A gymnast competed in 5 events during a state meet, earning scores of 14.2, 13.8, 14.5, 13… — ACT

A gymnast competed in 5 events during a state meet, earning scores of $14.2$ , $13.8$ , $14.5$ , $13.5$ , and $14.0$ . She has one event remaining. If her goal is to have an average (arithmetic mean) score of exactly $14.1$ for all 6 events, what score must she earn on her final event?

A
14.0
B
14.1
C
14.5
14.6Answer
E
15.1

Answer

14.6

To find the score needed on the final event, we first calculate the total sum of the scores from the first 5 events:

14.2 + 13.8 + 14.5 + 13.5 + 14.0 = 70.0

. Next, we find the total sum required for all 6 events to average exactly

14.1

14.1 \times 6 = 84.6

. Finally, we subtract the sum of the first 5 events from this target total:

84.6 - 70.0 = 14.6

. Therefore, the required score on the final event is 14.6.

Step-by-Step Solution

Calculate the sum of the scores from the first 5 events.

14.2 + 13.8 + 14.5 + 13.5 + 14.0 = 70.0

To find the missing score, we need to compare the current total score to the target total score.

Calculate the target total score for all 6 events to achieve an average of

14.1

14.1 \times 6 = 84.6

Since the average is the sum divided by the number of events, the total sum is the average multiplied by 6.

Subtract the sum of the first 5 events from the target total sum to find the required final score.

84.6 - 70.0 = 14.6

The difference between the required total sum and the current sum represents the score needed on the final event.

Key Concept

Calculating a missing value in a data set to achieve a target arithmetic mean.

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