The following graph shows the number of hours per week worked by Wendy, Thandi and Sindi. Study the graph and…

Question

The following graph shows the number of hours per week worked by Wendy, Thandi and Sindi. Study the graph and answer the questions.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for questions 2.1.2, 2.1.3, and 2.1.4 based on the provided graph.

2.1.2 Determine median number of hours worked over the six weeks.

List all hours worked by Wendy, Thandi, and Sindi over the six weeks.
- Wendy's hours: $4, 2, 4, 4, 6, 5$
- Thandi's hours: $6, 4, 3, 4, 7, 6$
- Sindi's hours: $5, 3, 4, 3, 6, 5$ Combined list of all hours: $\{4, 2, 4, 4, 6, 5, 6, 4, 3, 4, 7, 6, 5, 3, 4, 3, 6, 5\}$
Arrange the combined list of hours in ascending order.
Sorted list: $\{2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7\}$
There are $N=18$ data points.
Calculate the median.
Since there is an even number of data points, the median is the average of the two middle values, which are the $(\frac{N}{2})^{\text{th}}$ and $(\frac{N}{2}+1)^{\text{th}}$ values.
The $\frac{18}{2} = 9^{\text{th}}$ value is 4.
The $(\frac{18}{2}+1) = 10^{\text{th}}$ value is 5.
$\text{Median} = \frac{9^{\text{th}} \text{ value} + 10^{\text{th}} \text{ value}}{2}$ $\text{Median} = \frac{4+5}{2}$ $\text{Median} = \frac{9}{2}$ $\text{Median} = 4.5$
The median number of hours worked over the six weeks is $\boxed{\text{4.5 hours}}$ .

2.1.3 Calculate the mean number of hours that Thandi worked?
List Thandi's hours for each week.
Thandi's hours: $6, 4, 3, 4, 7, 6$
Calculate the sum of Thandi's hours.
$\text{Sum} = 6+4+3+4+7+6 = 30 \text{ hours}$
Calculate the mean number of hours.
There are 6 weeks.
$\text{Mean} = \frac{\text{Sum of hours}}{\text{Number of weeks}}$ $\text{Mean} = \frac{30}{6}$ $\text{Mean} = 5$
The mean number of hours that Thandi worked is $\boxed{\text{5 hours}}$ .

2.1.4 What was the mean number of hours worked in the busiest week?
Calculate the total hours worked by all students for each week to identify the busiest week.
- Week 1: $4 (\text{Wendy}) + 6 (\text{Thandi}) + 5 (\text{Sindi}) = 15$ hours
- Week 2: $2 (\text{Wendy}) + 4 (\text{Thandi}) + 3 (\text{Sindi}) = 9$ hours
- Week 3: $4 (\text{Wendy}) + 3 (\text{Thandi}) + 4 (\text{Sindi}) = 11$ hours
- Week 4: $4 (\text{Wendy}) + 4 (\text{Thandi}) + 3 (\text{Sindi}) = 11$ hours
- Week 5: $6 (\text{Wendy}) + 7 (\text{Thandi}) + 6 (\text{Sindi}) = 19$ hours
- Week 6: $5 (\text{Wendy}) + 6 (\text{Thandi}) + 5 (\text{Sindi}) = 16$ hours The busiest week is Week 5, with a total of 19 hours worked.
Identify the hours worked by each student in the busiest week (Week 5).
- Wendy: 6 hours
- Thandi: 7 hours
- Sindi: 6 hours
Calculate the mean number of hours worked in the busiest week.
There are 3 students.
$\text{Mean} = \frac{\text{Total hours in Week 5}}{\text{Number of students}}$ $\text{Mean} = \frac{6+7+6}{3}$ $\text{Mean} = \frac{19}{3}$ $\text{Mean} \approx 6.33$
The mean number of hours worked in the busiest week is $\boxed{\text{6.33 hours}}$ .

For question 2.2, the image provides the contents of the box of pens:
- 5 black pens
- 4 blue pens
- 2 red pens
- 9 green pens However, the specific questions (e.g., 2.2.1, 2.2.2) related to these pens are not visible in the image. Please send those questions so I can help you solve them!

The following graph shows the number of hours per week worked by Wendy, Thandi and Sindi. Study the graph and answer the questions.

Step-by-step solution

List all hours worked by Wendy, Thandi, and Sindi over the six weeks.

Arrange the combined list of hours in ascending order.

Calculate the median.

List Thandi's hours for each week.

Calculate the sum of Thandi's hours.

Calculate the mean number of hours.

Calculate the total hours worked by all students for each week to identify the busiest week.

Identify the hours worked by each student in the busiest week (Week 5).

Calculate the mean number of hours worked in the busiest week.

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