Question

the data show the number of points the winning team scored in a college football bowl game. find the mean and modal class for the data.

class | frequency
12-20 | 10
21-29 | 12
30-38 | 5
39-47 | 8
48-56 | 3
57-65 | 1

send data to excel

part: 0 / 2

part 1 of 2

find the mean. round your answer to one decimal place, if necessary.

the mean number of points scored by the winning team is points.

Explanation:

Step1: Find midpoints of each class

For class \(12 - 20\), midpoint \(x_1=\frac{12 + 20}{2}=16\)
For class \(21 - 29\), midpoint \(x_2=\frac{21 + 29}{2}=25\)
For class \(30 - 38\), midpoint \(x_3=\frac{30 + 38}{2}=34\)
For class \(39 - 47\), midpoint \(x_4=\frac{39 + 47}{2}=43\)
For class \(48 - 56\), midpoint \(x_5=\frac{48 + 56}{2}=52\)
For class \(57 - 65\), midpoint \(x_6=\frac{57 + 65}{2}=61\)

Step2: Calculate \(f_i\times x_i\) for each class

• \(f_1 = 10\), so \(f_1x_1=10\times16 = 160\)
• \(f_2 = 12\), so \(f_2x_2=12\times25 = 300\)
• \(f_3 = 5\), so \(f_3x_3=5\times34 = 170\)
• \(f_4 = 8\), so \(f_4x_4=8\times43 = 344\)
• \(f_5 = 3\), so \(f_5x_5=3\times52 = 156\)
• \(f_6 = 1\), so \(f_6x_6=1\times61 = 61\)

Step3: Find total frequency (\(N\)) and total \(f_ix_i\)

\(N=\sum f_i=10 + 12+5 + 8+3 + 1=39\)
\(\sum f_ix_i=160 + 300+170 + 344+156 + 61=1191\)

Step4: Calculate the mean

Mean \(\bar{x}=\frac{\sum f_ix_i}{N}=\frac{1191}{39}\approx30.5\) (rounded to one decimal place)

Answer:

The mean number of points scored by the winning team is \(\boldsymbol{30.5}\) points.