3 3 Measures of Central Tendency and Dispersion from grouped data.notebook October 23, 2017

Transcription

1 Warm Up a. Determine the sample standard deviation weight. Express your answer rounded to three decimal places. b. Use the Empirical Rule to determine the percentage of M&Ms with weights between and gram. c. Determine the actual percentage of M&Ms that weigh between and gram, inclusive. d. Use the Empirical Rule to determine the percentage of M&Ms with weights more than gram. e. Determine the actual percentage of M&Ms that weigh more than gram. Suppose you wanted to estimate the mean and standard deviation for an exam, but all the professor gave you was curve, maybe something like this one: What problems might you have? 1

2 The technique we'll use is to treat each individual as the midpoint of its class. So instead of 13 scores from 80 89, we'll say that there are 13 85's. Now we can just add these values from each class and divide by the total of the frequencies. Let's approximate the mean for this population. Here's the Algebra ese for the same process. 2

3 Let's try it again for good measure. The frequency distribution represents the 3 year rate of return of a random sample of 40 small capitalization growth mutual funds. Approximate the mean 3 year rate of return. Approximate Variance and Standard Deviation of a Variable from a Frequency Distribution To turn this into the standard deviation, simply take the square root. Please take a moment to highlight the differences between this and the typical variance formula from the last section. 3

4 Approximate Variance and Standard Deviation of a Variable from a Frequency Distribution Let's practice this using the first frequency distribution. Assume that this is the entire population of the class. Calculate the Variance and Standard Deviation Let's try it again. 4

5 A weighted mean occurs when certain values carry more weight than others. The easiest example is a GPA. An "A" in Statistics counts more than an "C" in Tennis not because it's more important or carries a higher meaning, but because the 4 credits for Statistics outweigh the 1 credit for Tennis. That's why your GPA will be closer to an "A" than a "C" the Statistics course counts for more. Here's how it works: Each letter grade is assigned a weight. At most schools, this means an A=4, B=3, etc. Here's how it works: Each letter grade is assigned a weight. At most schools, this means an A=4, B=3, etc. When calculating your GPA, the point value for each course is weighted by the number of credits. Here is how the GPA would be calculated for the "tennis" example from the previous slide. 5

6 Try it on your own. Here's the formula. 6

7 Try it again Marissa has just completed her second semester in college. She earned a B in her 5 hour calculus course, an A in her 3 hour social work course, an A in her 4 hour biology course, and a C in her 3 hour American literature course. Assuming that an A equals 4 points, a B equals 3 points, and a C equals 2 points, determine Marissa s gradepoint average for the semester. Most of the classes at THS are either 1 credit or 0.5 credits. FYI CP/ACP Honors AP 7