UNIT VII STUDY GUIDE Frequency Distribution & Measures of Central Tendency and Variation Course Learning Outcomes for Unit VII Upon completion of this unit, students should be able to: 2. Differentiate between descriptive and inferential statistics. 2.1 Compare and contrast advantages and disadvantages of percentiles. 2.2 Identify differences between frequency and cumulative frequency. 2.3 Compute mean, median, and mode. 5. Analyze health care statistics, vital statistics, descriptive statistics, data validity, and reliability. 5.1 Define measures of variability. 5.2 Identify positive and negative skewness. 5.3 Identify features of normal distributions. Reading Assignment Chapter 12: Frequency Distribution Chapter 13: Measures of Central Tendency and Variation Unit Lesson Welcome to Unit VII! In this unit, we will have a strong focus on data collection and methods. Chapters 12 and 13 will serve as a great conclusion and will help tie many of our principles that we have learned thus far. Now that we have worked hard to collect data, it is time to learn in more detail how to organize and analyze it. There are several methods of organizing data; Chapter 12 focuses on frequency distribution methods of organization. First of those methods mentioned, is ungrouped frequency distribution. This is a listing of all scores as they are obtained, and also can be a listing of scores from highest to lowest or lowest to highest. The second form of organization is grouped frequency distribution. This form of distribution is extremely helpful for larger scores and groups for organization (Koch, 2008). Some advantages to this method are bringing order and condensing data. Grouped frequency distribution is also generally listed from highest score to lowest score. Chapter 12 reviews many popular terms in statistics, so please pay close attention. Let's go ahead and review some of these terms together. Range- calculated by finding the difference between the largest score in the distribution and the smallest score. Example: If the highest score is 100 and the lowest is 10 the range becomes 90 (100-10=90). Class- a category to which a score can be placed. 1) Class interval- range of scores. 2) Class limits- end numbers of the class interval are the class limits. The smallest is the lower class unit and the largest is the upper class limit. 3) Class boundaries- measuring continuous variables. 4) Class size- size of class interval (difference between upper and lower class limit). Frequency- number of times a certain score appears in the distribution. You may remember doing this if you have ever used tally marks to count the time of occurrence between two different events or subjects. HTH 1306, Introduction to Health Care Statistics 1 Cumulative Frequency- sum of frequencies, starting at the lowest interval UNIT and including frequencies x STUDYthe GUIDE that are within that interval (Koch, 2008). Title So, how does one create a frequency distribution? Let's discuss the steps to creating an effective frequency distribution. First, you want to begin with determining the highest score and the lowest score. Second, arrange these scores from highest to lowest. Third, determine the range by subtracting the lowest score from the highest score. Fourth, identify the number of class intervals. Fifth, set the class limits, and finally, follow rules for subsequent computations (Koch, 2008, p. 221), this is very important to ensure consistency among your computations. Chapter 12 concludes with a brief discussion of percentiles and their importance along with their weaknesses. Moving on to chapter 13, there is a stronger focus on measurements and variabilities. These measures and values are commonly associated with central tendency. Central tendency refers to laying near the center of a distribution, hence its name. There are several types of these measures that are typically reported with these tendencies. Page 234 of the text contains a graphic showing the mean, median, and mode in a normal bellshaped curve (Koch, 2008). Let's begin by discussing the first measure of central tendency, the mean. The mean is the average, so it is computed just as you would any average score, as we did in Chapter 3. The formula for mean is: Mean = scores N (N= total number of scores) There can be several ways to calculate a mean, by weight or computed by a group of data. Please make sure to refer to your text for some excellent examples of these forms of mean calculations. The second measure of central tendency is the median. The median score is the middle score of a distribution, and scores are arranged from high to low, or low to high (Koch, 2008). Also referred to as the midpoint, the median divides the distribution into two halves. The third measure of tendency discussed in Chapter 13 is mode. The mode is a set of numbers that occurs most frequently, or the most common score of the distribution. Sometimes, a mode may not exist if a number or score does not present itself more than once. A distribution with a single mode is referred to as unimodal, and a distribution with two modes is referred to as bimodal. Frequency distribution uses curves to demonstrate different measurements. A bilaterally symmetrical curve is identical on both sides (just as the one pictured above). A bell shaped curve is a common most proportioned curve, also known as a \"normal\" distribution. Sometimes you may find a bell shaped curve that is still symmetrical, but vary greatly by height (peaked) or width (flat). One may also find skewed curves, these are NOT symmetrical in shape. When a curve is skewed, it affects the locations of the central tendency (Koch, 2008). Please refer to pages 239-240 for illustrations of negative and positive skews (Koch, 2008). Extreme skews can affect the tendency and mean of distribution. There are also other curves that one might encounter in their data. Some examples of these would be J-shaped curves, reverse J-shaped curves, U-shaped curve, bimodal, and multimodal. While it is very important to understand measures of central tendency, it is also important to identify similarities or dissimilarities in distributions. Variability is the difference between scores and their distributions (Koch, 2008). To better describe variability, we break them down into three measures: range, variance, and standard deviation. HTH 1306, Introduction to Health Care Statistics 2 This unit may seem a little intimidating at first, but please make sure you read UNIT through your chapters x STUDY GUIDE thoroughly and do the exercises for each area. This will help you practice utilizing Titlewhat you are learning. Reference Koch, G. (2008). Basic allied health statistics and analysis (3rd ed.). Clifton Park, NY: Delmar. HTH 1306, Introduction to Health Care Statistics 3