Chapter 02 Notes - Describing Distributions with Numbers - STAT 1450 COURSE NOTES CHAPTER 2 DESCRIBING DISTRIBUTIONS WITH NUMBERS Guided Notes

Chapter 02 Notes - Describing Distributions with Numbers -...

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S TAT 1450 C OURSE N OTES – C HAPTER 2 D ESCRIBING D ISTRIBUTIONS WITH N UMBERS Guided Notes associated with the Lecture Videos for the 1 st Half of Chapter 2 Connecting Chapter 2 to our Current Knowledge of Statistics In Chapter 1 we used graphical displays to summarize data. We will now shift to describing data numerically. We will describe centers and spreads of distributions; and contrast which are most appropriate in different situations. Many of the statistics are familiar to you from your K-12 years. For context, we’ll consider that a friend of yours from high school, cannot recall the difference between the mean and the median. Based upon what your current knowledge of means and medians. Briefly explain this difference between the two… We will see how these measures are useful in describing both the center and shape of a dataset. 2.1 Measuring Center: The _______ The mean x is an arithmetic average and is calculated by summing the observations and then dividing by the number of observations. It is considered the balance point of the distribution. The mathematical notation for the mean is 1 2 1 1 n n i i x x x x x n n L Example: Compute the mean for the Birthday Present Cost data. Name Type of Store Cost ($) Name Type of Store Cost ($) Ahmed Craf 30 Janet Clothing 35 Becky Flower 25 Jill Restaurant 30 Carter Health Club 25 Joaquin Restaurant 20 Dave N/A (self-made) 21 John Clothing 25 Esmerelda Clothing 49 Chapter 2, page 1
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2.2 Measuring Center: The __________ The median is the midpoint of a distribution—   the number such  that half of the observations are smaller  than it & the  other half are larger . To find the median of a distribution: 1. Arrange all, n, observations in order of size, from smallest to largest. 2. If n is odd, the median M is the center observation in the list. Or 2. If n is even, the median M is midway between the two center observations in the ordered list. Note: The median in the ordered list of observations can be found by counting up to the value at the ( 1) 2 n ” location. Example: Compute the Median, M , for the Birthday Present Cost data. Name Type of Store Cost ($) Name Type of Store Cost ($) Ahmed Craf 30 Janet Clothing 35 Becky Flower 25 Jill Restaurant 30 Carter Health Club 25 Joaquin Restaurant 20 Dave N/A (self-made) 21 John Clothing 25 Esmerelda Clothing 49 Chapter 2, page 2
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Two questions… a) Why might someone think that Esmerelda’s amount represented the median? Bc her value was 5 th in alphabetical order by ma,e, but not the 5 th number in ascending numerical order b) Can you provide a small data set of three values that might further clarify the concept of the Median? Points scored in an NBA basketball game ; 2, 13, 4; 13 is clearly not median Technology Tips – Computing Descriptive Statistics TI-83/84 Enter the data into L 1 . STAT    CALC    1-Var Stats    2 nd  1  (L 1 ) .  Enter. Enter.
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