Video: Calculating the Minimum Data Value to Meet a Given Mean

In order to get a C in math, William must have an average score of 70 or more. His test scores so far are 63.3, 85, 79.73, and 70.57. Calculate the minimum score William needs to get on his final test to earn a C.

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Video Transcript

In order to get a C in math, William must have an average score of 70 or more. His test scores so far are 63.3, 85, 79.73, and 70.57. Calculate the minimum score William needs to get on his final test to earn a C.

First of all, we need to know what an average is. We find the average score by taking the sum of all values and dividing that by the number of values. William’s average in math will be the sum of all his test scores divided by the number of tests he took. And this average needs to be greater than or equal to 70 in order for him to get a C. So let’s fill in what we know. William’s first test, he scored a 63.3. On his second test, he scored 85; on his third test, 79.73; on his fourth test, 70.57. And we don’t know what he scored on his final. That’s what we’re trying to find. So we’ll just add plus 𝐹.

How many tests did William take in math? He’s already taken four and he has one final test to take, for a total of five. And so we’ll divide by five. The first thing we can do is go ahead and add up his first four test results, which will give us 298.6. His final score will be added to this and then the average calculated by dividing by five. And we need this value to be greater than or equal to 70. So how do we go about finding 𝐹? Well, we can get the five out of the denominator by multiplying both sides of the equation by five. On the left side, the fives cancel out, leaving us with 298.6 plus 𝐹. And on the right side we have 70 times five, which is 350.

Again, we’re trying to get 𝐹 by itself. And so we subtract 298.6 from both sides. The 298.6 cancels out on the left. And then we have 350 minus 298.6, which is 51.4. And what this inequality tells us is that 𝐹, the final score, must be greater than or equal to 51.4 in order for William to get a 70 in math. Our question has specifically asked the minimum score that William can get to earn a C in the class. The lowest score that William can earn on his final and still get a 70 in his class is 51.4.

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