Two high school teachers, Ms. Brown and Mr. Sorrentino, are preparing their students to take the state’s standardized testing for the school year. In the previous school year, Ms. Brown and Mr. Sorrentino followed the same curriculum and teaching methods. Based on last year’s score report to the teachers, the students in both classrooms yielded an average score of 83. This year, Ms. Brown and Mr. Sorrentino are following different curriculums to determine whether this will raise their class averages.

Question

Compared to last year, Ms. Brown’s students spent an additional week studying probability and two additional weeks studying inequalities. Here are her students’ scores from this year’s report:

71
79
93
75
88
72
91
80
71
90

What is the difference between the means of Ms. Brown’s class based on the listed scores and information from the problem?

Answer 1

To find the mean of Ms. Brown's class based on the scores provided, we need to sum the scores and divide by the number of scores.

Here are the scores from Ms. Brown's class:

71, 79, 93, 75, 88, 72, 91, 80, 71, 90

Step 1: Calculate the sum of the scores.

\[ 71 + 79 + 93 + 75 + 88 + 72 + 91 + 80 + 71 + 90 = 79 + 93 + 75 + 88 + 72 + 91 + 80 + 71 + 90 = <br> 71 + 79 = 150 <br> 150 + 93 = 243 <br> 243 + 75 = 318 <br> 318 + 88 = 406 <br> 406 + 72 = 478 <br> 478 + 91 = 569 <br> 569 + 80 = 649 <br> 649 + 71 = 720 <br> 720 + 90 = 810 \]

The total sum of the scores is 810.

Step 2: Count the number of scores.

There are 10 scores in total.

Step 3: Calculate the mean.

Mean = Total Sum of Scores / Number of Scores

\[ \text{Mean} = \frac{810}{10} = 81 \]

Step 4: Determine the difference between this year's mean and last year's mean.

Last year's average score was 83.

Now, we find the difference:

\[ \text{Difference} = \text{Last Year's Mean} - \text{This Year's Mean} = 83 - 81 \]

The difference is:

\[ \text{Difference} = 2 \]

Thus, the difference between the means of Ms. Brown's class based on this year's scores and last year's average is 2.