IB Math Studies Yr 1

Name_________________________________

Date: ____________

Lesson 3-1: Intro to Bivariate Stats

Learning Goals:

#1: What is Bivariate data? How do you calculate 2-variable data on the calculator? #2: How do we create a scatterplot?

Review of Descriptive Stats: Answer this question based on Unit 2

The table shows the frequency of the number of visits to the doctor per year for a group of children.

Calculate the following: Mean = Median = IQR = Standard Deviation = 3rd Quartile = 1st Quartile = Range = Intro to Bivariate Stats: Try to complete these sentences.

1. The taller you are the ______________________ your foot is. The ________________ you are the smaller your foot is.

2. The newer your car the ______________________ it’s worth. The ____________ your car the less it’s worth.

3. Describe the relationship you see in the graph to the right which is depicting the number of hours of training received at a job and the productivity of a company. What conclusion can you make?

Definitions:

- Bivariate Data: The words we use then we have ___________ ______________________ data.

- Scatterplot: A plot of the pairs; points are __________ connected.

- Explanatory Variable:

- Response Variable:

IB Math Studies Yr 1

1-VARIABLE STATS vs. 2-VARIABLE STATS

When answering IB statistic questions moving forward, you are going to have to identify 1-variable stats versus 2-variable stats. Below are examples of each:

1-Variable Statistics

2-Variable Statistics

2-VARIABLE STATS ON THE CALCULATOR

With 2-variable statistics, you can find the measures of mean and standard deviation in the calculator. The steps are given below: 1) Press STAT EDIT and enter the data into your calculator

L1 is the x-variable, L2 is the y-variable 2) Press STAT CALC and goto 2: 2-Var Stats 3) Make sure to have XList: L1 and YList: L2. Frequency has to be blank! Then press CALCULATE

Let’s Try one! Below are the heights and weights of ten students from a high school gym class.

Calculate the following: Mean height, �̅�, of the students = Standard deviation of the heights = Mean weight, �̅�, of the students = Standard deviation of the weights =

MEAN

�̅� = mean of x − variable

�̅� = mean of y − variable

STANDARD DEVIATION

𝜎𝑥 = standard deviation of x − variable

𝜎𝑦 = standard deviation of y − variable

IB Math Studies Yr 1

CREATING A SCATTER PLOT

A scatter plot is a visual representation of 2-variable statistics. When expressed as a scatter plot, it can help you to identify the type of relationship between your variables. Below are the steps to create a scatter plot: 1) Choose an appropriate scale for the x-axis and label it. Pay attention to the scale given to you

in the question. Feel free to use a break in the beginning of your label! 2) Choose an appropriate scale for the y-axis and label it. Pay attention to the scale given to you

in the question. Feel free to use a break in the beginning of your label! 3) Carefully plot the coordinates for each point (x, y).

Let’s Try one! Below are the heights and weights of ten students from a high school gym class.

Create a scatterplot of this data. Use a scale of 1cm to represent 10cm on the x-axis and 2cm to represent 20kg on the y-axis.

IB Math Studies Yr 1

PUTTING IT ALL TOGETHER…

As part of his IB Biology field work, Barry was asked to measure the circumference of trees, in centimetres, that were growing at different distances, in metres, from a river bank. His results are summarized in the following table.

a. State whether distance from the river bank is a continuous or discrete variable.

b. On graph paper, draw a scatter diagram to show Barry’s results. Use a scale of 2 cm to represent 10 m on the x-axis and 1 cm to represent 10 cm on the y-axis.

c. Write down (i) the mean distance, �̅�, of the trees from the river bank; (ii) the mean circumference, �̅�, of the trees.

IB Math Studies Yr 1

Name_________________________________

Date: ____________ Lesson 3-1 Homework

1. In the month before their IB Diploma examinations, eight male students recorded the number of hours they spent on social media. For each student, the number of hours spent on social media (x) and the number of IB Diploma points obtained (y) are shown in the following table.

a. Use your graphic display calculator to find

(i) �̅�, the mean number of hours spent on social media; (ii) �̅�, the mean number of IB Diploma points.

b. On graph paper, draw a scatter diagram for these data. Use a scale of 1 cm to represent 5 hours on the x-axis and 2 cm to represent 10 points on the y-axis.

IB Math Studies Yr 1

REVIEW OF UNITS 1 AND 2

The length, in cm, of six baseball bats was measured. The lengths are given below.

104.5, 105.1, 104.8, 105.2, 104.9, 104.9

a. Calculate the exact value of the mean length.

b. Write your answer to part (a) in the form a × 10k where 1 ≤ a < 10 and k ∈ Z.

c. Marian calculates the mean length and finds it to be 105 cm. Calculate the percentage error made by Marian.