Five classmates want to know how many of the 2688 students in their school prefer pop music. They each randomly survey 64 students. The table shows the results. Use the results from each classmate to make an inference about the number of students in the school who prefer pop music.

Based on Shannon's results, the number is __
students.

Based on Trey's results, the number is __
students.

Based on Robert's results, the number is __
students.

Based on Callie's results, the number is __
students.

Based on Lani's results, the number is __
students.

Question 2
Describe the variation of the five inferences. Which one would you use to describe the number of students at the school who prefer pop music? Explain.
The greatest is __
students. The least is __
students. The median of the data is __
. The mode of the data is __
. So, use the inference of __
students to describe the number of students at the school who prefer pop music.

Question 1

Shannon: 882/2688

Trey: 1008/2688

Robert: 798/2688

Callie: 882/2688

Lani: 840/2688

Question 2

The greatest is 1008/2688 students.

The least is 798/2688 students.

The median of the data is 882/2688 students.

The mode of the data is 882/2688 students.

So, use the inference of 882/2688 students to describe the number of students at the school who prefer pop music.

Step-by-step explanation

Question 1

Shannon: Because 21/64 in Shannon's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 21 gets us 882/2688 who might prefer pop music in the entire school without surveying all of the students.

Trey: Because 24/64 in Trey's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 24 gets us 1008/2688 who might prefer pop music in the entire school without surveying all of the students.

Robert: Because 19/64 in Robert's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 19 gets us 798/2688 who might prefer pop music in the entire school without surveying all of the students.

Callie: Because 21/64 in Callie's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 21 gets us 882/2688 who might prefer pop music in the entire school without surveying all of the students.

Lani: Because 20/64 in Lani's survey stated they preferred pop music, we can apply it to the entire school of 2688 students. 2688 divided by 64, then multiplied by 20 gets us 840/2688 who might prefer pop music in the entire school without surveying all of the students.

Question 2

Using Shannon's or Callie's survey would best describe the number of students in the entire school because their individual results (21/64) is the average of all of the individual results of the 5 students. If you decide to use any of the other individual survey results, you will not get the closest answer to the actual amount of students who prefer pop music in the entire school.

Using the individual survey results to estimate the number of students who prefer pop music in the entire school:

The greatest was Trey's results, which estimated about 1008 out of 2688 students in the entire school who would prefer pop music.

The least was Robert's results, which estimated about 798 out of 2688 students in the entire school who would prefer pop music.

The median of the data was 882 out of 2688 students in the entire school who would prefer pop music, as shown in Shannon's and Callie's individual survey results.

To find the median, list the results least to greatest, then look at the number that is in the exact middle. If there is no middle, but instead two middle numbers, find the average of the two.

The mode of the data was Shannon's or Callie's results, which estimated about 882 out of 2688 students in the entire school who would prefer pop music.

To find the mode, look for the number or result that it repeated the most (Ex: the result of 21/64 students who preferred pop music was found twice compared to the other individual survey results which did not repeat more than once).

So, in the end using Shannon's or Callie's individual survey results to estimate the amount of students in the entire school who prefer pop music is the best way to do so.

Please comment if you think I made a mistake, misunderstood, or missed something.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b