Module 01 – Basics Of Statistics Case Assignment
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Module 01 – Basics Of Statistics Case Assignment
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 varyamong 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. (infinitepossibilities)
- 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.
- Allqualitative 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 quantitativevariables 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 samplemean is ____________.
- The symbol used for the populationmean 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 samplestandard deviation is ____________.
- The symbol used for the populationstandard deviation is ____________.
Basics Of Statistics Case Assignment
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!
2 Allisha Langdon Rasmussen College B094 Geometry STA3215CBE – Statistics Allisha Wise Page 12
RUBRIC
Excellent Quality
95-100%
Introduction 45-41 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Literature Support
91-84 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Methodology
58-53 points
Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score
50-85%
40-38 points
More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.
83-76 points
Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.
52-49 points
Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality
0-45%
37-1 points
The background and/or significance are missing. No search history information is provided.
75-1 points
Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.
48-1 points
There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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