Deliverable 1 - Descriptive Statistics

Module 01 – Basics of Statistics

Class Objectives:

· Define and categorize variables.

· Calculate measures of center and variation using formulas and excel.

Module 01 - Part 1

In statistics, we want to study populations to understand how they function and work. To do this, we need to use variables to identify what we would like to study.

· A _________________________ is a characteristic or property of an individual experimental (or observational) unit in the population.

· This term comes from the idea that a characteristic will vary among the units in a population.

Example. Looking at this class as a population, what could be a variable that we may want to study?

Depending on the response to your variables, they can be classified as either quantitative or qualitative variables.

· _________________________________ variables have a response that requires a numerical answer.

· Which variables that we found would be quantitative?

· _________________________________ variables have a response that requires a non-numerical answer.

· Which variables that we found would be qualitative?

Examples. Define the following variables as quantitative or qualitative.

a) How many pets do you own?

b) What types of pets do you own?

c) How friendly are your pets on a scale from 1-4 (4 being very friendly and 1 being mean)?

d) How much does your pet weigh?

Looking specifically at quantitative variables, we can label them as discrete or continuous.

*Note: this categorization does NOT apply to qualitative variables!

· A __________________________________ variable is a quantitative variable that can take on any value between two specific values. (infinite possibilities)

· Examples:

· A ___________________________ variable is a quantitative variable that can only take on a certain number of values (limited possibilities).

· Examples:

Examples. Define the following variables as discrete or continuous.

a) Number of students who are blonde

b) Students’ heights

c) Color of students’ hair

d) Dog’s weight

e) Sum of rolling two dice

For both qualitative and quantitative variables, we also have another level of classification: nominal, ordinal, interval, and ratio.

· ________________________ scales are used for labeling variables without any quantitative value.

· All qualitative variables will fall into this category along with any quantitative variables that don’t hold any numerical significance.

· Hint: “nominal” sounds like “name”.

· Examples:

· ________________________ scales the order of the values is what’s important and significant, but the differences between each on its own is not really known.

· They are typically scales of non-numeric concepts like satisfaction, happiness, discomfort, etc.

· Hint: “Ordinal” sounds like “order”

· Examples:

· ___________________________ scales are numeric scales in which we know not only the order, but also the differences between the values.

· Note: They don’t have a “true zero”.

· Examples:

· __________________ scales are the best form of measurement because they tell us about the order, the exact value between units, AND they have an absolute zero.

· Basically, it has all properties of an interval variable and has a clear definition of what is means for the variable to equal zero = there is none of that variable.

· Examples:

Examples. Describe the level of measurement for each variable below.

a) Numbers printed on your favorite team’s jerseys.

b) GPA

c) Getting 1st, 2nd, or 3rd place

d) Time of Day

e) Religious preference

Review

· A variable is a characteristic or property of an individual experimental (or observational) unit in the population.

· Variables can be quantitative or qualitative.

· If they are quantitative, they can be discrete or continuous.

· For all variables (quantitative and qualitative), they have a level of measurement, either Nominal, Ordinal, Interval, or Ratio.

*Refer to Module 01 Example Excel Document*

Review

· A variable is a characteristic or property of an individual experimental (or observational) unit in the population.

· All variables can be defined as either qualitative (non-numerical) or quantitative (numerical).

· Only quantitative variables can be defined as continuous (decimals, infinite) or discrete (whole numbers, limited).

· All variables have one level of measurement:

· Nominal variables: Name only (qualitative or meaningless numbers)

· Ordinal variables: variables can be ordered

· Interval variables: distance adheres to the number line(no true zero)

· Ratio variables: distance adheres to the number line (true zero!)

Module 01 - Part 2

In statistics, we oftentimes look at samples of the population. We do this because studying a population would be far too time-consuming (and often impossible).

When taking a sample, we gather the data and can use it to draw conclusions about the population.

These conclusions will either be about the measures of center or the measures of variation.

· _________________________________________________ in statistics tell us about the “middle” of the data.

Why do we care about the measures of center?

There are four measures of center: Mean, Median, Mode, and Midrange.

1) ___________________ - commonly known as the “ average ”. To calculate the mean, you add all the data together and divide by the number of data.

· Formula:

· In excel, use _____________________________.

· The symbol used for the sample mean is ____________.

· The symbol used for the population mean is ____________.

Advantages	Disadvantages

2) _____________________ - the data value that lies in the middle of the data when arranged in ascending (or descending) order.

· In excel, use _______________________________.

Advantages	Disadvantages

3) ____________________ - the data value(s) that occur(s) the most .

· When you have two values that occur the same greatest frequency, we call the data set ______________________.

· When more than two data values occur with the same greatest frequency, we call the data set ___________________________.

· When no data value is repeated, we say that there is ________________________.

· In excel, use ________________________.

· In order to return multiple results, MODE.MULT must be entered as an array formula. This means that several vertical cells must be selected before you enter the formula.

· Array formulas are entered by pressing CTRL, SHIFT, and ENTER at the same time.

Advantages	Disadvantages

4) ______________________________ - the value midway between the maximum and minimum data values.

· This is the same idea as a midpoint.

· Formula:

· In excel, use ___________________________________________________.

Advantages	Disadvantages

· __________________________________________________________ are the measurements that tell us how spread out the data points are.

· There are three measures of variation: Range, Variance, and Standard Deviation.

1) __________________________ - the difference between the maximum and minimum values.

· Formula: Range = maximum value – minimum value

· In excel, use __________________________________.

Advantages	Disadvantages

2) ____________________________ - the expectation of the squared deviation of a random variable from its mean. Informally, how spread out the data is.

· Formula:

· In excel, use ________________________.

Advantages	Disadvantages

3) ___________________________________________________________ - the measure of how much data values deviate away from the mean.

· If individual observations vary greatly from the group mean, the standard deviation is ___________; and vice versa.

· Formula:

· In excel, use __________________________________.

· The symbol used for the sample standard deviation is ____________.

· The symbol used for the population standard deviation is ____________.

Advantages	Disadvantages

Review

· List the Measures of Center and their Excel formulas.

· List the Measures of Variation and their Excel formulas.

Variables You Should Know!

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2	Allisha Langdon Rasmussen College B094 Geometry

STA3215CBE - Statistics Allisha Wise Page 12