Question

1. a survey of a high school track team asked the 40 members how many hours per week (rounded to the nearest hour) they spend running outside of team practices. the 40 responses are summarized in the histogram below. to the nearest hundredth of an hour, what is the average number of hours spent running for the 40 respondents? a. 2.75 b. 2.90 c. 3.25 d. 3.40 e. 6.00

Explanation:

Step1: Determine the mid - point and frequency of each class

From the histogram:

• For 0 hours: Mid - point \(x_1 = 0\), Frequency \(f_1=4\)
• For 1 hour: Mid - point \(x_2 = 1\), Frequency \(f_2 = 6\)
• For 2 hours: Mid - point \(x_3 = 2\), Frequency \(f_3 = 6\)
• For 3 hours: Mid - point \(x_4 = 3\), Frequency \(f_4 = 10\)
• For 4 hours: Mid - point \(x_5 = 4\), Frequency \(f_5 = 9\)
• For 5 hours: Mid - point \(x_6 = 5\), Frequency \(f_6 = 4\)
• For 6 hours: Mid - point \(x_7 = 6\), Frequency \(f_7 = 1\)

Step2: Calculate the sum of the product of mid - points and frequencies

\(\sum_{i = 1}^{7}f_ix_i=4\times0 + 6\times1+6\times2 + 10\times3+9\times4+4\times5+1\times6\)
\(=0 + 6+12 + 30+36+20+6\)
\(=110\)

Step3: Calculate the total frequency

The total number of respondents \(n=\sum_{i = 1}^{7}f_i=4 + 6+6 + 10+9+4+1=40\)

Step4: Calculate the average

The average \(\bar{x}=\frac{\sum_{i = 1}^{7}f_ix_i}{n}=\frac{110}{40}=2.75\)

Answer:

A. 2.75