A damage control officer is reviewing the completion times (in minutes) for various emerge… — Armed Services Vocational Aptitude Battery (ASVAB)

A damage control officer is reviewing the completion times (in minutes) for various emergency response drills. Match each statistical description on the left with its correctly calculated value on the right.

Mean of the drill times $12, 18, 15, 11,$ and $14$ minutes $14$
Median of the drill times $9, 14, 8, 13, 16,$ and $12$ minutes $12.5$
Mode of the drill times $10, 15, 12, 10, 18, 10,$ and $14$ minutes $10$
Fourth drill time needed to achieve a mean of $15$ minutes, if the first three times are $16, 12,$ and $14$ minutes $18$

Answer

Mean pairs with 14; Median pairs with 12.5; Mode pairs with 10; Missing drill time pairs with 18.

Each statistical operation maps strictly to one correct outcome. Calculating the arithmetic mean gives 14, evaluating the sorted middle yields 12.5, counting frequencies identifies 10 as the mode, and algebraic substitution for a target mean resolves to 18.

Step-by-Step Solution

Calculate the mean of the first data set.

12 + 18 + 15 + 11 + 14 = 70

70 \div 5 = 14

The mean requires summing all given values and dividing by the count of the values.

Calculate the median of the second data set.

Sorted list:

8, 9, 12, 13, 14, 16

. The median is

(12 + 13) \div 2 = 12.5

The median is the exact middle value. For an even number of data points, it is the average of the two middle numbers in a sorted list.

Identify the mode of the third data set.

The number

10

appears three times, which is more than any other number.

The mode is the value that occurs most frequently in the distribution.

Calculate the missing value for the fourth scenario.

Total needed:

15 \times 4 = 60

. Current sum:

16 + 12 + 14 = 42

. Missing value:

60 - 42 = 18

To achieve a specific mean, the total sum must equal the mean multiplied by the number of events. Subtracting known events yields the missing event.

Key Concept

Measures of Central Tendency

Alternative Method

To find the missing drill time for a target mean of 15, you can use the deviation method: 16 is (+1), 12 is (-3), and 14 is (-1). The sum of these deviations is -3. To balance the average, the missing value must counteract this with an opposite deviation of +3. Therefore, the missing value is 15 + 3 = 18.

Estimated Time:1m 30s

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Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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