Question

two methods are used to collect data to estimate the average shoe size of seventh - grade boys.
method 1
six boys are randomly selected, asked their shoe size, and the answers recorded.
method 2
the six boys with the largest shoes are asked their shoe size and the answers recorded. the results are shown in the table below.

method 1 student shoe size	method 2 student shoe size

calculate the mean for each method. round to the nearest hundredth, if necessary.
the mean shoe size for method 1 is
the mean shoe size for method 2 is

Explanation:

Step1: Calculate the sum for Method 1

The shoe sizes for Method 1 are \(8.5, 8, 7, 12.5, 7.5, 9\).
Sum \(= 8.5 + 8 + 7 + 12.5 + 7.5 + 9\)
\(= 8.5 + 8 = 16.5\); \(16.5 + 7 = 23.5\); \(23.5 + 12.5 = 36\); \(36 + 7.5 = 43.5\); \(43.5 + 9 = 52.5\)

Step2: Find the mean for Method 1

Mean \(= \frac{\text{Sum}}{\text{Number of values}} = \frac{52.5}{6}\)
\(= 8.75\)

Step3: Calculate the sum for Method 2

The shoe sizes for Method 2 are \(12.5, 12, 12.5, 11.5, 11, 13\).
Sum \(= 12.5 + 12 + 12.5 + 11.5 + 11 + 13\)
\(= 12.5 + 12 = 24.5\); \(24.5 + 12.5 = 37\); \(37 + 11.5 = 48.5\); \(48.5 + 11 = 59.5\); \(59.5 + 13 = 72.5\)

Step4: Find the mean for Method 2

Mean \(= \frac{\text{Sum}}{\text{Number of values}} = \frac{72.5}{6}\)
\(\approx 12.08\) (rounded to the nearest hundredth)

Answer:

The mean shoe size for Method 1 is \(8.75\).
The mean shoe size for Method 2 is \(12.08\).