Question

The table below shows the heights of students in a group.

Student
Height
(in inches)
A
50
B
54
C
52
D
56
E
48


What is the mean height of the students in the group? (1 point)

48 inches

49 inches

51 inches

52 inches

Peter asked the students of his class their football scores and recorded the scores in the table shown below:
Football Scores
Score
Number of
Students
0
5
1
3
2
12
3
2
4
6
5
6
6
4


Based on the table, what is the mean football score? (1 point)

1.3

1.8

2.9

3.5

Answer 1

`\bar x = 52inch\\\bar x_w = 2.92`

Explanation:

According to the data recorded in the table, the average of the students' heights is calculated with the expression for the arithmetic mean:

`\bar x =(1)/(n) \sum x_i`

`\bar x = (1)/(5)(48 + 50 + 52 + 54 + 56) = (260)/(5) = 52`inch.

In the same way, the weighted average must be used to find the average football score:

`\bar x_w = (\sum x_i * w_i)/(\sum w_i)`, where wi are the frequencies of each response.

`\bar x_w = (0 * 5 + 1 * 3 + 2 * 12 + 3 * 2 + 4 * 6 + 5 * 6 + 6 * 4) / (5 + 3 + 12 + 2 + 6 + 6 + 4) = (111)/(38) = 2.92`

Answer 2

1. 52

2. 2.9

Explanation:

To find the mean, we take all the numbers, add them up then divide by the number of numbers.

1. mean height

mean = (50+54+52+56+48)/5

=260/5

=52

52 inches

2. mean score

There are 5+3+12+2+6+6+4 students = 38 students

Multiply the number of students times the score and add together

total points = (0*5+1*3+2*12+3*2+4*6+5*6+6*4)

= 111

The mean is the total points divided by the number of students

mean = 111/38

=2.92