Scatter Plots Scatter plots are a graphic representation of collated biviariate data via a mathematical diagram using Cartesian coordinates. The data is presented as a series of dots arranged on the horizontal and vertical axis. The presentation of this data communicates how much one variable is affected by another. The relationship between the two variables is referred to as the correlation. Scatter plots are employed as the scatter of these dots communicates where a relationship is likely to exist between the variables (Booker, Bond, Sparrow & Swan, 2004).

Vocabulary Variables: 1: a quantity that can change or carry, taking on different values. 2: a letter or symbol representing a varying quantity, for example n in 10 + n Bivariate data: Data that involves two variables. Correlation: A casual, complementary, parallel, or reciprocal relationship, especially a structural, functional, or qualitative correspondence between two comparable entities. Positive correlation: A correlation in which large values of one variable are associated with large values of the other and small with small: the correlation coefficient is between 0 and +1. Negative correlation: A correlation in which large values of one variable are associated with small values of the other, the correlation coefficient is between 0 and -1.

Vocabulary Coefficient: A number or symbol multiplied with a variable or an unknown quantity in an algebraic term. Cartesian Coordinates: A system of representing points in space in terms of their distance from a given origin measured along a set of mutually perpendicular axes. X axis: The horizontal axis of a graph. Y axis: The vertical axis of a graph. Cluster: Numbers which tend to crowd around a particular point in a set of values. Plot: To represent data graphically on a chart. Trend line: A line of best fit (a line on a graph indicating a statistical trend.

Assumed Prior Knowledge Students will have carried out an extensive amount of graph work throughout their schooling and will therefore be familiar with the processes of collating data, how to construct the 'frame' of the graph and how to label the appropriate axis.

Use scatter plots to investigate and comment on relationships between two continuous variables. - using authentic data to construct scatter plots, make comparisons and draw conclusions.

Declarative & Procedural Knowledge Declarative Knowledge (will know) Procedural Knowledge (be able to) D1: The sequential processes required to construct a scatter plot. D2: The importance of accurate data collation. D3: How to determine whether a scatter plot is an appropriate way to represent that particular set of data. D4: The features of a scatter plots. D5: Appropriate terminology for this topic. P1: Collate and analyse data for a pair of variables. P2: Use a line of best fit to identify if there is a positive or negative relationship between the two variables. P3: Explore the characteristics and users of scatter plots. P4: Interpret bivariate data in tables and graphs. P5: Choose axes and scales while constructing a scatter plot. P6: Enter personal data for a statistical investigation. P7: Use patterns in scatter plots to draw conclusions.

Learning Federation Resource

Key Question “Do you think there is a relationship between the length of a person’s foot and the span of their hand from their little finger to their thumb?”

Data Table Number of PeopleFoot Length’s (in cm)Hand Span’s (in cm)

Minimum and maximum lengths Number of PeopleFoot Length’s (in cm)Hand Span’s (in cm)

An example of a Positive Relationship

An example of a Negative Relationship

An example of no relationship between two variables

What is the relationship in you scatter plot? Discuss amongst yourselves the type of relationship the variables have in your graph. What relationship did you come up with?

Extension Question How did you discover the kind of relationship that your graph has? And how does this information relate back to the Key Question of: “Do you think there is a relationship between the length of a person’s foot and the span of their hand from their little finger to their thumb?”

A Final Point “Although children need to learn that data can be displayed in a variety of ways and come to terms with many of these representations, it is equally important that they understand that the choice of display depends on the question being asked of the data.“