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

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 –W–Will either be given or found by – ALWAYS ROUND UP!

Calculate the Class Width Round up for convenience

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 Pulse RateFrequency

Calculate Class Width

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 RateFrequency

Identify corresponding UCL Make sure you leave no gaps where numbers would fit in. Pulse RateFrequency

Finish by... Calculating frequency for each class All values should be included totals should match up! Pulse RateFrequency

Relative Frequency Tables Same Classes Sum must be close to 1

Relative frequency distribution tables Pulse RateRelative Frequency % % % % % %

Cumulative Frequency Replace lower class limits with “less than...” Add each cell to previous cells Pulse RateFrequency Less than 7012 Less than 8026 Less than 9037 Less than Less than Less than Less than 13040

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 scoreFreqNormal Dist frequencies start low increase to maximum decrease to be come low again. Relatively symmetric

Last Digits of Female Pulse Rates Last digit Freq

Randomly Selected Pennies Wt. (grams) of penniesFrequency