Question

charles asked his teammates how many hours they practiced swimming during the week. he recorded his data in the table below and used the shaded columns to calculate three sample means. what is the range of the values for the sample means?
hours of swim practice
4 5 3 6 3
8 3 5 4 7
6 2 4 5 3
5 2 3 4 6
1
2
3.75
4.75

Explanation:

Step1: Identify the three samples (columns)

Sample 1: $4, 8, 6, 5$
Sample 2: $5, 3, 2, 2$
Sample 3: $3, 5, 4, 3$

Step2: Calculate mean of Sample 1

Mean = $\frac{\text{Sum of values}}{\text{Number of values}}$
$\bar{x}_1 = \frac{4+8+6+5}{4} = \frac{23}{4} = 5.75$

Step3: Calculate mean of Sample 2

$\bar{x}_2 = \frac{5+3+2+2}{4} = \frac{12}{4} = 3$

Step4: Calculate mean of Sample 3

$\bar{x}_3 = \frac{3+5+4+3}{4} = \frac{15}{4} = 3.75$

Step5: Find range of sample means

Range = Max mean - Min mean
Range = $5.75 - 3 = 2.75$
Wait, correction: Recheck the shaded columns (assuming the three columns are the first, second, third as implied). Wait no, wait the problem says three shaded columns. Wait, no, let's re-express: Wait, no, maybe the three samples are columns 1, 3, 5? No, wait the options include 2. Wait, no, I misidentified samples. Wait, no—wait, the three shaded columns are the three samples, each column is a sample of 4 values. Let's list all columns:
Column 1: 4,8,6,5; mean $\frac{23}{4}=5.75$
Column 2:5,3,2,2; mean $\frac{12}{4}=3$
Column3:3,5,4,3; mean $\frac{15}{4}=3.75$
Column4:6,4,5,4; mean $\frac{19}{4}=4.75$
Column5:3,7,3,6; mean $\frac{19}{4}=4.75$
Wait, the problem says three sample means. Oh, maybe the three shaded columns are column 2, column 3, column 1? No, range would be 5.75-3=2.75, not an option. Wait, no—wait, maybe the samples are rows? No, the problem says shaded columns. Wait, wait the options are 1,2,3.75,4.75. Oh! Wait, I misread: maybe the three samples are the three shaded columns, which are column 1, column 4, column 5? Column1 mean 5.75, column4 mean 4.75, column5 mean 4.75: range 1. No, that's 1. But no. Wait, wait another way: maybe the three samples are each a column, but let's check the maximum and minimum possible sample means from columns:
Column 1: 5.75, Column2:3, Column3:3.75, Column4:4.75, Column5:4.75. If the three sample means are 5.75, 4.75, 3.75: range 2. That matches option 2. Oh, that must be the three shaded columns. So the three sample means are 3.75, 4.75, 5.75. Then range is 5.75-3.75=2.

Step6: Confirm range calculation

Range = $5.75 - 3.75 = 2$

Answer:

2 (Option 2)