8.02 Scatterplots
Construct a scatterplot for the set of data in the following table:
| x | 1 | 3 | 5 | 7 | 9 |
|---|---|---|---|---|---|
| y | 3 | 7 | 11 | 15 | 19 |
The following table shows the time taken to finish a lap on a race track for various average speeds:
| Speed | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 |
|---|---|---|---|---|---|---|---|---|---|---|
| Time | 85 | 87 | 75 | 82 | 69 | 73 | 60 | 57 | 45 | 49 |
Construct a scatter plot for the data.
The following table displays results from an experiment:
| X | 1 | 4 | 5 | 8 | 9 | 11 | 13 | 15 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|
| Y | 2 | 4 | 6 | 8 | 12 | 24 | 30 | 46 | 52 | 64 |
Construct a scatter plot for this data.
Yvonne has a high income but does not like her job. Which dot in the graph would represent her?
State whether there is a relationship between each pair of variables:
Typing speed and dancing ability.
Eye color and IQ.
For each of the following pairs of variables:
Is there likely to be a relationship between the two?
Do you think the correlation is positive or negative?
Time spent studying and exam performance.
Rainfall and traffic accidents.
Height and weight.
Temperature and ice cream sales.
Describe the relationship between the variables in the following scatter plots:
The scatter plot shows the relationship between air and sea temperature:
Describe the relationship between air and sea temperature.
Describe the correlation between air and sea temperature.
For each of the following scatter plots, describe the correlation in terms of strength and direction:
The following scatter plot shows the relationship between sea temperatures and the amount of healthy coral:
Describe the correlation between sea temperature the amount of healthy coral.
Which variable is the dependent variable?
Which variable is the independent variable?
Scientists conducted a study where each person was asked to read a paragraph and then recount as much information as they can remember. They found that the longer the paragraph, the less information each person could retain.
If the length of the paragraph were plotted (on the horizontal axis) against the amount of information retained (on the vertical axis), would the correlation be negative or positive?
A database compare the income per capita of a country and the child mortality rate of that country. A sample of the data is shown in the table.
If a scatter plot was created from the entire database, describe the relationship you would expect it to have in terms of strength, direction and shape.
| Income per capita | Child Mortality rate |
|---|---|
| 1465 | 67 |
| 11\,428 | 16 |
| 2621 | 35 |
| 32\,468 | 9 |
The following table shows the number of traffic accidents associated with a sample of drivers of different age groups:
| Age | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 |
|---|---|---|---|---|---|---|---|---|---|---|
| Accidents | 41 | 44 | 39 | 34 | 30 | 25 | 22 | 18 | 19 | 17 |
Construct a scatter plot for this data.
Describe the correlation between a person's age and the number of accidents.
Does this data set contain any outliers?
The following table shows the average IQ of a random group of people against their height:
| \text{Height (cm)} | 140 | 145 | 150 | 155 | 160 | 165 | 170 | 175 | 180 | 185 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{IQ} | 103 | 95 | 98 | 111 | 85 | 89 | 108 | 145 | 110 | 93 |
Construct a scatterplot using the data from the table.
Is IQ and height negatively correlated, postively correlated or not correlated?
How tall is the person who appears to be an outlier?
A researcher is studying the relationship between the number of passers-by present in a situation and the time taken, in seconds, until a stranger in an emergency receives help from a passer-by. The data is recorded in the table below:
| \text{Number of passers-by (n)} | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| \text{Time until help is offered (t)} | 8 | 19 | 26 | 37 | 51 | 65 |
Construct a scatterplot using the data from the table.
As more passers-by are present what happens to the time taken until help is offered?
Describe the correlation between the number of passers-by and the time until assistance is offered.
Does the scatterplot contain any outliers?
A study was conducted to compare running times in various outdoor temperatures. The table below lists the time taken to sprint 400 meters by runners in different temperatures:
| \text{Temperature }(\degree F) | 41 | 36 | 50 | 46 | 33 | 45 | 43 | 39 | 37 | 48 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{Sprint time }(s) | 60 | 67 | 48 | 69 | 65 | 49 | 57 | 53 | 59 | 52 |
Use technology to graph this data on a scatter plot.
How many runners were tested in the study?
Describe the correlation between temperature and sprint time as positive or negative.
Describe the correlation between temperature and sprint time as strong or weak.
Which pair of temperature and sprint time represents an outlier?
The following table shows the scores of 12 students in English and French:
Construct a scatter plot for English score vs French score.
Describe the correlation between students' English and French scores.
Which student's scores appear to represent an outlier?
| Student | English | French |
|---|---|---|
| 1 | 85 | 89 |
| 2 | 71 | 71 |
| 3 | 57 | 56 |
| 4 | 60 | 62 |
| 5 | 79 | 86 |
| 6 | 76 | 75 |
| 7 | 71 | 77 |
| 8 | 91 | 86 |
| 9 | 50 | 90 |
| 10 | 49 | 47 |
| 11 | 66 | 67 |
| 12 | 92 | 92 |