<p> Nelson/Finizio Algeo I Period 5/6 Quiz Date: 5/11/05 Frequency Tables, Line Plots, and Histograms KEY I. Important Vocabulary 1. Range: the difference between the highest and lowest values 2. Mode: the number or value that occurs the most frequently 3. Median: the number in the middle when data is arranged from least to greatest. 4. Bi-Modal: when you have 2 modes 5. Clusters: data points that are close together 6. Line Plot: a graphic representation in which “x’s” above a number line indicate the frequency of each value 7. Histogram: a graphic representation in which shades boxes above a number line indicate the frequency of each value.</p><p>Sample Problem #1 Arrange the following data into a Frequency Table. </p><p>Grades students received on their English Exam</p><p>73, 53, 78, 93, 100, 72, 79, 84, 97, 92, 56, 93, 72, 93, 93, and 72</p><p>Step #1: Set up your Frequency Table. In order to do this you must first list all your number from least to greatest in a frequency table</p><p>Grade Tally Frequency 53 1</p><p>56 1 Range = 47 72 3</p><p>73 1 Mode = 93 78 1</p><p>79 1 Median = 79 84 1</p><p>92 1</p><p>93 4</p><p>97 1</p><p>100 1</p><p>Total 16 Sample Problem #2 Using the same data from Sample Problem #1 group the data into intervals. </p><p>Grades students received on their English Exam</p><p>73, 53, 78, 93, 100, 72, 79, 84, 97, 92, 56, 93, 72, 93, 93, and 72</p><p>Grade Tally Frequency 50-59 = F 2</p><p>60-69 = D</p><p>70-79 = C 6</p><p>80-89 = B 1</p><p>90-100 = A 7</p><p>Total 16</p><p>Sample Problem #3 Using the following data create a line plot. </p><p>Ages of Mothers of a Class of Students</p><p>35, 41, 43, 42, 42, 39, 36, 44, 35, 40, 45, and 42.</p><p>Step #1: Figure out what your Range is in this data. In order to do this you must subtract the smallest number from the largest number in you data. </p><p>45- 35 10 Range</p><p>Step #2: Draw a number line starting with 35 and ending with 59. Place X’s above each number indicating the frequency of each age.</p><p>X X X X X X X X X X X X 35 36 37 38 39 40 41 42 43 44 45</p><p>Mode = 42 Range = 10 Median = 41.5 Explanation: Since there is an even number of data in this problem (12). You must take the 2 number that are in the middle of the data (41 and 42) and average them. When you do this you get 41.5. Sample Problem #4 Finding Percentage What percentage of the class Mothers is 42 years old? X X X X X X X X X X X X 35 36 37 38 39 40 41 42 43 44 45</p><p>Step #1: Look at the line plot and see how many mothers are 42 years old. </p><p>In this problem there are 3 mothers that are 42 years old. </p><p>Step #2: See how much total data there is. </p><p>In this problem there were 12 total data taken. </p><p>Step #3: Set up a fraction in which the number of 42 year old Mothers is over the total data taken. In other words how many Mothers out of the total are 42? </p><p>3 42 year old Mothers 12 Total number of Mothers</p><p>Step #3: Divide 3 by 12. </p><p>3 12 .25</p><p>Step #4: Change a fraction to a percent. You do this by multiplying by 100 or moving you decimal point 2 spaces to the right. Remember that if you need to round you must round to the nearest percent. Therefore if you were left with 25.6% this would round to 26% </p><p>25% of the Mothers of the class are 42 years old. </p><p>Sample Problem #5 Create a Histogram using the line plot from Sample Problem #3</p><p>Shade in your X’s</p><p>X X X X X X X X X X X X 35 36 37 38 39 40 41 42 43 44 45</p><p>Sample Problem #6 Find the Range, Mode, and Median</p><p>90, 90, 40, 50, 90, 50, 60, 50, and 40</p><p>Range: To find the range take the largest number (90) and subtract the smallest number (40) from it.</p><p>90- 40 50 Range</p><p>Mode: Mode is defined as the number or value that occurs most frequently. In this problem 90 and 50 both occur 3 times. Therefore they will both be the mode (Bi-Modal).</p><p>90 & 50 Modes</p><p>Median: To find the Median first place the data in order from least to greatest. 40,40,50,50,50,60,90,90,90</p><p>Median</p><p>Next you must pick out the number that is in the middle of the data. This is your Median.</p><p>Practice Problems 1. Arrange the following data into a frequency table. </p><p>Judy asked 16 people how many pets they have. She recorded the following data. 2,0,5,1,0,2,6,2,0,3,1,3,4,3,8,3</p><p>Pets Tally Frequency 8 7 6 5 4 3 2 1 0</p><p> a. How many students have 2 Pets? 3</p><p> b. What is the number of pets that most students have? 3</p><p> c. How many students have 3 or more pets?</p><p>12</p><p> d. What percentage of the students has 3 pets? 25% 2. Arrange the following data into a line plot and histogram The following is a list of NBA franchises and the number of Championships they’ve won Franchise Number of Championships Boston Celtics 16 Minneapolis/ LA Lakers 11 Chicago Bulls 6 Philadelphia/Golden State Warriors 3 Syracuse Nationals/Philadelphia 76ers 3 Detroit Pistons 2 New York Knicks 2 Houston Rockets 2 Milwaukee Bucks 1 Portland Trail Blazers 1</p><p>Line Plot</p><p>Histogram</p><p>Questions</p><p> a. What percentage of the franchises won 3 Championships? 20%</p><p> b. What is the mode of the data? 2</p><p> c. What percentage of the franchises won 2 Championships? 30% d. Do you notice any clusters? If so circle them on your line plot. 3. Arrange the following data in a line plot and histogram. The following is a list of Major League Baseball teams and the number of Championships they’ve won.</p><p>Team Championships New York Yankees 26 St. Louis Cardinals 9 Boston Red Sox 6 New York Giants 5 Philadelphia Athletics 5 Pittsburgh Pirates 5 Los Angeles Dodgers 5 Cincinnati Reds 5 Detroit Tigers 4 Oakland Athletics 4</p><p>Line Plot</p><p>Histogram</p><p>Questions a. What percentage of teams won 4 championships? 20%</p><p> b. What percentage of teams won 5 championships? 50%</p><p> c. What is the mode of the data? 5</p><p> d. What is the range of the data? 22</p><p> e. Are there any clusters in this data? If so, circle them on your line plot. </p><p> f. Do you notice any outliers, if so who is it? New York Yankees 4. Find the Range, Mode, and Median in the following set of data.</p><p>25,18,20,25,20,30,35</p><p>Range:17</p><p>Mode: 20 & 25</p><p>Median: 25</p><p>5. Find the Range, Mode, and Median in the following set of data.</p><p>4.5,4.8,4.2,5.0,4.8,4.1,4.5,4.2,4.8</p><p>Range: 0.9</p><p>Mode: 4.8</p><p>Median: 4.5</p><p>6. Find the Range, Mode, and Median in the following set of data.</p><p>59,56,61,60,62,63,60,61,63,61,57,60,61,65</p><p>Range: 9</p><p>Mode: 61</p><p>Median: 61</p>