. | Goals Scored | Number of Games | | :--- | :--- | | 0 | 3 | | 1 | 5 | | 2 | 4 | | 3 | 2 | | 9 | 1 | Which of the following statements best describes how the mean and the median

The table below shows the distribution of the number of goals scored by a soccer team in e… — SAT

The table below shows the distribution of the number of goals scored by a soccer team in each of its $15$ games last season.

Goals Scored	Number of Games
$0$	$3$
$1$	$5$
$2$	$4$
$3$	$2$
$9$	$1$

Which of the following statements best describes how the mean and the median of the number of goals scored will change if the game with $9$ goals is removed from the dataset?

A
Both the mean and the median values will remain unchanged.
B
The median value will be reduced, while the mean value will not change.
The mean value will be reduced, while the median value will not change.Answer
D
Both the mean and the median values will be reduced.

Answer

The mean value will be reduced, while the median value will not change.

To find the effect of removing the game with

9

goals, we compare the mean and median before and after its removal. The initial dataset has

15

games. The median is the

8\text{th}

value, which is

1

. The initial mean is

(0 \times 3 + 1 \times 5 + 2 \times 4 + 3 \times 2 + 9 \times 1) / 15 = 28/15 \approx 1.87

. If the game with

9

goals is removed, there are

14

games remaining. The new median is the average of the

7\text{th}

and

8\text{th}

values, which are both

1

, so the median remains

1

. The new mean is

(0 \times 3 + 1 \times 5 + 2 \times 4 + 3 \times 2) / 14 = 19/14 \approx 1.36

. The mean value decreases (is reduced) while the median value remains the same.

Step-by-Step Solution

Calculate the initial mean and median of the dataset of

15

games.

The initial mean is approximately

1.87

and the initial median is

1

To establish the baseline values before removing any data.

Calculate the new mean and median of the dataset of

14

games after removing the game with

9

goals.

The new mean is approximately

1.36

and the new median is

1

To determine the values after the outlier is removed.

Compare the initial and new values for both the mean and median.

The mean decreases from approximately

1.87

1.36

, while the median remains

1

To select the statement that correctly describes the change in both statistical measures.

Key Concept

Effect of outliers on mean and median

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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