Describing Distributions Flashcards
If the graph of your data is skewed, what center and measure of spread should you use?
Center: Median
Measure of Spread: IQR
How to interpret R2 (Coefficient of Determination)
Coefficient of Determination : (R2 as a percent) of the change in (Y) can be explained by the change in (X)
Example Problem:
Given that R2 is .99, Y = height, and X= age, describe what it means in the context of the situation.
-99% of the change in height (Y) can be explained by the change in age (X)
Pie Chart
Stem Plot
What type of graph would you make with this information?
Ogive
Dot Plot
What is the center?
The middle of the distribution, first located by finding the highest peak. It is measured by mean, median, or mode.
What is IQR?
What is its equation?
When do you find the IQR for spread?
- Inner Quartile Range
- Q3-Q1=IQR
- You use it when the shape of the graph is skewed
Histogram
Bar Graph
What is mean; its equation?
The average; the sum of the data divided by the number of numbers.
What is a median?
The middle # when the numbers are in numerical order.
What is the mode and when is it used to describe the center of a graph?
- The number that occurs the most
- When the graph’s shape is bimodal
What is a Population?
Used to measure all possible outcomes in a particular study.
How do you find the outliers in a set of data?
Low outliers: Q1-(1.5*IQR)
High outliers: Q3+(1.5*IQR)
True or False. When looking at the United States, the city of New York is a population.
False
Practice Problem A study found correlation r=0.61 between the sex of a worker and his or her income. You conclude that
A. Women earn more than men on the average.
B. Women earn less than men on average.
C. An arithmetic mistake was made; this is not a possible value of r.
D. This is nonsense because r makes no sense here.
D. This is nonsense because r makes no sense here.
Practice Problem
Which of the folowing would not be a correct interpretation of a correlation of r=-.30?
A. The variances are inversely related.
B. The coefficient of determination is 0.09.
C. 30% of the varitaion between the variables is linear.
D. There exists a weak relationship between the variables.
E. All of the above statements are correct.
C. 30% of the varitaion between the variables is linear.
What is the value of correlation for operating cost per hour and number of passenger seats in the plane? Interpret the correlation.
r=0.75
There is a strong positive linear relationship between the operating cost per hour and the number of passenger seats on the plane.
Practice Problem A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number of y service calls in a month at each location. It was given that r=0.86. What percent of the variation in number of service calls is explained by the linear relation between number of service calls and number of machines?
A. 86%
B. 93%
C. 74%
D. None of these
E. Can’t tell from the information given
C. 74% The question is asking for r2 and since r=0.86, you would square 0.86 and get 0.74.
What is a qualitative variable?
A variable that describes non numerical values.
What are the two types of qualitative graphs covered in class?
Pie Chart
Bar Graph
What is a Quantitative variable?
A numerical variable that represents a measurable quantity.
What are the four types of quantitative graphs covered in class?
Stem Plot
Histogram
Dot Plot
Ogive
which of the following is Quantitative?
a. age
b. time
c. gender
d. number of girls in a class
e. number of people in a class
a and e
What is range?
What is its equation?
When do you find range?
- The maximum value minus the minimum value in the data set
- Max- Min
- You find the range for boxplots and its five-number summary
What is the range for correlation coefficient?
-1 to 1
How do you find the residual?
y-ŷ
What is a Sample?
A portion of a population
True or False. A class in a school is a sample.
True
What are the possible measures of spread?
Range
IQR
Variance
Standard Deviation
What is standard deviation?
What is its equation?
When do you use standard deviation to find spread?
- The average distance from the mean
- You use it when the shape of the graph is symmetric
What is a two way table?
IDK, There is a row, column. Add all the number of column and row will give the total amount of the study.
What is variance?
What is its equation?
- The square of standard deviation
What are the things required to interpret correlation?
Form, strength, and direction
What is a Risidual
The vertical distance from a expected point to the regression line.
What is the equation to find the slope (b)?
b=r(Sy/Sx)
What is the general equation for a least square regression line
ŷ=a+bx
What are the symbols for Correla2tion and Coefficient of Determination?
R = Correlation
R2 = Coefficient of Determination
Which type of quantitative graph organizes your one variable data chronologically so that, for example, all of the data in the 20-29 region would be grouped together with a 2 on one side of a line and a list of the changing ones place (2 2 3 4 4 7)?
Stem Plot
Which type of 1-variable quantitative graph does not necessarily need a y-axis label and stacks a dot over it’s x value for each count?
Dot Plot
Which quantitative graph divides its data into Bin and Counts?
Histogram
What quantitative graph divides its x-values into groups and then adds the previous y-values quantity to its own?
Ogive
