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 72 76 80 72 88 68 76 88 60 72 76 80 72 96 76 60 68 72 80 72 80 68 104 88 64 72 88 88 68 64 60 124 68 80 76 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 ...

Pulse Rate Frequency • Round up: There are 7 classes

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 60 70 80 90 100 110 120 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 70-79 80-89 12 14 11 90-99 100-109 110-119 120-129 1 1 0 1

Relative Frequency Tables • • Same Classes Sum must be close to 1 relative frequency  class  all frequency frequencie s

Relative frequency distribution tables Pulse Rate 60-69 70-79 80-89 90-99 100-109 110-119 120-129 Relative Frequency 30% 40% 27.5% 2.5% 2.5% 0 2.5%

Cumulative Frequency • • Replace lower class limits with “less than...” Add each cell to previous cells Pulse Rate Less than 70 Less than 80 Less than 90 Less than 100 Less than 110 Less than 120 Less than 130 37 38 39 39 40 Frequency 12 26

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 70-89 90-109 110-129 130-149 Relatively symmetric Freq Normal Dist 24 frequencies start low...

228 490 increase to maximum...

232 26 decrease to be come low again.

• Last Digits of Female Pulse Rates Last digit Freq 0 9 1 2 3 0 8 0 4 5 6 7 8 9 6 0 7 0 10 0

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