Math Assignment 2 deadline 15 hours

ASSIGNMENT 1 - SCMA 1000 –STATISTICS REVISED 2022

Two students are permitted to work together on this assignment, but it is perfectly alright to work alone if you prefer. However, dividing up the work and having one person do part and the other person do a different part is a

VERY BAD IDEA!!!

Why - because you will need to know all of this to pass the midterm exam and if you do not do the work, you are likely to do poorly on the exam. The purpose of permitting you to work together is to encourage discussion which will allow both students to have a better understanding of how to do each step. In the spaces below indicate which students are to receive credit for this submission. Only 2 students can get credit for this submission.

Student

Last Name

First Name

Student Number

Student 1

Student 2

1.    Describe the data you selected and why you assume there is a relationship. Make sure to answer both part a and part b.

Describe your data and its relationship. This should be short and simple. What are your elements, what are your three variables and how did you find or measure them? When you do this you are providing me with enough information to know if you did the rest of the assignment correctly but I can’t/ don’t want to have to read pages to find the answer

a.

DESCRIBE WHAT YOU DECIDED TO ANALYZE

b1.

What are your elements?

b2.

What is the name of your first variable?

What does this variable measure?

What scale of measurement is this variable?

b3.

What is the name of your second variable?

What does this variable measure?

What scale of measurement is this variable?

b4.

What is the name of your third variable?

What does this variable measure?

What scale of measurement is this variable?

c.

Is this a sample or a population?

c.

What do you think the relationship is between your two quantitative variables?

d.

How did you collect your data?

3.

Create a data table based on your observations in the template provided below. What goes into a data table and how it is organized was covered in the first week. Values must be entered into the table as it exists here. Do not change the spacing or put more than one piece of information into a cell. If the table does not format properly, you should ask yourself why. You are not permitted to put any alphanumeric characters in the first two variables. Only one number per cell is permitted. Do NOT include symbols such as $ or :. Failure to follow this will result in a zero for this component.

4. Entry of Data Table

Put the names of your elements and variables in the first blank row. Then enter the specific values for each observation in a line across the table. You are required to have 15 elements and 3 variables (2 quantitative, 1 categorical) per element. If these criteria are not met, your mark will be reduced. You must also submit your data set in the excel spreadsheet provided.

Element

Values for Variable 1 (Quantitative)

Values for Variable 2 (Quantitative)

Values for Variable 3 (Categorical)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

4

Using techniques introduced in Chapter 2 – create graphical analyses (charts) of your three variables. At least one must be a histogram, and one must be a bar chart. What you do with the third variable is up to you as long as it is appropriate for the kind of variable that it is. Please realize that a chart with 15 points on it is NOT a histogram. You must decide how to group the data into classes before you can make a histogram. Again, refer to Chapter 2 for instructions. Note: To create a histogram, you will have to create a classification table in addition to the raw data table. You can insert your histogram or bar chart in several ways. 1. Build it in Excel and insert that here, 2. Create it with another program and paste it in space a, b, or c. 3. Draw it by hand, scan it in and paste that picture here. If you use this method, make sure the contrast is good.

a.

Put your histogram here. If what you put here is NOT a histogram, your mark will be 0

b.

Put your bar chart here. This requires you to think! What kind of data can appropriately be displayed in a bar chart? If what you put here is NOT a bar chart or if the variable used is not appropriate for a bar chart, your mark will be 0. Note: you must think about this and NOT assume the variables are used in order.

c.

Put your graphic analysis of your remaining variable in the space below. Make sure to use one of the techniques discussed in class. It is acceptable to use one of the graphic analyses you have already used for this variable, if you choose to.

5.

Prepare a set of descriptive statistics. Note that each section has more slots than there are statistics. It is up to you to decide how many you should include. Also, if you use a type of statistic that is not appropriate to the overall description, you will not receive any points.

a.

Statistics that tell you about the center of the distribution. You must name the statistic and show the appropriate values for each variable. If the measure is not related to the centre of the distribution, it will not count.

Name of Statistic

Value for Variable 1

Value for Variable 2

b.

Statistics that tell you about the variability of the distribution. Only statistics described in the text as showing shape will get credit here. If the measure is not related to the shape of the distribution, it will not count.

Name of Statistic

Value for Variable 1

Value for Variable 2

c.

Statistics that tell you about the shape of the distribution. What are the key variables that provide information about shape? Are there any other variables that describe the distribution that you would include.

Name of Statistic

Value for Variable 1

Value for Variable 2

6

Create a box and whisker plot for your first variable . You only have space to do one because you cannot change this template. Creating this data representation for the categorical variable will result in an immediate 0 for this section.

THIS MUST BE DONE USING VARIABLE 1!

a

What are the values you need to create your box and whisker plot?

Name of Value

Value

b

What is the whisker length for your box and whisker plot?

c

Are there any outliers? Yes or No

Yes ☐ No ☐

d

Put plot here.

7

a

Use statistical techniques to determine whether or not a linear relationship exists between your two quantitative variables and how strong that relationship is. The correct answers are two related numbers. Do not type words in the value space. Again, this is Chapter 3 and you been doing this type of calculation since Grade 7 but you must think about what I am asking for.

Name of Statistic

Value

b

Show the relationship between the two variables graphically. Then show the two calculated numbers that describe the relationship between the two variables. What conclusions can you draw from this? Does it give the same result as Question 7?

Put chart here.

8

a

What is the probability for each condition of your categorical variable? This is Chapter 4. You must build a frequency table for your variable. Please try to limit this to two to three categories and do NOT fill up all the rows in this table unless you cannot avoid it.

Groups

Frequency

Relative Frequency

b

Now take your first quantitative variables and break it into categories. Do this by determining the 40th percentile and the 70th percentile. Numbers at or below the 40th percentile will be labeled LOW. Scores at or above the 70th percentile will be labeled HIGH. The remaining scores will be labeled MIDDLE. Now complete the table below based on these results.

Groups

Frequency

Relative Frequency

LOW

MIDDLE

HIGH

9

Finally, create a tree diagram based on these two contingency tables which shows the conditional probability of each variable. Tree diagrams can be found in Chapter 4. Insert it in the space below.

10

Now draw some conclusions about what all this data means. Try to make sure that you have some conclusion from each of the steps in the process. In other words, what do you conclude from the graphic representations, from the statistical analysis, from the relationship question, from the box and whisker and from the tree diagram?