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The number of hours that Terry, Dan, Jenny, and Lucy watch television during the week is given in the table below. Using the mean as the measure of center, arrange the four names in order starting with the person who generally spends the most hours watching TV and ending with the person who generally spends the least hours watching TV.

[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Lucy (hours)} & \text{Dan (hours)} & \text{Terry (hours)} & \text{Jenny (hours)} \\
\hline
7 & 4 & 3 & 3 \\
5 & 3 & 2 & 5 \\
6 & 2 & 1 & 4 \\
7 & 4 & 4 & 5 \\
6 & 3 & 2 & 4 \\
8 & 7 & 4 & 6 \\
10 & 5 & 5 & 8 \\
\hline
\end{array}
\][/tex]

Calculate the mean number of hours for each person and list them in order from most to least hours of TV watched.



Answer :

GinnyAnswer
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.

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