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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. • 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 80 64 72 76 80 88 68 76 60 72 76 72 96 76 68 72 80 80 68 104 64 72 88 68 64 60 68 80 76 72 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 n Procedure: • Determine the number of classes – Will either be given or found by – ALWAYS ROUND UP! n Calculate the Class Width • Round up for convenience class width maximum - minimum # of classes 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 40 6 . 324 ... • Round up: There are 7 classes Pulse Rate Frequency Calculate Class Width • class width maximum - minimum # of classes class width 124 - 60 7 9 . 142 ... 10 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 60708090- 100110120- Frequency Identify corresponding UCL • Make sure you leave no gaps where numbers would fit in. Pulse Rate Frequency 60-69 70-79 80-89 90-99 100-109 110-119 120-129 Finish by... • Calculating frequency for each class • All values should be included totals should match up! Pulse Rate Frequency 60-69 12 70-79 14 80-89 11 90-99 1 100-109 1 110-119 0 120-129 1 Relative Frequency Tables • Same Classes • Sum must be close to 1 relative frequency class frequency all frequencie s Relative frequency distribution tables Pulse Rate Relative Frequency 60-69 30% 70-79 40% 80-89 27.5% 90-99 2.5% 100-109 2.5% 110-119 0 120-129 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 50-69 Freq Normal Dist 24 frequencies start low... 70-89 228 90-109 490 increase to maximum... 110-129 232 130-149 Relatively symmetric 26 decrease to be come low again. Last Digits of Female Pulse Rates • Last digit 0 1 2 3 4 5 6 7 8 Freq 9 0 8 0 6 0 7 0 10 Randomly Selected Pennies Wt. (grams) of pennies 2.40-2.49 2.50-2.59 2.60-2.69 2.70-2.79 2.80-2.89 2.90-2.99 3.00-3.09 3.10-3.19 Frequency 18 19 0 0 0 2 25 8