Question

Unit 6 Lesson 3 Classwork (Adapted from Math Vision Project) Data Distribution A lot of information can be obtained from looking at data plots and their distributions. It is important when describing data that we use context to communicate the shape, center, and spread. Shape and spread: Modes: uniform (evenly spread- no obvious mode), unimodal (one main peak), bimodal (two main peaks), or multimodal (multiple locations where the data is relatively higher than others). Skewed distribution: when most data is to one side leaving the other with a "tail". Data is skewed to side of tail. (if tail is on left side of data, then it is skewed left). Normal distribution and standard deviation: curve is unimodal and symmetric. Data that has a normal distribution can also describe the data by how far it is from the mean using standard deviation. Outliers: values that stand away from the body of the distribution. For a box-and-whisker plot, points are considered outliers if they are more than 1.5 times the interquartile range (length of bo beyond quartiles 1 and 3. A point is also considered an outliner if it is more than two standard deviations from the center of a normal distribution. Variability: values that are close together have low variability; values that are spread apart have high variability. Center: Analyze the data and see if one value can be used to describe the data set. Normal distributions make this easy. If not a normal distribution, determine if there is a 'center' value that best describes the data. Bimodal or multimodal data may not have a center that would provide useful data There are representations of test scores from six different classes found below, for each 1. Describe the data distribution. 2. Compare data distributions between Anderson and Williams. Compare data distributions between Williams and Lemon. 3, 4 Compare data distributions between Croft and Hurlea. 5. Compare data distributions between Jones. Spencer, and Anderson. 6. Compare data distributions between Spencer and the other histograms 7. Which distributions are most similar? Different? Explain your answer. Page Data set I: Williams's class Data set II: Lemon's class e Data set IIl: Croft's Class Data set IV: Anderson's Class box) ve ns Data set V: Hurlea's class Data set VI: Jones' class scribes 12%- an Page / 18 Page | 19 Data set VII: Spencer's class Data set VIll: Overall Achievement Test Scores Achievement Test Scores Tast Bars 82 70 72 74 Pace/2 Mr. Cole gave a ten-point quiz to his math classes. A total of 50 students took the quiz. Mr. Cole scores Creating histograms quizzes and listed the scores alphabetically as follows. 2nd period Math 4h period Math 1 period Math 9,8, 10, 5,9, 7, 8,9, 8, 5. 8, 10, 8, 8, 5 4, 5, 8,6, 8, 9, 5, 8, 5, 1, 5, 5, 7, 5, 7 6, 4, 5, 7, 5, 9, 5, 4, 6, 6, & 5, 7, 5, 8, 1, 8, 7, 10, 9 S. Use ALL the quiz data to make a frequency table with intervals. Use an interval of 2. Frequency Score 0-1 2-3 4-5 6-7 8-9 10-11 6. Use your frequency table to make a histogram for the data. 20i 16 14- 12 10 8- 6 10 14 Page | 22 7. Describe the data distribution of the histogram you created. Include words such as mode, skewed, outlier, normal, symmetric, center, ond spreod, if they apply-Hint: Don't forget standard deviation) scored the Create a graph of your choice (histogram, boxplot, dotplot) for 1" and 3 period. 9. Which class performed better? 10. Justify your answer by comparing the shape, center, and spread of the two classes. (Hint: Don't forget standard deviation.) Page | 23

Answer 1

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Frequeny Score 5. 0- 2 2-3 17 4-5 6-7 LO 8-9 18 Jo-L S