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

Let’s solve each part step by step.

---

Problem 1a: Complete the table for ages and salaries of 10 employees.

We read each point from the scatter plot:

- Employee A: Age = 20, Salary = $1400 (since it's halfway between 1000 and 2000? Wait — let’s check grid carefully)

Actually, looking at the graph:

The x-axis is “Age (years)” from 10 to 60, with major ticks every 10 years → so each small square is 1 year.

The y-axis is “Salary ($)” from 0 to 5000, with major ticks every 1000 → so each small square is $100.

Now read each point:

- A: x=20, y=1400 → Age 20, Salary $1400
- B: x=23, y=2100 → Age 23, Salary $2100
- C: x=25, y=2100 → Age 25, Salary $2100
- D: x=27, y=3000 → Age 27, Salary $3000
- E: x=29, y=2700 → Age 29, Salary $2700
- F: x=38, y=2500 → Age 38, Salary $2500
- G: x=38, y=3500 → Age 38, Salary $3500
- H: x=45, y=2900 → Age 45, Salary $2900
- I: x=45, y=4000 → Age 45, Salary $4000
- J: x=50, y=3600 → Age 50, Salary $3600

Wait — let me double-check some points because sometimes they’re not exactly on lines.

Looking again:

- Point A: clearly at age 20, salary 1400? Actually, if each small box is $100, then from 1000 up 4 boxes = 1400 → yes.
- B: age 23 (3 boxes right of 20), salary 2100 (1 box above 2000) → yes.
- C: age 25, same height as B → 2100 → yes.
- D: age 27, salary 3000 → yes.
- E: age 29, salary 2700 → 7 boxes above 2000 → yes.
- F: age 38, salary 2500 → halfway between 2000 and 3000 → yes.
- G: same age as F (38), but higher — 3500 → yes.
- H: age 45, salary 2900 → just below 3000 → yes.
- I: age 45, salary 4000 → exact line → yes.
- J: age 50, salary 3600 → 6 boxes above 3000 → yes.

So table:

| Employee | Age (years) | Salary ($) |
|----------|-------------|------------|
| A | 20 | 1400 |
| B | 23 | 2100 |
| C | 25 | 2100 |
| D | 27 | 3000 |
| E | 29 | 2700 |
| F | 38 | 2500 |
| G | 38 | 3500 |
| H | 45 | 2900 |
| I | 45 | 4000 |
| J | 50 | 3600 |

✔ Table complete.

---

Problem 1b: Comment briefly on the relationship between salary and age.

Looking at the data:

As age increases, salary tends to increase overall — but not perfectly. For example:

- At age 38, one person earns $2500, another $3500 → big difference.
- At age 45, one earns $2900, another $4000 → also big difference.
- From age 20 to 27, salary goes up; then dips a bit at 29 and 38; then rises again.

So general trend: positive correlation — older employees tend to earn more, but there are exceptions. It’s not a perfect straight line.

Answer: There is a general positive relationship — as age increases, salary tends to increase — but it’s not consistent for all employees. Some younger people earn more than some older ones, and vice versa.

---

Problem 1c: Why may it not be reasonable to estimate salary of an employee aged 58?

Our data only goes up to age 50 (employee J). Age 58 is outside the range of our data.

This is called extrapolation — guessing beyond what we’ve observed. We don’t know if the pattern continues. Maybe salaries plateau after 50, or drop, or rise sharply — we can’t tell from this data.

Also, real-world factors like retirement, promotions, or job changes might affect salaries at older ages that aren’t reflected here.

Answer: Because 58 is outside the age range in the data (which stops at 50), we cannot reliably predict salary using this information. The pattern might change beyond age 50.

---

Problem 2a: Draw the scatter plot for bird watchers’ data.

Data given:

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

Plot these points:

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

On the grid provided (x-axis temp 0–35, y-axis birds 0–80), mark each point.

Since I can’t draw here, you would place dots at those coordinates.

But since the question says “Draw”, and we’re answering textually, we’ll note that the student should plot those six points.

However, for Final Answer purposes, we don’t need to describe the drawing — just answer parts b.

Wait — actually, part 2a asks to draw, but since we’re giving final answers in text, perhaps we skip describing the drawing and go to 2b.

But let’s see — the instruction says “Solve the problem accurately.” So for 2a, since it’s a drawing task, maybe we just confirm the points to plot.

But in Final Answer section, we’ll list what needs to be done.

Actually, re-reading: the user wants us to solve the problem. Since 2a is “draw”, and we can’t draw, perhaps we state the coordinates to plot.

But let’s proceed to 2b first.

---

Problem 2b: What does your diagram tell you about the change in number of birds as temperature increases?

Looking at the data:

As temperature goes up:
5°C → 70 birds
10°C → 52 birds
15°C → 42 birds
20°C → 26 birds
25°C → 12 birds
30°C → 4 birds

Clearly, as temperature increases, the number of birds decreases.

It’s a strong negative correlation.

Answer: As temperature increases, the number of birds visiting the bird table decreases. There is a clear downward trend.

---

Now, compiling Final Answers.

Note: For 2a, since it’s a drawing task, and we’re to provide final answer, perhaps we list the points to plot. But the instruction says “provide only the final correct answer” — so for 2a, maybe we say “Plot the points: (5,70), (10,52), (15,42), (20,26), (25,12), (30,4)” — but that’s not really an “answer”, it’s instructions.

Alternatively, since the worksheet expects the student to draw, and we’re solving, perhaps for 2a we just acknowledge it’s done by plotting those points.

But to follow format strictly, let’s structure Final Answer per sub-question.

Final Answer will include:

1a: Completed table
1b: Brief comment
1c: Explanation
2a: List of points to plot (since we can't draw)
2b: Observation

But wait — the original problem has two main questions, each with subparts.

Let me write Final Answer accordingly.

──────────────────────────────────────

Final Answer:

1a. Completed Table:

| Employee | Age (years) | Salary ($) |
|----------|-------------|------------|
| A | 20 | 1400 |
| B | 23 | 2100 |
| C | 25 | 2100 |
| D | 27 | 3000 |
| E | 29 | 2700 |
| F | 38 | 2500 |
| G | 38 | 3500 |
| H | 45 | 2900 |
| I | 45 | 4000 |
| J | 50 | 3600 |

1b. There is a general positive relationship: as age increases, salary tends to increase, but it is not consistent — some older employees earn less than younger ones, and salaries vary even at the same age.

1c. It is not reasonable to estimate the salary of a 58-year-old employee because 58 is outside the range of the data (which only goes up to age 50). Predicting beyond the known data (extrapolation) is unreliable since the pattern may change.

2a. Plot the following points on the grid:
(5, 70), (10, 52), (15, 42), (20, 26), (25, 12), (30, 4)

2b. As temperature increases, the number of birds seen decreases. There is a strong negative correlation — higher temperatures are associated with fewer birds visiting the bird table.