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# Applied 40S March 23, 2009

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Understanding the standard deviation and introduction to histograms.

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### Applied 40S March 23, 2009

1. 1. Working With Grouped Data A quot;fewquot; balloons by ﬂickr user ɹǝɯıʇɹoɯ
2. 2. Let's apply what we've learned ... HOMEWORK The mean math marks and standard deviation for two classes are shown below. Assume that 68 percent of the marks in each class are within one standard deviation of the mean mark. mean mark (μ) standard deviation (σ) Class A 74 4 Class B 72 8 (a) In which class is the set of marks more dispersed? (b) Bert in Class A and Beth in Class B each have a mark of 82%. How many standard deviations are they from their class means? Who appears to have the better mark?
3. 3. HOMEWORK The following numbers represent the number of cars sold by Metro Motors in one week: Monday Tuesday Wednesday Thursday Friday Saturday 4 5 8 9 7 4 1. Determine the following statistics: (a) mean (b) mode (c) median (d) range 2. Which measure of central tendency may be the least signiﬁcant? Explain.
4. 4. HOMEWORK The two sets of data show the weights of potatoes in bags. There are six bags in each set. Set #1 49 51 48 52 47 53 Set #2 40 60 45 55 35 65 The mean weight of each set of bags is 50 pounds. Which set has the greater standard deviation? How do you know? (Do not do any calculations.)
5. 5. HOMEWORK 78 92 62 52 65 59 A class of 30 students received the 53 63 68 73 71 63 following marks in a mathematics 69 74 73 81 55 71 examination. Calculate the mean, 75 81 84 77 80 75 median, range, and standard deviation. 41 57 91 62 65 49 http://nlvm.usu.edu/en/nav/frames_asid_145_g_4_t_5.html
6. 6. Measures of Dispersion (Variability) determine how quot;spread outquot; or variedquot; a set of data is. Standard Deviation (σ): How is the standard deviation calculated numerically? μ
7. 7. Measures of Dispersion (Variability) determine how quot;spread outquot; or variedquot; a set of data is. Standard Deviation (σ): What's the difference between quot;σquot; and quot;squot;? The symbol for standard deviation of a population or large sample is quot;σquot; (sometimes written as quot;σx quot;), and the symbol for standard deviation of a sample is 's'. A large sample is deﬁned as a sample with 30 or more data items. In this course, we will use only quot;σquot; (sigma), which represents the standard deviation of the population. Let's take a look at a visual explanation of why we calculate the standard deviation this way ... http://www.seeingstatistics.com/
8. 8. Peter's goal is to maintain his marks at least 2.5 standard deviations above the mean in all of his subjects. Determine the minimum marks he must obtain in each subject. Subject Mean Standard Deviation Minimum Mark Chemistry 66 7 English 62 12 Math 68 8 Physics 73 4
9. 9. Teacher Adams has a large math class with 38 students. The mean class mark is 65 percent, and the standard deviation is 18 percent. Do you think this is an easy class for Teacher Adams to teach? Explain.