Create a bar graph that displays the data from the frequency table in Example 1. See the examples on p Does our graph look different?

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1 A frequency table is a table with two columns, one for the categories and another for the number of times each category occurs. See Example 1 on p Create a bar graph that displays the data from the frequency table in Example 1. See the examples on p Does our graph look different? It is important to label each axis properly, and when you are creating a bar graph for qualitative data the bars should not touch. Looking at Example 4 on p. 249 as a reference, when would someone prefer to use a frequency table or a bar graph? A pie chart is often used when you want to compare the relative sizes of categories. See p TQ12. Explain the difference between how information is displayed in a frequency table, a bar graph, and a pie chart. Create charts to display the data on the board :21:08 1/7 DescribingData.pdf (#3)

2 The same data can be displayed different ways depending on the effect you wish a chart to have. See p Quantitative data can also be displayed on a bar graph called a histogram. Two important differences are: 1. On a histogram the bars touch 2. There is a numerical scale on the horizontal axis in addition to the scale on the vertical axis. See Example 11 on p See TIN 3 on p. 256 TQ13: Explain the differences between a bar graph for qualitative data and a histogram. How can you summarize a set of scores numerically? Measures of central tendency are used to describe a typical data value of a set. The of a data set is the sum of the data values divided by the number of data values. Find the mean of this set: /7 DescribingData.pdf (2/7)

3 The of a data set is the middle number of a set after the values are listed in order. First list the values from smallest to largest, or from largest to smallest. If there are an odd number of data values, the middle value is the median. If there are an even number of data values, the average of the two middle values is the median. Find the median of this data set: Find the median of this data set: The of a data set is the most common data value of the set. If no value occurs more than once, there is no mode. If multiple values occur with the greatest frequency, there is more than one mode. Find the mode of this data set: Find the mode of this data set: Blue Red Red Blue Green Find the mode of this data set: /7 DescribingData.pdf (3/7)

4 See Examples 16 and 20 on p. 259 and 261. Find the mean and mode. Income (thousands of dollars) Frequency See Example 17 on p Which measure of central tendency can be strongly affected by outliers? TQ14: What does the mean tell you about a set of data? TQ15: What does the median tell you about a set of data? TQ16: What does the mode tell you about a set of data? TQ17: When is the median preferred instead of the mean to describe a typical data value? TQ18: Which measure of central tendency can be used to summarize qualitative data? Find the mean and mode of the number of siblings of the students in this class. First create a frequency table. 4/7 DescribingData.pdf (4/7)

5 Suppose two classes took a statistics test and their scores are listed below. Class A Class B In each class, the mean, median, and mode test score is 75. What is different about the two sets of data? The easiest measure of variability to calculate is usually the. To find the range, find the difference between the largest value and the smallest value. Find the range of the test scores for each class above. Here are the test scores for students in another class. Find the range Is the range a good measure of the variability of the test scores in this class? Why or why not? TQ19: What is a weakness of the range as a measure of variability? Since people often want a measure of variation that uses information from all of the data values, the is often used instead of the range. A large standard deviation means that the data values are widely spread apart with a lot of variability. A small standard deviation means that the data set is more consistent with the values close together. One of the above classes has a standard deviation of 18.3 and the other has a standard deviation of 2.1. Which one is class A and which one is class B? 5/7 DescribingData.pdf (5/7)

6 How can you use the standard deviation to determine whether a set of data is close together or spread apart? You need to compare the relative size of the standard deviation to the data values. For example, if you are studying heights of children measured in inches and you have a standard deviation of 10 inches, then the data are spread apart because 10 inches makes a lot of difference when measuring the height of a child. But if you are studying the prices of cars at a dealership and the standard deviation is 10 dollars, the data are close together because 10 dollars doesn t make a lot of difference when considering the prices of cars. TQ20: What does the standard deviation tell you about a set of data? Quartiles divide the data into quarters. The first quartile (Q1) is above 25% of the data. The second quartile (Q2) is above 50% of the data. The third quartile (Q3) is above 75% of the data. Which quartile is the same as the median? Quartiles are often provided as part of the 5 number summary of a set of data: Minimum, Q1, Median, Q2, Maximum Suppose the 5 number summary for the sale price of all used iphone 5 units on ebay during February is given below What percent of iphone 5 units sold for less than $160? What percent of iphone 5 units sold for more than $160? What percent of iphone 5 units sold for between $160 and $250? A 5 number summary is presented visually by creating a boxplot. 6/7 DescribingData.pdf (6/7)

7 See Example 32 on p For store 1: What percent of the service times are more than 2.9 minutes? What percent of the service times are between 1.8 minutes and 2.9 minutes? For store 2: What percent of the service times are less than 2.1 minutes? What percent of the service times are between 0.5 minutes and 9.6 minutes? TQ21: What numbers are included in a data set s 5 number summary? Homework Practice problems: 1-6, 7ab, 8ab, 9ab, 10ab, 11, 12, 15 Graded: Canvas assignment Describing Data 1 Graded: Canvas assignment Describing Data 2 7/7 DescribingData.pdf (7/7)