Week 2 Statistics: Mean, Median, and Standard Deviation When given a list of numbers {data}, you can nd the following by: sum of the numbers how many numbers there are 0 Median -> the middle number of the data once it is ordered from smallest to greatest o If there are two numbers in the middle, the median is the average between those two numbers 0 Lower quartile -> the median of the smaller half of the data 0 Upper quartile -> the median of the bigger half of the data 0 Standard Deviation -> measures how far apart the numbers are in the data 0 Bigger SD means more spread out data and smaller SD means more clustered data 0 Found using 2 m N 0 Mean {the average value of the numbers} -> X The Value in the data distribution u The population Mean N Total Number of Observations Practice (find the mean and median of the following sets of data} 1. 25, 35,11, 26, 19, 30, 23 2. 41, 32, 33, 40, 33, 4-5, 29, 40 Practice (word problems} 3. A student's scores on their first four history tests were 80, 85, 88 and 95. To get an A in the class, they need to have an average of 90 or better. What score must they make on the fifth test to get an A? 4. The dot plot of GPA for two schools is shown to the right. - - a. Which of the two schools have a higher median GPA? . I I : lIlllIllI U." 0.5 LI) [.5 I." 2.5 J." 3.5 -I.IJ SchoolA b. Which of the two schools have a higher standard deviation? 0.0 0.5 Lil [.5 1.0 2.5 J.\" 3.5 Ll} School B Week 2 Trigonometry Given a right triangle, there are two main properties that you need to know. Pythagorean Theorem The Trigonometric Ratios . hypotenuse leg SOHCAHTOA C a SOH Sin 0 = = Opposite Hypotenuse Hypotenuse Opposite CAH Cose= Adjacent b L Hypotenuse -leg 0 - - TOA Tan 0 = Opposite Adjacent a2 + 62 = c2 Adjacent Practice (find the following trigonometric ratios for the given triangle) A sin C = 29 COS C = 21 tan C = B 20 sin A = 34 COS A = tan A = 30 B Practice B Based on the triangle on the right, order the following from smallest to greatest. 17 cm 8 cm sin A, cos A, and tan A