IB Math Studies – Topic 6

Statistics

Daniela and Megan

IB Course Guide Description

IB Course Guide Description

IB Course Guide Description

Descriptive StatisticsDifferent Types of Data: Categorical vs. Quantitative

• Categorical – Describes a particular quality or characteristic. It can be divided into categories. – Example: The color of my shoes or different breeds of puppies

Organizing categorical data:

or or

• Quantitative – Contains a numerical value. The information collected is termed numerical data.– Discrete – Takes exact number values and is often the result of counting.

• i.e. number of TVs or number of houses on a street– Continuous – Takes numerical values within a certain range and is often a result of measuring.

• i.e. the height of seniors or the weight of freshman

Organizing Quantitative Data:

Different Types of Distribution

24 families were surveyed to find the number of people in the family. The results are:

5, 9, 4, 4, 4, 5, 3, 4, 6, 8, 8, 5, 7, 6, 6, 8, 6, 9, 10, 7, 3, 5, 6, 6

a) Is this data discrete or continuous?

b) Construct a frequency table for the data.

c) Display the data using a column graph.

d) Describe the shape of the distribution. Are there any outliers? a) There are no outliers, all the numbers are generally close to one another.

e) What percentage of families have 5 or fewer people in them?

Discrete

Number Frequency

3 2

4 4

5 4

6 5

7 2

8 3

9 2

10 1

Frequency0

1

2

3

4

5

6

345678910

21%

Continuous Data

Mean, Mode, Range, Median

Mean, the average - Mode, most often –Range, subtract the smallest from the largest.

Median, the middle number, When they’re lined up –From the greatest to the least.

• Find the Mean, Mode, Range and Median– Mean: 5.17– Mode: 5– Range: 7– Median: 5

• Q1 = 3+4 = 7/2 = 3.5• Q3 = 6+7 = 13/2 = 6.5• IQR (inner-quartile range) = Q3- Q1 6.5 – 3.5 = 3 IQR = 3

Practice

a. Median – 5.5

b. Lower Quartile – 4

c. Upper Quartile – 8

d. Inner- Quartile Range – 4

Box and Whisker Plots

2 Variable-Statistics: Correlation

Pearson’s Correlation Coefficient

Example: Pearson’s Correlation Coefficient

4

2.73305.1

Considering that it’s positive and very close to 1, it’s strong.

r = .98

How to do Correlation Coefficient on the Calculator

Least Squares Regression

The x2 Test of Independence

The x2 Test of Independence

• Null Hypothesis – trying to prove that your variables are independent.

• Degrees of Freedom – the number of rows on your table minus the number of columns on your table– There’s also expected frequency values

The x2 Test of Independence