Unit 6/7: Data & Statistics



151419157185546.1-6.5006.1-6.5center4500452120Unit 6/7: Data & Statistics11540067000Unit 6/7: Data & Statisticscenter790007945755pebblebrook high schoolAlgbra 21154000pebblebrook high schoolAlgbra 2right230023114020177600980020176.1 Compound Interest The Number of times compounded per year can pounded annually, n = 1Compounded quarterly, n = 4Compounded semiannually, n = 2Compounded monthly, n = 12Section 6.1 Homework6.2 Mean, Median, & Mode Example #1: Calculate the mean, median, mode. Number of siblings: 0, 1, 2, 3, 4, 5 or moreNumber of hours you study math: 0, 1, 2, 3 or more 1st digit of cell phone # (NOT THE AREA CODE) 1, 2, 3, 4, 5, 6, 7, 8, 9A Box and Whisker plots shows the median, the quartiles, and the extremes for a numerical set of data. The box portion contains about 50% of the data values. The two whiskers each contain about 25% of the data values. It shows how spread out the data values are. They are useful for comparing sets of data.Least Value: _________________1st Quartile: __________________Median: _____________________3rd Quartile: __________________Greatest Value: _______________Interquartile Range (IQR): _____________Range: ______________________Example #2: Create a Box & Whisker PlotNumber of siblings: 0, 1, 2, 3, 4, 5 or moreNumber of hours you study math: 0, 1, 2, 3 or more 1st digit of cell phone # (NOT THE AREA CODE) 1, 2, 3, 4, 5, 6, 7, 8, 9You Try…..Using the data: Find the mean, median, & modeCreate a Box & Whisker Plot. State the IQR & Range.Section 6.2 HomeworkFor the following groups of numbers, calculate the mean, median and mode for each.Create a Box & Whisker Plot. State the IQR & Range.18, 24, 17, 21, 24, 16, 29, 18Mean_______IQR _______Median______Range _______Mode_______75, 87, 49, 68, 75, 84, 98Mean_______IQR _______Median______Range ______ Mode_______ 3. 55, 47, 38, 66, 56, 64, 44, 63, 39Mean_______IQR ________Median______Range _______Mode_______6.3 Standard Deviation & VarianceVariance – a numerical value that tells us how spread out the data is. I.e. range & IQRStandard deviation – a variance that shows how close to the mean that data are.Example #1. Calculate the mean & standard deviation.The height (in inches) of 5 preschoolers, age 3.31, 36, 34, 32.5, 34, 33Data (x)x - xData - mean(x - x)2(data – mean)2Average of (data – mean)2(data – mean)2The test scores of 5 students: 95, 78, 83, 63, 62Data (x)x - xData - mean(x - x)2(data – mean)2Average of (data – mean)2(data – mean)2 The age of 5 students in Algebra 2: 16, 17, 18, 17, 16Data (x)x - xData - mean(x - x)2(data – mean)2Average of (data – mean)2(data – mean)2You Try….Use the data to find the mean & standard deviation.Data (x)x - xData - mean(x - x)2(data – mean)2Average of (data – mean)2(data – mean)2Section 6.3 Homework Data (x)x - xData - mean(x - x)2(data – mean)2Average of (data – mean)2(data – mean)2#4 #5Data (x)x - xData - mean(x - x)2(data – mean)2Average of (data – mean)2(data – mean)26.4 Normal DistributionNormal distribution is a visual representation of how the standard deviation and how it compares to the mean.Skew Left – when majority of the data is above the mean.Skewed Right – when majority of the data is below the mean.Normal Curve – is when the mean is in the center of the data.Example #1: Sketch a normal curve. Mean = 45; Standard Deviation = 5Mean = 80; Standard Deviation = 15 Mean = 80; Standard Deviation = 4Example #2: A set of data has a mean of 62 and a standard deviation of 5.plete the normal distribution curve.What percentage of data falls between 42 and 58?What percentage of data is greater than 34?What percentage of data is less than 50?Example #3: 174 students took the Algebra 2 final exam. The mean was 68.5 and the standard deviation was 7.3. Complete the normal distribution curve.Find the number of students who received a grade 2 standard deviations above the mean. Find the number of students who received a grade of 61 or below.How many students scored within 1 standard deviation?Section 6.4 HomeworkQuestion #1Question #2Section 6.5 Z-ScoresZ-score – tells the number of standard deviations the value is from the mean.z-score = value-meanstandard deviationExample #1: Calculate the z-scoreLewis earned 80 on his biology midterm and a 71 on his history midterm. In the biology class the mean score was 75 with a standard deviation of 4. In the history class the mean score was 73 with a standard deviation of 3.a. Convert each score to a standard z-score.b. On which test did he do better compared to the rest of the class?Example #2: CompareThe scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the middle 68% of students will get a “C”, what is the lowest mark that a student can have and still be awarded a C?Section 5.5 Homework1. A normal distribution of scores has a standard deviation of 10. Find the z-score that is 24 points above the mean. 2. A normal distribution of scores has a standard deviation of 5.6. Find the z-scores corresponding to each of the following values:a) A score of 60, where the mean score of the sample data values is 40. b) A score of 20, where the mean score of the sample data values is 50. 3. IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.a) Convert Einstein’s IQ score to a z-score. b) Is Einstein’s IQ usual or unusual? Explain.4. Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. Find the z-score corresponding to a woman with a height of 70 inches and determine whether the height is unusual. 5. Three students take equivalent stress tests. Which is the highest relative score: A, B, or C? SHOW ALL WORK!!a) A score of 144 on a test with a mean of 128 and a standard deviation of 34.b) A score of 90 on a test with a mean of 86 and a standard deviation of 18. c) A score of 18 on a test with a mean of 15 and a standard deviation of 5. ................
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