## The low temperatures in Anchorage, Alaska, for a week were − 6, − 3, − 1, 1, − 3, − 9, and − 14 degrees Celsius. What two temperatures could

Question

The low temperatures in Anchorage, Alaska, for a week were − 6, − 3, − 1, 1, − 3, − 9, and − 14 degrees Celsius. What two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers?

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5 months 2021-12-31T02:34:35+00:00 1 Answer 0 views 0

1. The two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers are -1 and -9

Step-by-step explanation:

The formula of the average of a set of data is $$A=\frac{S}{N}$$ , where

• S is the sum of the data in the set
• N is the number of the data in the set

∵ The low temperatures in Anchorage, Alaska, for a week were

− 6, − 3, − 1, 1, − 3, − 9, and − 14 degrees Celsius

∴ The set of the data is { -6 , -3 , -1 , 1 , -3 , -9 , -14}

– Add the data in the set

∵ S = -6 + -3 + -1 + 1 + -3 + -9 + -14

S = -35

∵ The set has 7 data

N = 7

– Use the formula of the average above to find it

∴ $$A=\frac{-35}{7}$$

A = -5

∴ The average of the original set of numbers is -5

To keep the average the same after removing two numbers multiply the average by the new number of data to find the new sum

∵ The number of data after removing two numbers is 5

N = 5

A = -5

– By using the rule of average

∴ $$-5=\frac{S}{5}$$

– Multiply both sides by 5

∴ -25 = S

The new sum is -25

– Lets find which two numbers of have a sum of -10 because

the difference between -35 and -25 is -10

-1 + -9 = -10

-6 + -3 + 1 + -3 + -14 = -25

∴ We could removed -1 and -9

The two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers are -1 and -9