https://file.aiquickdraw.com/mathbot/file/1726893323996whh58a17.jpg

Let's break down the image and address each part of the problem systematically:

### a) Percentile Rank
Bettina found a job offering a wage between **$10.00 and $10.99**. The table shows that 29 employees earn in this wage range. To calculate her percentile ranking, we need to know her position relative to all the employees.

- The total number of employees in the data is:
  \[
  27 + 29 + 51 + 38 + 23 + 15 + 8 = 191
  \]

- Employees earning less than $10.00 are in the range **$9.25–$9.99**, with **27** employees.

To find her percentile rank, we calculate how many people earn less than $10.00 and use that to find her rank:
\[
\text{Percentile Rank} = \frac{\text{number of employees earning less than her wage}}{\text{total number of employees}} \times 100
\]
\[
\text{Percentile Rank} = \frac{27}{191} \times 100 \approx 14.14\%
\]

Thus, Bettina would be in the **14th percentile** in terms of wages.

---

### b) Median Wage Range (50th Percentile)

The median is the wage at the 50th percentile, which means it divides the dataset into two equal halves. To find this, we need to locate the middle value of the employees.

- There are **191 employees**, so the median falls at the position:
  \[
  \text{Median position} = \frac{191 + 1}{2} = 96\text{th employee}
  \]

Now we count employees cumulatively until we reach the 96th employee:
- First wage range: 27 employees (\$9.25–\$9.99)
- Second wage range: 29 employees (\$10.00–\$10.99), cumulative total = 56 employees
- Third wage range: 51 employees (\$11.00–\$11.99), cumulative total = **107 employees**

Since the median falls at the 96th position, it lies in the **\$11.00–\$11.99** wage range.

---

### Relationship between Median and Percentile Rank
The **median** represents the **50th percentile**, meaning half of the employees earn less than this wage, and half earn more. Percentile rank, on the other hand, is a measure of how an individual wage compares to the entire dataset. Bettina’s wage falls in the 14th percentile, meaning 14% of employees earn less than her, and 86% earn more.

---

Would you like more details or have any questions?

### Related Questions:
1. How is the percentile rank different from the median?
2. If Bettina’s wage increases to \$11.50, how would her percentile rank change?
3. What is the difference between the mean and median wage?
4. Can you calculate the range of wages in the 25th percentile?
5. What does a high percentile wage mean in terms of income distribution?

### Tip:
Always remember that the **median** is not affected by extreme values (outliers), while the **mean** can be, making the median a more reliable measure in skewed distributions.

Bettina is investigating how much she can expect to earn as an early childhood educator. She found a job offering a wage between $10.00 and $10.99. She wants to know what percentile she falls into compared to other workers in her field and also the median wage range in Saskatchewan.

Learn how to calculate percentile rank and median wage range using a dataset of early childhood educators' wages in Saskatchewan. This problem includes detailed steps and formulas suitable for high school students.

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