How To Find The Average If One Number Is Missing

Determining a Missing Data Value Given the Mean

In this section we will be looking at examples where we have been given the average or hateful but we are missing ane of the values from the set that has that mean.

This might sound kind of confusing, so let's get correct to some examples.

Example #1:

Sunil wants to earn an 88% in her Chemistry course. She has one quiz left to take.

On the first v quizzes, she received a 74%, 92%, 83%, 98%, 100%. What must she score on the 5^thursday quiz to get the 88% she wants?

Footstep 1: Recall the steps for determining the mean.

We would add together up all of the scores and divide by how many scores there are.

Step two: Fix the trouble as if you lot were determining the mean. We can use an x to represent the quiz class that we don't know.

Step three: Now we are ready to solve.

Start by multiplying both sides past 6.

74 + 92 + 83 + 98 + 100 + x = 528

Side by side, nosotros will add all the values together on the left side.

Finally, nosotros will subtract the 447 from the 528 points nosotros need to earn full to make up one's mind the score of the 6^thursday quiz.

Let's check out another case.

Instance #2:

Frank wants to accept a bowling boilerplate of 215.

The beginning 7 games he scored 159, 182, 225, 240, 198, 200, 230. What must he score in the 8th game to take an average of 215?

Step 1: Ready up the problem using the method for determining the mean.

Stride two: Multiply both sides by 8 to eliminate the fractions.

Step 3: Add up the scores on the left side of the equation.

Stride 4: Subtract this value from the 1720.

Frank would have to score a 286 in social club to accept a bowling average of 215.

Let's Review:

If you are given a mean and asked for one of the data values, yous tin still use the basic method for determining the mean, but work backwards. Generally we add up all the values and then carve up by the number of values. In this case, working backwards, we multiply by the number of values (instead of dividing) and and then subtract (instead of adding). Yous should be left with a information value from the set.

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Math
Probability and Statistics