To determine the order of people based on the average (mean) number of hours they spend watching television per week, we first need to calculate the mean hours for each person. Here is the step-by-step solution:
1. Calculate the Mean Hours for Each Person:
- Lucy:
[tex]\[
\text{Lucy’s hours} = [7, 5, 6, 7, 6, 8, 10]
\][/tex]
[tex]\[
\text{Lucy’s mean} = \frac{7 + 5 + 6 + 7 + 6 + 8 + 10}{7} = \frac{49}{7} = 7.0
\][/tex]
- Dan:
[tex]\[
\text{Dan’s hours} = [4, 3, 2, 4, 3, 7, 5]
\][/tex]
[tex]\[
\text{Dan’s mean} = \frac{4 + 3 + 2 + 4 + 3 + 7 + 5}{7} = \frac{28}{7} = 4.0
\][/tex]
- Terry:
[tex]\[
\text{Terry’s hours} = [3, 2, 1, 4, 2, 4, 5]
\][/tex]
[tex]\[
\text{Terry’s mean} = \frac{3 + 2 + 1 + 4 + 2 + 4 + 5}{7} = \frac{21}{7} = 3.0
\][/tex]
- Jenny:
[tex]\[
\text{Jenny’s hours} = [3, 5, 4, 5, 4, 6, 8]
\][/tex]
[tex]\[
\text{Jenny’s mean} = \frac{3 + 5 + 4 + 5 + 4 + 6 + 8}{7} = \frac{35}{7} = 5.0
\][/tex]
2. Arrange in Descending Order by the Mean Hours:
Based on the calculated means,
- Lucy: 7.0 hours
- Jenny: 5.0 hours
- Dan: 4.0 hours
- Terry: 3.0 hours
To order them from the most hours to the least hours:
1. Lucy (7.0 hours)
2. Jenny (5.0 hours)
3. Dan (4.0 hours)
4. Terry (3.0 hours)
So, the names in order from the person who generally spends the most hours watching TV to the one who spends the least are:
Lucy, Jenny, Dan, and Terry.
