Bivariate Data

NZ Level 6 (NZC) Level 1 (NCEA)

Describing Statistical Relationships

Lesson

We've already looked at scatterplots and how to describe relationships between different sets of variables.

Here is a summary of different types of linear relationship:

- Positive relationship: as one variable increases, the other variables also increases.
- Negative relationship: as one variable increases, the other variables decreases.
- No relationship: there is no correlation between the variables.

Remember!

The closer the dots in a scatterplot are to a straight line, the stronger the correlation.

Once we can identify the type of relationship between two variables, we can make inferences about these variables and use them in everyday life. For example, say there is a *positive relationship* between study and results. From this, we can say that the *more* someone studies, the *better* they will do in their exams.

Let's look through some more examples now.

Identify the type of relationship represented by the following scatter plot.

A) Negative linear B) No relationship C) Positive linear

Think: The values on the $x$`x` axis as representing one variable, and the values on the $y$`y` axis as representing another variable. How does the $y$`y`-variable change as the $x$`x`-variable increases?

Do: When we look at this graph, we can see that as $x$`x`-variable increases, the $y$`y`-variable also increases. So this graph is an example of an A) negative linear relationship.

The marks of $12$12 students in Maths and Sport were recorded in the following table.

Student |
Mark in Maths |
Mark in Sport |
---|---|---|

$1$1 | $63$63 | $44$44 |

$2$2 | $92$92 | $74$74 |

$3$3 | $60$60 | $52$52 |

$4$4 | $79$79 | $70$70 |

$5$5 | $88$88 | $67$67 |

$6$6 | $81$81 | $60$60 |

$7$7 | $61$61 | $73$73 |

$8$8 | $91$91 | $86$86 |

$9$9 | $72$72 | $84$84 |

$10$10 | $42$42 | $93$93 |

$11$11 | $66$66 | $57$57 |

$12$12 | $92$92 | $92$92 |

Which of the following scatterplots correctly represents the data from the table?

ABCABCIs the relationship between students' marks in Maths and Sport positive or negative?

Positive

ANegative

BPositive

ANegative

BIs the relationship between students' marks in Maths and Sport strong or weak?

Strong

AWeak

BStrong

AWeak

BWhich student has a score that represents an outlier?

Student 10

AStudent 4

BStudent 12

CNone of the students

DStudent 10

AStudent 4

BStudent 12

CNone of the students

D

Scientists were looking for a relationship between the number of hours of sleep we receive and the effect it has on our motor and process skills. Some subjects were asked to sleep for different amounts of time, and were all asked to undergo the same driving challenge in which their reaction time was measured. The table shows the results, which are to be presented as a scatter plot.

Amount of sleep (hours) | Reaction time (seconds) |
---|---|

$9$9 | $3$3 |

$6$6 | $3.3$3.3 |

$4$4 | $3.5$3.5 |

$10$10 | $3$3 |

$3$3 | $3.7$3.7 |

$7$7 | $3.2$3.2 |

$2$2 | $3.85$3.85 |

$5$5 | $3.55$3.55 |

By moving the points, create a scatter plot for the observations in the table.

Loading Graph...According to the results, which of the following is true of the relationship between amount of sleep and reaction time?

As the amount of sleep decreases, the reaction time decreases.

AAs sleeping time decreases, reaction time improves.

BSleeping for longer improves reaction time.

CThe amount of sleep has no effect on the reaction time.

DAs the amount of sleep decreases, the reaction time decreases.

AAs sleeping time decreases, reaction time improves.

BSleeping for longer improves reaction time.

CThe amount of sleep has no effect on the reaction time.

D

Plan and conduct investigations using the statistical enquiry cycle: A justifying the variables and measures used B managing sources of variation, including through the use of random sampling C identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays D making informal inferences about populations from sample data E justifying findings, using displays and measures.

Investigate a given multivariate data set using the statistical enquiry cycle

Investigate bivariate numerical data using the statistical enquiry cycle