Unit 6, Lesson 3
What a Point in a Scatter Plot Means
Grade 8
3.1
Warm-up
What questions do you have about these data?
| car | weight (kg) |
fuel efficiency (mpg) |
|---|---|---|
| A | 1,549 | 25 |
| B | 1,610 | 20 |
| C | 1,737 | 21 |
| D | 1,777 | 20 |
| E | 1,486 | 23 |
| F | 1,962 | 16 |
| G | 2,384 | 16 |
| H | 1,957 | 19 |
| I | 2,212 | 16 |
| J | 1,115 | 29 |
| K | 2,068 | 18 |
| L | 1,663 | 19 |
| M | 2,216 | 18 |
| N | 1,432 | 25 |
| O | 1,987 | 18 |
| P | 1,580 | 26 |
| Q | 1,234 | 30 |
| R | 1,656 | 23 |
A scatterplot with 20 data points. The horizontal axis is labeled “weight, in kilograms” and the numbers 1,000 through 2,500, in increments of 250, are indicated. The vertical axis is labeled “fuel efficiency, in miles per gallon” and the numbers 14 through 32, in increments of 2, are indicated. The graph shows the trend of the 20 data points moving linearly downward and to the right. The approximate coordinates of 11 selected data points are as follows: 1,130 comma 28. 1,240 comma 30. 1,400 comma 25. 1,490 comma 23. 1,550 comma 25. 1,590 comma 26. 1,650 comma 19. 1,740 comma 21. 1,775 comma 20. 1,950 comma 19. 2,200 comma 16.
3.3
Activity
A clothing store keeps track of the average monthly temperature in degrees Celsius and coat sales for that month in dollars.
| temperature (degrees Celsius) |
coat sales (dollars) |
|---|---|
| -5 | 1,550 |
| -3 | 1,340 |
| 3 | 1,060 |
| 8 | 1,070 |
| 15 | 680 |
| 21 | 490 |
| 23 | 410 |
| 21 | 510 |
| 17 | 600 |
| 11 | 740 |
| 6 | 940 |
| -2 | 1,390 |
- What does the point represent?
- Use the table to find the coat sales for the month with the lowest average temperature.
- Use the graph to estimate the average monthly temperature for the month with the smallest coat sales. Explain how you used the scatter plot to estimate the answer.
- If there were a point at what would it represent? Assume this point follows the trend of the other data and use the scatter plot to estimate a value for .
- What would a point at represent? Assume this point follows the trend of the other data and use the scatter plot to estimate a value for .
- Would it make sense to use this trend to estimate the value of sales when the average monthly temperature is 60 degrees Celsius? Explain your reasoning.
Student Lesson Summary
Scatter plots show two measurements for each individual from a group. For example, this scatter plot shows the weight and height for each dog from a group of 25 dogs.
A scatterplot. Horizontal, from 6 to 30, by 3’s, labeled dog height, inches. Vertical, from 0 to 112, by 16’s, labeled dog weight, pounds. 24 data points. Trend upward and to right.
We can see that the tallest dogs are 27 inches, and that one of those tallest dogs weighs about 75 pounds while the other weighs about 110 pounds. This shows us that dog weight is not a function of dog height because there would be two different outputs for the same input. But we can see a general trend: taller dogs tend to weigh more than shorter dogs. There are exceptions. For example, there is a dog that is 18 inches tall and weighs over 50 pounds, and there is another dog that is 21 inches tall but weighs less than 30 pounds.
When we collect data by measuring attributes like height, weight, area, or volume, we call the data numerical data (or measurement data), and we say that height, weight, area, or volume is a numerical variable.
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