Let’s solve each part step by step.
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Problem 1a: Complete the table for ages and salaries of 10 employees.
We read each point from the scatter plot:
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A: Age = 20, Salary = $1400
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B: Age = 23, Salary = $2100
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C: Age = 25, Salary = $2100
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D: Age = 26, Salary = $3000
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E: Age = 29, Salary = $2700
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F: Age = 38, Salary = $2500
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G: Age = 38, Salary = $3500
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H: Age = 45, Salary = $2900
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I: Age = 46, Salary = $4000
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J: Age = 50, Salary = $3600
*(Note: We estimate based on grid lines — each small square is 1 year horizontally and $100 vertically.)*
✔ Table filled:
| Employee | Age (years) | Salary ($) |
|----------|-------------|------------|
| A | 20 | 1400 |
| B | 23 | 2100 |
| C | 25 | 2100 |
| D | 26 | 3000 |
| E | 29 | 2700 |
| F | 38 | 2500 |
| G | 38 | 3500 |
| H | 45 | 2900 |
| I | 46 | 4000 |
| J | 50 | 3600 |
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Problem 1b: Comment briefly on the relationship between salary and age.
Looking at the points: As age increases, salary tends to go up — but not perfectly. For example:
- At age 38, one person earns $2500, another earns $3500 → big difference.
- At age 25 vs 26: salary jumps from $2100 to $3000.
- Overall trend: older employees tend to earn more, but there are exceptions.
So: There is a
positive correlation — generally, as age increases, salary increases — but it’s not strong or perfect. Some younger people earn more than some older ones.
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Problem 1c: Why may it not be reasonable to use this info to estimate salary of an employee aged 58?
The oldest employee in the data is 50 years old (employee J). Age 58 is
outside the range of our data. This is called
extrapolation — guessing beyond what we’ve seen. The pattern might change after age 50 (maybe salaries plateau or drop), so we can’t trust the trend to continue.
Also, only 10 people — not enough to make reliable predictions far outside the data.
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Problem 2a: Draw the scatter plot for bird watchers’ data.
We have these pairs (Temperature, Number of birds):
- (5, 70)
- (10, 52)
- (15, 42)
- (20, 26)
- (25, 12)
- (30, 4)
On the graph provided:
- X-axis: Temperature (°C) from 0 to 35
- Y-axis: Number of birds from 0 to 80
Plot each point:
- At x=5, y=70 → top left
- x=10, y=52
- x=15, y=42
- x=20, y=26
- x=25, y=12
- x=30, y=4 → bottom right
You’ll see the points go downward from left to right.
*(Since we can’t draw here, imagine plotting those 6 points — they form a clear downward slope.)*
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Problem 2b: What does your diagram tell you about the change in number of birds as temperature increases?
As temperature goes up, the number of birds visiting the table goes down.
Example:
- At 5°C → 70 birds
- At 30°C → only 4 birds
This is a
negative correlation — when one thing increases, the other decreases.
Possible reason: Birds may prefer cooler weather, or food sources change with heat.
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Final Answer:
1a. Completed Table:
| Employee | Age (years) | Salary ($) |
|----------|-------------|------------|
| A | 20 | 1400 |
| B | 23 | 2100 |
| C | 25 | 2100 |
| D | 26 | 3000 |
| E | 29 | 2700 |
| F | 38 | 2500 |
| G | 38 | 3500 |
| H | 45 | 2900 |
| I | 46 | 4000 |
| J | 50 | 3600 |
1b. Generally, as age increases, salary tends to increase — but not always. There’s a positive trend, but with noticeable variation (e.g., two 38-year-olds earn very different amounts).
1c. It’s not reasonable because 58 is outside the age range of the data (max is 50). Predicting beyond the data (extrapolation) is unreliable — the pattern might not hold.
2a. Plot the six points: (5,70), (10,52), (15,42), (20,26), (25,12), (30,4) on the given grid. They will show a downward trend.
2b. As temperature increases, the number of birds visiting the table decreases. This shows a negative correlation — hotter days mean fewer birds come to the feeder.
Parent Tip: Review the logic above to help your child master the concept of interpreting scatter plots worksheet.
