QuestionFind the missing number in the data set 18, 16, 9, 12, 23 if the mean is 15.

Studdy Solution

STEP 1

Assumptions1. The data set includes18,16,9,12,23, and a missing number. . The mean of this data set is15.

STEP 2

The mean of a data set is calculated by summing all the numbers in the data set and then dividing by the count of numbers in the data set. We can write this as $Mean = \frac{Sum\, of\, all\, numbers}{Count\, of\, numbers}$

STEP 3

We know the mean is15 and the count of numbers is6 (including the missing number). We can set up the equation $15 = \frac{Sum\, of\, all\, numbers}{6}$

STEP 4

To find the sum of all numbers, we can multiply both sides of the equation by6 $15 \times6 = Sum\, of\, all\, numbers$

STEP 5

Calculate the sum of all numbers $Sum\, of\, all\, numbers =15 \times =90$

STEP 6

Now we can find the missing number by subtracting the sum of the known numbers from the total sum. We can write this as $Missing\, number = Sum\, of\, all\, numbers - Sum\, of\, known\, numbers$

STEP 7

Plug in the values for the sum of all numbers and the sum of known numbers (18,16,9,12,23) to calculate the missing number $Missing\, number =90 - (18 +16 +9 +12 +23)$

STEP 8

Calculate the sum of known numbers $Sum\, of\, known\, numbers =18 +16 + +12 +23 =78$

STEP 9

Subtract the sum of known numbers from the total sum to find the missing number $Missing\, number =90 -78 =12$ The missing number in the data set is12.

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