Video Transcript
The given table shows the test scores of six different subjects for Richard and Robert. If the mean of test scores for Robert is 0.2 points greater than the mean of test scores for Richard, what is the value of 𝑥?
Let’s think about the information we were just given. We were told that Robert’s mean score is equal to Richard’s mean score plus 0.2. We remember that the mean is the sum of all data points divided by the number of data points. The mean of Robert’s test scores would then be equal to 𝑥 plus 8.2 plus 5.9 plus 9.1 plus 7.2 plus 6.3 divided by six. And we know that all of this must be equal to the mean of Richard’s test score: 8.8 plus 7.4 plus 6.5 plus 8.3 plus 7.9 plus 5.8 divided by six plus the additional 0.2 points.
On the left side, for Robert’s mean score, we could do a little bit of simplifying. We can add everything but the 𝑥 together so that we have 𝑥 plus 36.7 over six. And for Richard, we can go ahead and calculate the mean by adding all the values in the numerator and dividing them by six. All the values in the numerator sum to 44.7. When we divide 44.7 by six, we get 7.45. And we can’t forget to bring that 0.2 down. 7.45 plus 0.2 equal 7.65. We’ll give ourselves a little bit more room.
Remember, the goal here is to solve for 𝑥. And to get 𝑥 by itself, we need to get six out of the denominator. We do that by multiplying both sides of the equation by six. On the left, we’re left with 𝑥 plus 36.7. And on the right, 7.65 times six equals 45.9. Then, we subtract 36.7 from both sides of the equation. On the left, 36.7 cancels out and on the right, 45.9 minus 36.7 equals 9.2.
What we’re saying is, if Robert scored 9.2 in that missing test score, his mean score would be 7.65. Richard’s mean score would be 7.45. And Robert’s mean score would be 0.2 points higher than Richard’s mean score. The question specifically asked us to find the value for 𝑥. And so, we say that 𝑥 equals 9.2.
