2The following represents my results when playing an online sudoku game…at www.websudoku.com. 30 min0 min
3Introduction A student gets a test back with a score of 78 on it. A 10th-grader scores 46 on the PSAT Writing testIsolated numbers don’t always provide enough information…what we want to know is where we stand.
4Where Do I Stand?Let’s make a dotplot of our heights from 58 to 78 inches.How many people in the class have heights less than you?What percent of the dents in the class have heights less than yours?This is your percentile in the distribution of heights
5Finishing…. Calculate the mean and standard deviation. Where does your height fall in relation to the mean: above or below?How many standard deviations above or below the mean is it?This is the z-score for your height.
6Let’s discussWhat would happen to the class’s height distribution if you converted each data value from inches to centimeters. (2.54cm = 1 in)How would this change of units affect the measures of center, spread, and location (percentile & z-score) that you calculated.
7National Center for Health Statistics Look at Clinical Growth Charts at
8PercentilesValue such that r% of the observations in the data set fall at or below that value.If you are at the 75th percentile, then 75% of the students had heights less than yours.
9Test scores on last AP Test. Jenny made an 86 Test scores on last AP Test. Jenny made an 86. How did she perform relative to her classmates?6 79 03Her score was greater than 21 of the 25 observations. Since 21 of the 25, or 84%, of the scores are below hers, Jenny is at the 84th percentile in the class’s test score distribution.
10Find the percentiles for the following students…. 6 79 03Find the percentiles for the following students….Mary, who earned a 74.Two students who earned scores of 80.
11Cumulative Relative Frequency Table: Age of First 44 Presidents When They Were InauguratedAgeFrequencyRelative frequencyCumulative frequencyCumulative relative frequency40-4422/44 = 4.5%2/44 =4.5%45-4977/44 = 15.9%99/44 = 20.5%50-541313/44 = 29.5%2222/44 = 50.0%55-591212/44 = 34%3434/44 = 77.3%60-644141/44 = 93.2%65-6933/44 = 6.8%4444/44 = 100%
13Interpreting… Why does it get very steep beginning at age 50? When does it slow down? Why?What percent were inaugurated before age 70?What’s the IQR?Obama was 47….
14Describing Location in a Distribution Interpreting Cumulative Relative Frequency GraphsUse the graph from page 88 to answer the following questions.Was Barack Obama, who was inaugurated at age 47, unusually young?Estimate and interpret the 65th percentile of the distributionDescribing Location in a Distribution6511584714
15Median Income for US and District of Columbia. FrequencyRelativeCumulative35 to < 40140 to < 451045 to < 501450 to < 551255 to < 60560 to < 65665 to < 703
16Graph it: Median Income ($1000s) Frequency Relative Cumulative 35 to < 4011/51 = 0.02040 to < 451010/51 = 0.1961111/51 = 0.21645 to < 501414/51 = 0.2752525/51 = 0.49050 to < 551212/51 = 0.2363737/51 = 0.72555 to < 6055/51 = 0.0984242/51 = 0.82460 to < 6566/51 = 0.1184848/51 = 0.94165 to < 7033/51 = 0.0595151/51 = 1.000
18What is the relationship between percentiles and quartiles?
19Z-Score – (standardized score) It represents the number of deviations from the mean.If it’s positive, then it’s above the mean.If it’s negative, then it’s below the mean.It standardized measurements since it’s in terms of st. deviation.
20Discovery:Mean = 90St. dev = 10Find z score for809573