frequency distribution
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Frequency Distribution. Objectives: Create Frequency Distributions Analyze Frequency Distribution. What is a Frequency Distribution?. Allows us to understand and interpret the nature of the distribution of a data set. - PowerPoint PPT PresentationTRANSCRIPT
Frequency Distribution
Objectives: Create Frequency DistributionsAnalyze Frequency Distribution
What is a Frequency Distribution?
• Allows us to understand and interpret the nature of the distribution of a data set.
• Shows how data is partitioned among classes by listing the classes along with the number of data values in each.
PULSE RATES (BEATS PER MINUTE) of FEMALES
76 72 88 60 72 68 80 64 68 6880 76 68 72 96 72 68 72 64 8064 80 76 76 76 80 104 88 60 7672 72 88 80 60 72 88 88 124 64
Creating a Frequency Distribution Table
• Lower Class Limits: smallest numbers that can belong to the different classes
• Upper Class Limits: largest numbers ...• Class Boundaries: numbers used to separate
the classes, but w/out the gaps created by class limits
• Class Midpoints: values in the middle of the classes
• Class width: difference b/w 2 consecutive lower/upper class boundaries
Procedure:
• Determine the number of classes– Will either be given or found by– ALWAYS ROUND UP!
n
n
Calculate the Class Width
• Round up for convenience
classes of #minimum-maximum width class
Lower Class Limit
• Select either the lowest data value or a convenient value below the minimum as the first lower class limit.
Cont...
• Using the class width and the first lower class limit begin listing the lower class limits in a vertical column by adding the class width.
Adding the upper class limits
• Identify the corresponding upper class limits to each class making sure that the classes do not overlap
Finish by...
• Taking the total values in each class and listing them is column number 2
Things to watch out for:
• Confusing the class width and the class boundaries– Class width is the difference between lower or
upper class limits!• Make sure you include all classes, even
those with 0 data values. • The sum of column 2 should be the # of
values in data set
Example using Female Pulse Rates
• Step 1: Find total # of classes– n=40
• Round up: There are 7 classes
...324.640
Pulse Rate Frequency
Calculate Class Width
•
classes of #minimum-maximum width class
10...142.97
60-124 width class
Begin filling in table
• Choose 60 as the first lower class limit because it is both the minimum value and a convenient value
• Add the class width and record in following rows
Pulse Rate Frequency60-70-80-90-100-110-120-
Identify corresponding UCL
• Make sure you leave no gaps where numbers would fit in.
Pulse Rate Frequency60-6970-7980-8990-99100-109110-119120-129
Finish by...
• Calculating frequency for each class
• All values should be included totals should match up!
Pulse Rate Frequency60-69 1270-79 1480-89 1190-99 1100-109 1110-119 0120-129 1
Relative Frequency Tables
• Same Classes• Sum must be close to 1
sfrequencie allfrequency classfrequency relative
Relative frequency distribution tables
Pulse Rate Relative Frequency60-69 30%70-79 40%80-89 27.5%90-99 2.5%100-109 2.5%110-119 0120-129 2.5%
Cumulative Frequency
• Replace lower class limits with “less than...”
• Add each cell to previous cells
Pulse Rate Frequency
Less than 70 12
Less than 80 26
Less than 90 37
Less than 100 38
Less than 110 39
Less than 120 39
Less than 130 40
Interpreting Frequency Distributions
Normal Distribution (Bell Curve) within a frequency distribution table:
Frequencies start low, increase in frequency, then return to low.
Distribution is approximately symmetric
IQ Scores of 1000 Adults
IQ score Freq Normal Dist
50-69 24 frequencies start low...
70-89 228
90-109 490 increase to maximum...
110-129 232
130-149 26 decrease to be come low again.
Relatively symmetric
Last Digits of Female Pulse RatesLast digit
Freq
0 91 02 83 04 65 06 77 08 109 0
Randomly Selected Pennies
Wt. (grams) of pennies Frequency2.40-2.49 182.50-2.59 192.60-2.69 02.70-2.79 02.80-2.89 02.90-2.99 23.00-3.09 253.10-3.19 8