A weather researcher recorded the daily high temperatures, in degrees Fahrenheit, for 5 co… — ACT

A weather researcher recorded the daily high temperatures, in degrees Fahrenheit, for $5$ consecutive days in a mountain town: $68^\circ\text{F}$ , $74^\circ\text{F}$ , $71^\circ\text{F}$ , $65^\circ\text{F}$ , and $72^\circ\text{F}$ . If the daily high temperature on the 6th day is $x^\circ\text{F}$ , and the mean high temperature for all $6$ days is $72^\circ\text{F}$ , what is the value of $x$ ?

A
$10$
B
$72$
C
$74$
$82$ Answer
E
$88$

Answer

82

To achieve a target mean of

72^\circ\text{F}

over

6

days, the total sum of all

6

daily high temperatures must be

6 \times 72 = 432^\circ\text{F}

. Adding the

5

recorded temperatures gives

68 + 74 + 71 + 65 + 72 = 350^\circ\text{F}

. Subtracting

350

from

432

yields

82^\circ\text{F}

, which is the temperature needed on the 6th day.

Step-by-Step Solution

Calculate the total sum of the temperatures for the first

5

days.

68 + 74 + 71 + 65 + 72 = 350

To find the missing value, we first need the combined total of the known data points.

Determine the required total sum for all

6

days using the target mean.

\text{Total Sum} = 6 \times 72 = 432

The mean of

6

values is equal to the sum of all

6

values divided by

6

Subtract the

5

-day sum from the total

6

-day sum to solve for

x

x = 432 - 350 = 82

The difference between the required total sum and the existing sum gives the value of the 6th data point.

Key Concept

Finding a missing data value using a target arithmetic mean

Estimated Time:1m 0s

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