AP Statistics – Chapter 1 – Flashcards
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Used with categorical data and it must add up to 100% Very rarely used (only to compare relation as a whole) For Categorical Data (I.e.: the colors of different socks)
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Pie Chart
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+ Used with Categorical Data + Usually Shows Frequency (Count) + Bars are free standing (Don't Touch) + Bars can be in any order + Used for categorical data (I.e.: the colors of different socks)
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Bar Graph
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Data from surveys, experiments, and observational studies
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Quantitative Data
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+ Title + Axes Labeled + Constant Scale
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What makes a Good Graph?
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+ Draw a Horizontal Line and Scale Based on the Numbers + Title the Dot Plot and Label the Axes + Place One Dot Above the Appropriate Value for each data point
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Dot Plot (How is One Made)?
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+ Shape + Center + Spread + Outliers or Not
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What Four Attributes are Used to Interpret the Distribution of Quantitative Data
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+ Bell + Uniform + Left - Skewed + Right - Skewed
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What are the Four Shapes of a Quantitative Data Graph?
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Ummm... Bell -shaped?
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Shape of a Bell Graph
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Shaped Like a Table: ____________________ I I (Except the lines touch) Remember that "Uniform" refers to all the data being the same
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Uniform Graph
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The mean pulls the graph to the left
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Left - Skewed
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The mean pulls the graph to the right
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Right - Skewed
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The median/mean
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What Two Concepts are Associated in Determining the Center of a Graph?
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How much variability from the first number to the last number Written: Lowest to Highest Intervals (Ex. 4 - 23)
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Spread of a Graph
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A way of determining spread, how many numbers the data ranges: Highest Value - Lowest Value = Range (Ex. 23 - 4 = 19) IS RESISTANT TO OUTLIERS
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Range
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Anything outside the norm of other points
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Outlier
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Quick picture or shape of distribution while including actual values
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Stemplot (Steam-and-Leaf Plot)
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1). Create a stem (all numbers in the tens place written vertically with a vertical line to the right) 2). Write a life in the appropriate row with increasing numbers of the ones place extending out 3). Include a key (and always include a title)
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How to Create a Stemplot
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Take one stem and break it into two when too much data (refer to Assignment 31 - Chapter 1: Data Set #1)
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Splitting Stems
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If there are any outliers
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What can Splitting the Stems help to identify?
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When there is too much data, or data is overcrowded
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When do we Split the Stem?
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Two sets of data share 1 stem (refer to Assignment #31 - Chapter 1: Data Set #1)
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Back-to-Back Stemplot
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Breaks values into classes/intervals of equal width and displays frequency/percent of each class. The bars touch because of the continuous interval. If there is a large sample size, a Histogram is the best choice for displaying the data (if, of course, it is quantitative)
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Histogram
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It only tells the frequency/percent, you can't see specific data points
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What is the Only Downside to a Histogram?
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Approximately Symmetric (Refer to Assignment #31 - Chapter 1: Data Set #1)
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When a Curve Appears to be a Bell, but is not Exact, What is the Shape Referred to As?
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Also known as Relative Cumulative Frequency Graph, an Ogive is used when we need to know how one value compares to others. An Ogive shows percents
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Ogive
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The bottom So right-skewed would mean that most of the data is found near the top (AKA, the "Left Side")
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In the Left-Most Set of a Back-to-Back Stemplot, where is the "Right Side" of the Data?
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Average Value The fair share; the amount everyone would get if they all had the same amount; the balancing point
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Mean
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n = the number of data entries
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When referring to Quantitative Data Distribution Graphs, what does n mean?
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"The sum of observations / n"
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Mean Formula
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No, because one number can make the mean much larger/smaller than it actually is
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Is Mean Resistant to Outliers?
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Typical Value Midpoint of distribution; half the observations are below this point and half are above
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Median
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+ Arrange all Numbers Smallest to Largest + In cases where n is odd, the median is the middle number + In cases where n is even, the median is the average of the two middle number
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How to Find Median
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Yes, because we are only interested in the positions of numbers, not their values
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Is Median Resistant to Outliers?
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When a graph is symmetric or approximately symmetric (because it is affected by outliers)
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When is Mean Used?
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When a graph is skewed or has outliers (because outliers don't affect it)
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When is Median Used?
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The amount of variability in the distribution
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Spread
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The IQR (middle 50% of data)
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What Can We Use to Improve the Distribution of Spread?
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Q1 Median of the lower half of data
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Quartile 1
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Q3 Median of upper half of data
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Quartile 3
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Q3 - Q1 Represents the middle 50% of data
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IQR
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Yes, because they are based on the median
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Are IQR and Quartiles Resistant to Outliers?
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[Anything beyond these values are outliers] Q1 - 1.5IQR Q3 + 1.5IQR
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Boundaries for Outliers
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Drop the value from the data set HOWEVER If there is an outlier that wasn't caused by an error, then you MUST include it in the data set
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If you know that an error occurred in your gathering of data, and in turn this creates an outlier, what can you do?
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Minimum, Quartile 1, Median, Quartile 3, and Maximum
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Five Number Summary
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Shows the Five Number Summary and Any Outliers + Box from Q1 to Q3 + Vertical Line inside the Box is the Median + Horizontal Lines Extend to Minimum and Maximum (Not Including Outliers) + Outliers are Dots Outside of Lines
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Box Plot
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+ Insert Data + 2nd - Stat Plot (Hit 2nd - y=) + Choose Plot 1 + Turn on Plot 1 + Go to the Fourth Option (Box Plot with the Dots) + Zoom 9 + Trace to Jump Between Values of the Five Number Summary
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How to Make a Box Plot and Find the Five Number Summary with a Calculator (TI - 84)
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Measure of relative location Finds what percent of observations lie at or below a certain value: # of values at or below a certain number / # of values
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Percentile
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Standard Deviation
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Most Common Measure of Spread
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Mean based; Looks at how far, on average, each observation is from the mean
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Standard Deviation
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Populations
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When determining Standard Deviation (or Variance), we divide by n in the case of:
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Samples
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When determining Standard Deviation (or Variance), we divide by (n-1) in the case of:
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When the mean is used (Data is skewed or outliers are used)
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When is the ONLY time we use Standard Deviation?
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Sx ? 0 Sx = 0 when there is no variability in the data set at all (all the observations are the same)
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What is always true about the value of Standard Deviation?
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The more spread out the data is
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When does Sx get larger?
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Sx has the same unit of measure as the original observations
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Why do we take the square root when finding Standard Deviation?
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+ Put Data into a List + Stat. ---> Calc. ---> 1 Variable Statistics + (Data is in the List you Put it In)
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How to Find Mean and Standard Deviation in the Calculator:
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x? = Mean ?x = Sum of x ?x^2 = Square each data point, then find the sum Sx = Standard Deviation of Sample (Divide by n-1) ?x = Standard Deviation of Population (Divide by n)
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Meanings of the Different Symbols You'll Encounter when Finding Sx in a Calculator
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No! Median and IQR are used for one distribution Mean and Sx are used for another
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Can you ever cross between using Mean and IQR, or Median and Standard Deviation?
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+ Put Data into a List + Go One List Over and Do all of the First List's Values ± the Correct Number (For example, L2 - 13 will go into the L3 column)
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How to Describe the Distribution of an Addition/Subtraction Error on a Calculator:
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+ Add/Subtract #a to each measure of center (Mean, Median, Quartiles) and to each measure of location (Percentiles) + Shape is unaffected + Spread is unaffected
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How will Adding or Subtracting the same #a to each observation affect the distribution?
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+ Put Data into a List (L1) + Go One List Over (L2) and Do all of L1's Values Multiplied by the Change (L1 * 23 information will go into L2)
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How to Describe the Distribution of an Multiplication/Division Error on a Calculator:
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+ Multiply/Divide #b to each measure of center/location (Mean, Median, Quartiles, Percentiles) + Multiply/Divide each measure of spread (IQR, Range, Sx) by |b| + Shape is never affected
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How will Multiplying or Dividing the same #b to each observation affect the distribution?
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Yes
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Is a Percentile affected by both a change in the addition/subtraction of a distribution as well as a multiplication/division change?
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No, only a multiplication/division change
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Is a Measure of Spread affected by both a change in the addition/subtraction of a distribution as well as a multiplication/division change?
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Yes
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Is a Measure of Center affected by both a change in the addition/subtraction of a distribution as well as a multiplication/division change?
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No, shape isn't affect by either
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Is Shape affected by both a change in the addition/subtraction of a distribution as well as a multiplication/division change?
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1.05x
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How would you go about doing x times 5%?
