IB Math Studies – Topic 6

IB Math Studies – Topic 6 Statistics

IB Course Guide Description

Continuous and Discrete Data Continuous: A numerical data which has values within a continuous range that has been measured. Discrete: A numerical data which has whole numbers and has been counted.

Presenting and Interpreting Data

Stem-and-leaf Plots • Stem-and-leaf, or at times called stemplot, is a easy way of writing down the data in groups. • Used for small data sets • For number with two digits, the first digit forms part of the stem and the second digit forms a leaf

Frequency Polygon • A line graph, utilized much like a histogram, that gives a visual • appreciation of the shape of the frequency distribution. • The midpoint of each bar is used to represent the whole interval. • Lines are then draw between these midpoints.

Histograms A histogram is a vertical column graph used to represent continuous grouped data. There are no gaps between the columns in a histograms as the data is continuous.

Box and Whisker Plot • Outliers are extraordinary data that are usually separated form the main body of the data. • The upper boundary = upper quartile + 1.5 X IQR • The lower boundary = lower quartile – 1.5 X IQR A box-and-whisker plot is a visual display of some of the descriptive statistics of a data set.

Summarizing the Data • Mean: is the arithmetic average obtained by adding all the scores and dividing by the total number of scores. • Mode: is the score that occurs most frequently. • Median: Is the middle score after they have been placed in order.

Grouped Discrete Data

Grouped Continuous Data

Measure of Dispersion • Range: is the difference between the maximum data value and the minimum data value. Range = maximum data value – minimum data value • Interquartile Range: is the range of the middle half (50%) of the data. • The data set has been divided into quarters by the lower quartile (Q1), the median (Q2) and the upper quartile (Q3). IQR = Q3 – Q1

Standard Deviation Standard Deviation: measures the deviation between scores and the mean. Ungrouped Data Grouped Discrete Data

Correlation • A correlation refers to the relationship or association between two variables

Line of Best Fit • Drawing a Line of Best Fit • Calculate mean of x values , and mean of y values • Mark the mean point on the scatter plot • Draw a line through the mean point that is through the middle of the data • equal number of points above and below line A scatter diagram indicates the relationship between two variables. If there is a relationship, we can draw in the “line of best fit”

Regression Line • The regression line is used for prediction purposes. • The regression line is less reliable when extended far beyond the region of the data. • The line of best fit on a scatter diagram is called a “regression line” and it can be calculated from the data pairs.

Correlation Coefficient • -1 indicates perfect negative correlation. • 0 indicates no correlation • +1 indicates perfect positive correlation. • 0.25 ≤ r < 0.5 = weak • 0.5 ≤ r < 0.75 = moderate correlation • 0.75 ≤ r <1 = strong correlation

The Chi-Squared Test • How many people are in the sample? • How many males? • How many females? • This is called a 2 x 2 contingency table.

Write the null hypothesis (H0) and the alternate hypothesis (H1). • Create contingency tables for observed and expected values. • Calculate the chi-square statistic and degrees of freedom. • Find the chi-squared critical value (booklet). • Depends on the level of significance (p)and the degrees of freedom (v). • Determine whether or not to accept the null hypothesis.

On the calculator: Put your contingency table in matrix A • STAT • TESTS • C: χ2 Test • Observed: [A] • Expected: [B] (this is where you want to go) • Calculate

IB Math Studies – Topic 6