Frequency Distribution Dr. Wajed Hatamleh WEEK 2 Frequency Distribution Dr. Wajed Hatamleh Dr. Wajed Hatamleh week 2

Learning Objectives Recognize the difference between grouped and ungrouped data Construct a frequency distribution Construct a histogram Dr. Wajed Hatamleh week 2 2

Overview Descriptive Statistics Inferential Statistics summarize or describe the important characteristics of a known set of population data Inferential Statistics use sample data to make inferences (or generalizations) about a population Dr. Wajed Hatamleh week 2

Important Characteristics of Data 1. Center: A representative or average value that indicates where the middle of the data set is located 2. Variation: A measure of the amount that the values vary among themselves 3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed) 4. Outliers: Sample values that lie very far away from the vast majority of other sample values 5. Time: Changing characteristics of the data over time Dr. Wajed Hatamleh week 2

Ungrouped Versus Grouped Data Ungrouped data have not been summarized in any way are also called raw data Grouped data have been organized into a frequency distribution Dr. Wajed Hatamleh week 2 7

WHAT THE HECK ARE ALL THOSE NUMBERS??? Example of Ungrouped Data 52 59 32 61 74 48 66 46 70 61 53 40 ? ? ? ? ? ? ? Dr. Wajed Hatamleh week 2

Frequency Distributions HELP!! That’s what a frequency distribution is for—to help impose order on the data A frequency distribution is a systematic arrangement of data values, with a count of how many times each value occurred in a dataset Dr. Wajed Hatamleh week 2

Key Concept When working with large data sets, it is often helpful to organize and summarize data by constructing a table called a frequency distribution. Dr. Wajed Hatamleh week 2

Definition Frequency Distribution (or Frequency Table) lists data values (either individually or by groups of intervals), along with their corresponding frequencies or counts Dr. Wajed Hatamleh week 2

Ungrouped Versus Grouped Data Ungrouped data have not been summarized in any way are also called raw data Grouped data have been organized into a frequency distribution Dr. Wajed Hatamleh week 2 7

Example of Ungrouped Data 42 30 53 50 52 55 49 61 74 26 58 40 28 36 33 31 37 32 23 43 29 34 47 35 64 46 57 25 60 54 Ages of a Sample of Nurses Managers from KFH, KSA Dr. Wajed Hatamleh week 2 8

Frequency Distribution of Nursing Manager’s Ages at KFH Class Interval Frequency 20-under 30 6 30-under 40 18 40-under 50 11 50-under 60 11 60-under 70 3 70-under 80 1 Dr. Wajed Hatamleh week 2 9

Data Range Smallest Largest 42 30 53 50 52 55 49 61 74 26 58 40 28 36 33 31 37 32 23 43 29 34 47 35 64 46 57 25 60 54 Smallest Largest Dr. Wajed Hatamleh week 2 10

Number of Classes and Class Width The number of classes should be between 5 and 15. Fewer than 5 classes cause excessive summarization. More than 15 classes leave too much detail. Class Width Divide the range by the number of classes for an approximate class width Round up to a convenient number Dr. Wajed Hatamleh week 2 11

Class Midpoint Dr. Wajed Hatamleh week 2 12

Relative Frequency Relative Class Interval Frequency Frequency 20-under 30 6 .12 30-under 40 18 .36 40-under 50 11 .22 50-under 60 11 .22 60-under 70 3 .06 70-under 80 1 .02 Total 50 1.00 Dr. Wajed Hatamleh week 2 13

Cumulative Frequency Cumulative Class Interval Frequency Frequency 20-under 30 6 6 30-under 40 18 24 40-under 50 11 35 50-under 60 11 46 60-under 70 3 49 70-under 80 1 50 Total 50 Dr. Wajed Hatamleh week 2 14

Class Midpoints, Relative Frequencies, and Cumulative Frequencies Relative Cumulative Class Interval Frequency Midpoint Frequency Frequency 20-under 30 6 25 .12 6 30-under 40 18 35 .36 24 40-under 50 11 45 .22 35 50-under 60 11 55 .22 46 60-under 70 3 65 .06 49 70-under 80 1 75 .02 50 Total 50 1.00 Dr. Wajed Hatamleh week 2 15

Cumulative Relative Frequencies Relative Cumulative Relative Class Interval Frequency Frequency Frequency Frequency 20-under 30 6 .12 6 .12 30-under 40 18 .36 24 .48 40-under 50 11 .22 35 .70 50-under 60 11 .22 46 .92 60-under 70 3 .06 49 .98 70-under 80 1 .02 50 1.00 Total 50 1.00 Dr. Wajed Hatamleh week 2 16

Frequency Distributions Another example week 2 DR. Wajed Hatamleh

week 2 DR. Wajed Hatamleh

week 2 DR. Wajed Hatamleh

Lower Class Limits are the smallest numbers that can actually belong to different classes week 2 DR. Wajed Hatamleh

Lower Class Limits Lower Class Limits are the smallest numbers that can actually belong to different classes Lower Class Limits week 2 DR. Wajed Hatamleh

Upper Class Limits Upper Class Limits are the largest numbers that can actually belong to different classes Upper Class Limits week 2 DR. Wajed Hatamleh

Class Boundaries are the numbers used to separate classes, but without the gaps created by class limits week 2 DR. Wajed Hatamleh

number separating classes Class Boundaries number separating classes - 0.5 99.5 199.5 299.5 399.5 499.5 week 2 DR. Wajed Hatamleh

number separating classes Class Boundaries number separating classes Class Boundaries - 0.5 99.5 199.5 299.5 399.5 499.5 week 2 DR. Wajed Hatamleh

midpoints of the classes Class Midpoints midpoints of the classes Class midpoints can be found by adding the lower class limit to the upper class limit and dividing the sum by two. week 2 DR. Wajed Hatamleh

midpoints of the classes Class Midpoints midpoints of the classes Class Midpoints 49.5 149.5 249.5 349.5 449.5 week 2 DR. Wajed Hatamleh

Class Width Class Width is the difference between two consecutive lower class limits or two consecutive lower class boundaries Class Width 100 week 2 DR. Wajed Hatamleh

Reasons for Constructing Frequency Distributions 1. Large data sets can be summarized. 2. Can gain some insight into the nature of data. 3. Have a basis for constructing graphs. week 2 DR. Wajed Hatamleh

Constructing A Frequency Table 1. Decide on the number of classes (should be between 5 and 20) . 2. Calculate (round up). (highest value) – (lowest value) class width  number of classes 3. Starting point: Begin by choosing a lower limit of the first class. 4. Using the lower limit of the first class and class width, proceed to list the lower class limits. 5. List the lower class limits in a vertical column and proceed to enter the upper class limits. 6. Go through the data set putting a tally in the appropriate class for each data value. week 2 DR. Wajed Hatamleh

Relative Frequency Distribution class frequency sum of all frequencies week 2 DR. Wajed Hatamleh

Relative Frequency Distribution 11/40 = 28% 12/40 = 40% etc. Total Frequency = 40 week 2 DR. Wajed Hatamleh

Cumulative Frequency Distribution Cumulative Frequencies week 2 DR. Wajed Hatamleh

Frequency Tables week 2 DR. Wajed Hatamleh

Recap In this Section we have discussed Important characteristics of data Frequency distributions Procedures for constructing frequency distributions Relative frequency distributions Cumulative frequency distributions Dr. Wajed Hatamleh week 2

A table that lists data values along with their counts is An olgive. A frequency distribution. A cumulative table. A histogram. Dr. Wajed Hatamleh week 2

The smallest numbers that can actually belong to different classes are Upper class limits. Class boundaries. Midpoints. Lower class limits. Dr. Wajed Hatamleh week 2

The smallest numbers that can actually belong to different classes are Upper class limits. Class boundaries. Midpoints. Lower class limits. Dr. Wajed Hatamleh week 2