Constructing and Interpreting Scatter Plots Worksheet | Fun and ... - Free Printable

Let's solve each part of the problem step by step.

---

Problem 1: Scatter Plot – Ages and Salaries

#### a. Complete the table for the ages and monthly salaries of 10 employees.

We are given a scatter plot with points labeled A to J. The x-axis is Age (years), and the y-axis is Salary ($).

We need to read the coordinates from the graph:

- Each square on the x-axis represents 1 year.
- Each square on the y-axis represents $100.

Let’s find the coordinates of each point:

| Employee | Age (years) | Salary ($) |
|----------|-------------|------------|
| A | 20 | 1500 |
| B | 24 | 2200 |
| C | 25 | 2200 |
| D | 26 | 3100 |
| E | 29 | 2800 |
| F | 38 | 2500 |
| G | 38 | 3700 |
| H | 45 | 3000 |
| I | 46 | 4000 |
| J | 50 | 3700 |

> ✔ Explanation:
> - For example, point A is at age 20 and salary $1500 (on the 15th grid line from bottom).
> - Point B is at age 24 and salary $2200.
> - Note that B and C have same salary but different ages.
> - G and F both at age 38, but G earns more than F.

---

#### b. Comment briefly on the relationship between salary and age for these employees.

Answer:
There appears to be a positive correlation between age and salary — as age increases, salary tends to increase. However, the relationship is not perfectly linear, and there are some exceptions (e.g., employee F is older than E but earns less). Overall, older employees tend to earn higher salaries, suggesting experience may play a role in pay.

---

#### c. Explain why it may not be reasonable to use this information to estimate the salary of an employee aged 58.

Answer:
It would not be reasonable to estimate the salary of a 58-year-old employee because:
- The data only includes employees up to age 50.
- Extrapolating beyond the range of the data (especially far beyond) can lead to inaccurate predictions.
- There may be other factors affecting salary (e.g., job role, performance, industry trends), and the trend might not continue beyond age 50.
- The pattern may change — for example, salaries might plateau or even decrease after a certain age.

> This is known as extrapolation, which is risky when making predictions outside the observed data range.

---

Problem 2: Bird Watching – Temperature vs Number of Birds

Given data:

| Temperature (°C) | 5 | 10 | 15 | 20 | 25 | 30 |
|------------------|-----|-----|-----|-----|-----|-----|
| Number of birds | 70 | 52 | 42 | 26 | 12 | 4 |

#### a. Draw the scatter plot for this information on the grid.

We’ll describe how to plot it since we can't draw here:

- X-axis: Temperature (°C), from 0 to 35
- Y-axis: Number of birds, from 0 to 80

Plot the following points:

- (5, 70)
- (10, 52)
- (15, 42)
- (20, 26)
- (25, 12)
- (30, 4)

> These points should form a downward-sloping pattern.

---

#### b. What does your diagram tell you about the change in the number of birds seen as the temperature increases?

Answer:
As the temperature increases, the number of birds visiting the bird table decreases. This suggests a negative correlation between temperature and bird visits.

> Possible explanation: Birds may prefer cooler temperatures or seek shelter during hot weather, so fewer come to feed when it's warmer.

---

✔ Final Summary

#### Problem 1
- Table completed using graph coordinates.
- Positive correlation between age and salary.
- Cannot predict salary for age 58 due to extrapolation risk.

#### Problem 2
- Scatter plot shows decreasing bird count with increasing temperature.
- Strong negative correlation — more birds at lower temps, fewer at higher temps.

---

Let me know if you'd like a visual sketch of the second scatter plot!