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25 Cards in this Set
- Front
- Back
Descriptive statistics
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Doesn't tell why the numbers are what they are. Just a bunch of numbers; have to organize it
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What is the purpose of a Grouped Frequency Distribution?
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Organizing a set of seemingly random data points/ scores by lowest and highest score. Purpose in constructing this type of distribution is to present the summary of set of scores efficiently as possible
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What are the steps (1-5) n in Grouped Frequency Distribution?
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Step 1: Find the Range (R). Take the highest score (H) minus the lowest score (L), plus one: R= (H-L) + 1
Ex: (82-28) + 1= 55 Step 2: Divide this range by 15: R/15 Ex. 55/15= 3.67 Step 3: Fine the first Preferred Real Class Interval Size that is larger than the value obtained in step 2. Round up to next acceptable value (ex. 1, 2, 3, 5, 10, 15, 25, 50, 100) after 100 anything multiples of 100. Ex. 5 is the first preferred real class interval size that is larger than 3.67 Step 4: Find the Apparent Class Interval Size by subtracting one from the real class interval size (Step 3). Ex. apparent class interval size is 5-1= 4 Step 5: Find beginning value for the 1st class interval. If the lowest number can evenly be divided by the preferred real class interval size (5) then use it. If lowest data point (28) can't be divided w/ acceptable value go lower 28--> 25 until you reach a number that can be divide evenly Ex: 25/5 = 5 |
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What are the acceptable values?
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ex. 1, 2, 3, 5, 10, 15, 25, 50, 100, after 100 anything multiples of 100.
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What are the steps (6-10) n in Grouped Frequency Distribution?
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Step 6: Start w/ 25 (b/c we were able to divide equally) not 28 as the apparent lower limit of the lowest class interval. Find the apparent upper limit of this lowest class interval by adding the apparent class interval size (step 4) to 25. Ex. 25 + 4= 29
Step 7: Find the next lowest interval. Add one to the apparent upper limit of the last interval to get next apparent low limit: 30-34 25-29 (29+1=30 so 30-24) Lowest class interval should be placed at the bottom of the page and the highest at class interval should be at the top of page. Step 8: Find the remaining class intervals by repeating step 3 until the highest interval includes the highest score. Step 9: Determine the frequency for each class interval. Make a tally mark beside the class interval in which each score falls. Step 10: Complete the grouped frequency distribution by placing a regular number beside each class interval, showing how many scores fell into that interval. Add up the frequencies; should equal the number of data points |
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class intervals
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range of values grouped together. Each class intervals have two values: lower (ex. 6) and upper value (ex. *)
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Bar graphs
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Use when one of the variables is on a nominal scale (categories) of measurement.
If data points have a true zero point then it is on a ratio scale and a histogram is used. * Don't connect bars b/c nominal scale (separate groups) and it is NOT an interval scale. |
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What kind of labels are on graphs?
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1. Title of the graph: Ex: Frequency of video gaming playing per week.
2. y-axis is titled: Frequency 3. x-axis is titled: what the data points represent: Ex: Hours/week playing video gaming Also x-axis is numbered by the midpoint for each class interval. Ex. 25-29 --> midpoint is 27. On histogram the first bar will have 27 as its middle point. On freq. polygons the first score (dot) on x-axis is found by figuring out what would be the next lower interval ex. 25-29 before that it would be 20-24 with a midpoint of 22. First dot is right on 22 at the zero y-axis (mark on x-axis before 27) do the same for the highest interval. Ex. 80-84 --> 85-89 with 87 as the midpoint and last dot on polygon at the zero y-axis |
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Histogram
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Use when both variables are at least on an interval scale
If data points have a true zero point then it is on a ratio scale Reminder: First bar will have the midpoint of the lowest class interval in the middle |
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Frequency polygon
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Same as a histogram; use when both variables are at least on an interval scale. Ratio/ interval scale.
* If not told which graph use either histogram or freq. polygon Reminder: first score (dot) on x-axis is found by figuring out what would be the next lower interval ex. 25-29 before that it would be 20-24 with a midpoint of 22. First dot is right on 22 at the zero y-axis (mark on x-axis before 27) do the same for the highest interval. Ex. 80-84 --> 85-89 with 87 as the midpoint and last dot on polygon at the zero y-axis |
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Class Interval
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range of scores that are grouped together as a single unit. Ex. 55-59
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Apparent lower limit
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of a class interval is the number written as the lower end of the class interval. Ex 55-59. 55 is the the _____
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Apparent upper limit
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of a class interval is the number written as the upper end of the class interval. Ex 55-59. 59 is the the _____
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Real lower limit
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of a class interval is the lowest value that would actually cause a case (score) to be placed in that class interval. Ex 55-59 has a real lower limit of 54.5 b/c any value btw 54.5 and 55 would be more reasonably placed in the class interval of 55-59 than in the class interval below it (50-54).
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Real upper limit
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of a class interval is the highest value that would actually cause a case (score) to be placed in that class interval. Ex 55-59 has a real lower limit of 59.5 b/c any value btw 59 and 59.5 would be more reasonably placed in the class interval of 55-59 than in the class interval above it (60-64).
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Apparent class interval size
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is the difference btw the apparent upper limit and the apparent lower limit of the class interval. Ex 55-59= 59-55= 4.
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Real class interval size
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the difference btw the real upper limit and the real lower limit of the class interval. Ex 55-59 class interval id 59.5-54.5 = 5. Note the real class interval is one greater than the apparent class interval size.
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10-20
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Number of class intervals a frequency distribution should contain
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4
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Not a preferred real class interval size
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Y-axis
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Axis on which frequency is plotted
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Labels and Midpoint of a class intervals
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Tickmark labels for the X-axis if a histogram
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How should bars be drawn on a histogram
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a bar should be drawn over each class interval, beginning and ending over the real lower and upper limits
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Apparent lower limit
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Should be an integer multiple of the real class interval size
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Real class interval size
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Always one unit smaller than the real class interval size
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Calculate the range of scores
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First step in constructing a grouped frequency distribution
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