An artillery spotter is recording the impact distances (in meters) from a target center fo… — Armed Services Vocational Aptitude Battery (ASVAB)

An artillery spotter is recording the impact distances (in meters) from a target center for five test rounds. The distances are $34$ , $41$ , $28$ , $52$ , and $40$ . A sixth round is fired. If the mean distance for all six rounds is exactly $41$ meters, what was the impact distance of the sixth round?

A
$10$
B
$39$
C
$40$
$51$ Cevap

Cevap

The correct impact distance of the sixth round is

51

meters.

To find a missing value when the mean is known, you must work backward using the total sum. Since the mean of

6

rounds is

41

, their total sum must be

41 \times 6 = 246

. The sum of the first five rounds is

195

. Subtracting the current sum from the required total sum (

246 - 195

) reveals that the sixth round must be

51

Adım Adım Çözüm

Calculate the required sum of the distances for all six rounds.

41 \times 6 = 246

The mean of a data set is its total sum divided by the number of items. To find the required total sum, multiply the target mean (

41

) by the total number of rounds (

6

Calculate the sum of the distances for the first five rounds.

34 + 41 + 28 + 52 + 40 = 195

This establishes the total distance that has already been accounted for by the initial test rounds.

Subtract the sum of the first five rounds from the required total sum to find the sixth round.

246 - 195 = 51

The difference between the total needed for all six rounds and the total already recorded gives the exact value required for the final round.

Anahtar Kavram

Solving for a missing value given a target mean

Soru

Cevap

Adım Adım Çözüm

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