Scatter Plots Worksheet, Examples, And Definition - Free Printable

Let's solve each of the three scatter plot problems step by step. For each problem, we will:

1. Plot the data points on the coordinate plane.
2. Determine the correlation (positive, negative, or no correlation) based on the pattern.

---

Problem 1

#### Data:
| x | y |
|---|---|
| 1 | 0 |
| 2 | 1 |
| 2 | 2 |
| 5 | 5 |

| x | y |
|---|---|
| 8 | 7 |
| 8 | 8 |
| 9 | 8 |
| 10| 10 |

#### Step 1: Plotting the Points

We'll plot all these points on the grid:
- (1,0), (2,1), (2,2), (5,5)
- (8,7), (8,8), (9,8), (10,10)

#### Step 2: Analyze the Pattern

Looking at the points:
- As $x$ increases, $y$ generally increases.
- The points form a roughly upward trend from bottom-left to top-right.
- There is some clustering (e.g., two points at $x=2$, two at $x=8$), but overall, the trend is positive.

✔ Correlation: Positive correlation

> Explanation: A positive correlation means that as one variable increases, the other tends to increase as well.

---

Problem 2

#### Data:
| x | y |
|---|---|
| 1 | 19 |
| 2 | 16 |
| 3 | 15 |
| 3 | 13 |

| x | y |
|---|---|
| 5 | 9 |
| 6 | 6 |
| 6 | 7 |
| 10| 3 |

#### Step 1: Plotting the Points

Points:
- (1,19), (2,16), (3,15), (3,13)
- (5,9), (6,6), (6,7), (10,3)

#### Step 2: Analyze the Pattern

As $x$ increases:
- $y$ decreases from 19 → 3
- Despite some variation (e.g., two points at $x=3$, $y=15$ and $y=13$; two at $x=6$, $y=6$ and $y=7$), the overall trend is downward.

✔ Correlation: Negative correlation

> Explanation: A negative correlation means that as one variable increases, the other tends to decrease.

---

Problem 3

#### Data:
| x | y |
|---|---|
| 1 | 9 |
| 1 | 15 |
| 3 | 4 |
| 5 | 8 |

| x | y |
|---|---|
| 5 | 10 |
| 6 | 19 |
| 8 | 13 |
| 8 | 5 |

#### Step 1: Plotting the Points

Points:
- (1,9), (1,15), (3,4), (5,8)
- (5,10), (6,19), (8,13), (8,5)

#### Step 2: Analyze the Pattern

Now observe:
- At $x = 1$: $y = 9$ and $15$ → different values
- At $x = 5$: $y = 8$ and $10$
- At $x = 8$: $y = 13$ and $5$
- No clear increasing or decreasing trend
- Points are scattered without a consistent direction

✔ Correlation: No correlation (or weak/no linear correlation)

> Explanation: When there’s no clear pattern or trend in the data, we say there is no correlation. Here, for similar $x$ values, $y$ varies widely, and no general direction exists.

---

✔ Final Answers:

1. Positive correlation
2. Negative correlation
3. No correlation

---

📌 Summary:

| Problem | Correlation Type |
|--------|------------------------|
| 1 | Positive |
| 2 | Negative |
| 3 | No correlation |

You would now plot each point on the provided grids accordingly. Since this is a worksheet, you'd draw the dots manually on the graph paper next to each problem.

Let me know if you'd like a visual representation or help plotting them!