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# Statistics STAT 1070

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This 4 page Class Notes was uploaded by Alikhan Ladhani on Monday February 22, 2016. The Class Notes belongs to STAT 1070 at Georgia State University taught by Professor Kemp in Spring 2016. Since its upload, it has received 62 views. For similar materials see Elementary Statistics in Statistics at Georgia State University.

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Date Created: 02/22/16

Math 1070 – Elementary Statistics Lecture notes prepared by Dr. Leslie Meadows (Coordinator Math 1070 and GSU Commons MILE) based on the texts: Elementary Statistics coordinating PowerPoint Slides.n for Math1070; Georgia State University and Elementary Statistics; Eleventh Edition. Mario F. Triola, and Chapter 2 – Summarizing and Graphing Data 2-2 – Frequency Distributions Definition A frequency distribution (or frequency table)- shows how data are partitioned among several categories (or classes) by listing the categories with the number (frequency) of data values in each of them. We’ll demonstrate the construction (and use) of frequency distributions based on the “raw data” from the following table: Table Pulse Rates (beats per minute) of Females and Males Definitions Lower class limits - the smallest numbers that can belong to the different classes. Upper class limits - the largest numbers that can belong to the different classes. Class boundaries - the numbers used to separate the classes, but without the gaps created by class limits. Class midpoints - the values in the middle of the classes (each class midpoint is computed by adding the lower class limit to the upper class limit and dividing the sum by 2). Class width - the difference between two consecutive lower class limits (or two consecutive lower class boundaries) in a frequency distribution. Example: The following is a frequency distribution table for the pulse rates of females (obtained from the original data above): Table-a Pulse Rates of Females a. Let’s identify the lower class limits: b. Let’s identify the upper class limits: c. Let’s identify class boundaries: d. Let’s identify the class midpoints: e. Let’s identify the class width: Why do we construct frequency distributions? 1. Large data sets can be summarized. 2. We can analyze the nature of data. 3. We have a basis for constructing important graphs. How do we construct a frequency distribution? 1. Determine the number of classes (should be between 5 and 20). 2. Calculate the class width (round up) ???????????????????? ???????????????????? ≈ (???????????? ???????????????????? − ???????????? ???????????????????? ) ???????????????????????? ???????? ???????????????????????????? 3. Starting point: Choose the minimum data value (or a convenient value below it) as the first lower class limit. 4. Using the first lower class limit and class width, proceed to list the other lower class limits. 5. List the lower class limits in a vertical column and proceed to enter the upper class limits. 6. Take each individual data value and put a tally mark in the appropriate class. Add the tally marks to get the frequenc(or we can simply use Excel to SORT and COUNT the data) Example: Using the steps given above, let’s construct a frequency distribution table for the pulse rates of males (original data repeated below in Table-b): Table -b Pulse Rates (beats per minute) of Males At this point, let’s open an Excel file (with the raw data already entered) and practice using the SORT and COUNT commands as we build our frequency distribution table for the Pulse Rates of Males. Table-c Pulse Rates of Males (frequency distribution) Step 1: Step 2: Step 3: Choose 55 Step 4: Step 5: Step 6: Relative (or Percentage) Frequency Distribution relative frequency distribution – a frequency distribution table in which each class frequency is replaced by a relative frequency (or proportion). ???????????????????? ???????????????????????????????????? ???????????????????????????????? ???????????????????????????????????? = ???????????? ???????? ???????????? ???????????????????????????????????????????? percentage frequency distribution – a frequency distribution table in which each class frequency is replaced by a percentage. ???????????????????????????????????????? ???????????????????????????????????? = ???????????????????? ???????????????????????????????????? × ????????????% ???????????? ???????? ???????????? ???????????????????????????????????????????? Example: Let’s construct a percentage relative frequency distribution table for the pulse rates of females – based on the given frequency distribution table. Table-a Pulse Rates of Females Table-d Relative Frequency Distribution of Pulse Rates of Females Cumulative Frequency Distribution cumulative frequency distribution – a frequency distribution in which the frequency for each class is the sum of the frequencies for that class and all pevious classes. Example: Let’s construct a cumulative frequency distribution table for the pulse rates of females – based on the given frequency distribution table. Table-a Pulse Rates of Females Table-e Cumulative Frequency Distribution of Pulse Rates of Females Critical Thinking: Interpreting Frequency Distributions In later chapters, there will be frequent reference to data with a normal distribution. One key characteristic of a normal distribution is that it has a “bell” shape. The frequencies start low, then increase to one (or two) high frequencies, then decrease to a low frequency. The distribution is approximately symmetric, with frequencies preceding the maximum being roughly a mirror image of those following the maximum. Example: Based on the criteria given above, do either of the frequency distributions given below appear to result from normally distributed data? Upper Class Limits Frequency Upper Class Limits Frequency 60 13 61.3 1 66 7 72 9 63.5 3 78 2 65.7 5 67.9 16 84 4 90 4 70.1 9 96 1 72.3 5 74.5 1 Gaps The presence of gaps can show that we have data from two or more different populations. However, the converse is not true (because data from different groups do not necessarily result in gaps).

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