An environmental scientist measures the daily water flow (in gallons per minute) from a na… — Armed Services Vocational Aptitude Battery (ASVAB)

An environmental scientist measures the daily water flow (in gallons per minute) from a natural spring over five days. The recorded values are $22$ , $18$ , $25$ , $20$ , and $17$ . If the scientist needs the average (mean) flow rate across a full six-day period to be exactly $21$ gallons per minute, what must the flow rate be on the sixth day?

A
$18$
B
$3$
$24$ Cevap
D
$20$

Cevap

24

To find the missing value for the sixth day, first determine the total sum required for all six days. Since the target mean is

21

, the required total sum is

21 \times 6 = 126

. Next, find the sum of the five days already recorded:

22 + 18 + 25 + 20 + 17 = 102

. The required flow rate for the sixth day is the difference between these two sums:

126 - 102 = 24

Adım Adım Çözüm

Calculate the sum of the water flow for the first five days.

22 + 18 + 25 + 20 + 17 = 102

This establishes how much total water flow has already been recorded.

Calculate the required total sum for the full six days to achieve the target mean.

21 \times 6 = 126

The formula for the mean is Total Sum divided by the Number of Values. Therefore, Total Sum = Mean × Number of Values.

Subtract the sum of the first five days from the target total sum.

126 - 102 = 24

The difference between the target six-day total and the current five-day total gives the required value for the sixth day.

Anahtar Kavram

Calculating a missing data point in a set when the target arithmetic mean is provided.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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