(12) students were asked their SAT Math scores: Warm – Up (12) students were asked their SAT Math scores: 600, 650, 505, 520, 800, 480, 740, 540, 630, 590, 400, 550 Construct And Describe the Histogram : HI! I’m SKEWED. …RIGHT? 0 1 2 3 4 5 FREQUENCY 400 480 560 640 720 800 880 S.A.T. MATH SCORES

Hey! I’m Approximately SYMMETRIC. HI! I’m SKEWED to the LEFT Warm – Up COMPARE these two distributions: Hey! I’m Approximately SYMMETRIC. HI! I’m SKEWED to the LEFT 0 1 2 3 4 5 FREQUENCY 0 1 2 3 4 5 FREQUENCY 400 480 560 640 720 800 880 S.A.T. MATH SCORES 300 380 460 540 620 700 780 S.A.T. VERBAL SCORES SAT Math scores have a higher center than Verbal scores. They both have equal spread. MATH VERBAL Center: 700 > 600 Unusualness: Nothing Nothing Spread: 480 = 480

Chapter 5 Describing Distributions Numerically

I. CENTER MEAN = Average. n = number of observations in data set MEDIAN = Middle. The Median of a distribution is the MIDDLE number after all ‘n’ observations have been ordered from smallest to largest. -If n is odd the Median is the center. -If n is Even the median is the mean of the two center observations. MODE = Most. The observation with the highest Frequency.

II. MEASURING SPREAD QUARTILES One way to measure spread of a data set is by the Range = difference between Largest and Smallest observations. But there is a better way… QUARTILES Quartiles are values used to examine the variability or spread of a set of data. There are three Quartiles (After the data set is arranged from smallest to largest): Q1 = The Middle of the First Half of the Data. 25% Q2 = The Middle or Median of the Data. 50% Q3 = The Middle of the Second Half of the 75% Data.

Inter-Quartile Range (IQR) = Q3 – Q1 EXAMPLE: 25, 26, 27, 35, 39, 41, 46 Q1 = ? Q2 or Median = ? Q3 = ? 26 35 41 IQR = 15 EXAMPLE: 25, 26, 27, 35, 39, 41, 46, 50 Q1 = ? Q2 or Median = ? Q3 = ? 26.5 37 43.5 IQR = 17 Inter-Quartile Range (IQR) = Q3 – Q1 (The middle 50%)

Measure of Spread (continued): The Standard Deviation = s or sx The standard deviation measures the spread of a distribution by examining the average difference (deviation) between each observations and the mean. s2 = Variance

Find the Standard Deviation for the following data set: 5, 12, 22 The Mean = 13 and n = 3 so…

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Since the Standard Deviation is the square root of variance then…

Find the Standard Deviation for the following data set: 4, 5, 5, 7, 9 The Mean = 6 and n = 5 so… Find the Standard Dev. 11.5, 12, 14.1, 25.2, 22, 15.8, 28.3, 47.5, 18