An environmental scientist measured the dissolved oxygen concentration, in milligrams per … — ACT

An environmental scientist measured the dissolved oxygen concentration, in milligrams per liter ( $\text{mg/L}$ ), at $6$ different monitoring locations along a river. The recorded concentrations for $5$ of the locations were $6.4$ , $7.2$ , $5.8$ , $8.0$ , and $7.6$ . If the mean dissolved oxygen concentration for all $6$ locations was exactly $7.1\text{ mg/L}$ , what was the dissolved oxygen concentration recorded at the $6\text{th}$ location?

A
$0.5\text{ mg/L}$
B
$7.0\text{ mg/L}$
C
$7.2\text{ mg/L}$
$7.6\text{ mg/L}$ Answer
E
$8.5\text{ mg/L}$

Answer

7.6\text{ mg/L}

To find the measurement at the sixth location, multiply the target mean by the total number of locations (

6 \times 7.1 = 42.6\text{ mg/L}

) to find the required sum of all measurements. Subtracting the sum of the five known measurements (

6.4 + 7.2 + 5.8 + 8.0 + 7.6 = 35.0\text{ mg/L}

) from

42.6\text{ mg/L}

gives

42.6 - 35.0 = 7.6\text{ mg/L}

Step-by-Step Solution

Calculate the total required sum for all 6 locations.

6 \times 7.1 = 42.6\text{ mg/L}

The mean of a dataset equals the sum of all values divided by the number of values (

N=6

Sum the 5 known location measurements.

6.4 + 7.2 + 5.8 + 8.0 + 7.6 = 35.0\text{ mg/L}

This determines the total concentration accounted for by the known locations.

Subtract the sum of the known measurements from the total required sum.

42.6 - 35.0 = 7.6\text{ mg/L}

The difference gives the exact measurement needed at the 6th location to achieve the target mean.

Key Concept

Finding a missing value given a target mean

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