Stats Test 1- Distributions

Front 1

Descriptive statistics

Back 1

Doesn't tell why the numbers are what they are. Just a bunch of numbers; have to organize it

Front 2

What is the purpose of a Grouped Frequency Distribution?

Back 2

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

Front 3

What are the steps (1-5) n in Grouped Frequency Distribution?

Back 3

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

Front 4

What are the acceptable values?

Back 4

ex. 1, 2, 3, 5, 10, 15, 25, 50, 100, after 100 anything multiples of 100.

Front 5

What are the steps (6-10) n in Grouped Frequency Distribution?

Back 5

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

Front 6

class intervals

Back 6

range of values grouped together. Each class intervals have two values: lower (ex. 6) and upper value (ex. *)

Front 7

Bar graphs

Back 7

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.

Front 8

What kind of labels are on graphs?

Back 8

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

Front 9

Histogram

Back 9

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

Front 10

Frequency polygon

Back 10

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

Front 11

Class Interval

Back 11

range of scores that are grouped together as a single unit. Ex. 55-59

Front 12

Apparent lower limit

Back 12

of a class interval is the number written as the lower end of the class interval. Ex 55-59. 55 is the the _____

Front 13

Apparent upper limit

Back 13

of a class interval is the number written as the upper end of the class interval. Ex 55-59. 59 is the the _____

Front 14

Real lower limit

Back 14

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).

Front 15

Real upper limit

Back 15

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).

Front 16

Apparent class interval size

Back 16

is the difference btw the apparent upper limit and the apparent lower limit of the class interval. Ex 55-59= 59-55= 4.

Front 17

Real class interval size

Back 17

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.

Front 18

10-20

Back 18

Number of class intervals a frequency distribution should contain

Front 19

4

Back 19

Not a preferred real class interval size

Front 20

Y-axis

Back 20

Axis on which frequency is plotted

Front 21

Labels and Midpoint of a class intervals

Back 21

Tickmark labels for the X-axis if a histogram

Front 22

How should bars be drawn on a histogram

Back 22

a bar should be drawn over each class interval, beginning and ending over the real lower and upper limits

Front 23

Apparent lower limit

Back 23

Should be an integer multiple of the real class interval size

Front 24

Real class interval size

Back 24

Always one unit smaller than the real class interval size

Front 25

Calculate the range of scores

Back 25

First step in constructing a grouped frequency distribution