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Central tendency

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Central tendency

1. 1. Amber Pettaway Period 6 Mr.AndradeDesktop Computers 4/11/2012
2. 2.  (Mean, median, and mode) are values that summarize a set of data. They are useful when analyzing data.
3. 3.  Average the sum of a set of data divided by the number of data.86  100|90|45|70|0|86|75|54|34|2|32|70|70|70|50 To find the mean find the sum of data.  0+2+32+34+44+54+70+70+70+70+75+86+90+100=797  Divide it by the number of data  797/15=53.13
4. 4.  The middle value of the data set.  100|90|45|70|0|86|75|54|34|2|32|70|70|70|50 To find the median place all the data in numerical order, then find the middle number. If there are two middle numbers then you must find the average.  100|90|45|70|0|86|75|54|34|2|32|70|70|70|50 The median is 54
5. 5.  The most common value in the data set.  100|90|45|70|0|86|75|54|34|2|32|70|70|70|50 To find the mode find the number that is shown the most it helps if you put it in numerical order. If there is no value appearing more than once then there is no mode  100|90|45|70|0|86|75|54|34|2|32|70|70|70|50  The mode is 70
6. 6.  The difference between the greatest and the least values in a data set.  100|90|45|70|0|86|75|54|34|2|32|70|70|70|50 To find the range of the students grades subtract the least value from the greatest value.  100-0=100
7. 7.  Extreme value that separates form the rest of the data.  100|90|45|70|0|86|75|54|34|2|32|70|70|70|50 Outliers affect the mean. The outlier changes the mean and median. So you must drop the outlier to have a more accurate mean and median. 100+90+45+70+0+86+75+54+34+32+70+70+70+50=846 846/14= 60.4
8. 8.  Jessica’s test scores in Algebra for the first semester are 93, 79, 88, 77, 92, 88, 80, 34, 84, 88. Calculate the range, mean, median, and mode. Then make and explain a prediction for next semester’s test scores. Mean: 80.3 Median: 34, 77, 79, 80, 84, 88, 88, 88, 92, 93 84+88= 172/2= 86 Mode: 88 Range : 93-34=54
9. 9.  A furniture manufacturer keeps records of how many units are defective each day: {7, 12, 9, 8, 10, 14, 8}  Mean- 9.7 How could you verify this decision? To verify this decision you need to use mean. When using mean you are able to understand the average of how many that are defective a day.  Mean- 9.7
10. 10.  Mr. Wharton records his students’ scores on the last science test: {94, 88, 88, 94, 94, 84, 94, 88, 84, 94}  Mean- 90.2  Range- 10 Predict the outcome of the mean and range if there were 2 20’s added to the science tests? Explain.  Mean- 78.5  Range- 74 When two twenties are added to the science test you have a better chance of the average decreasing than increasing.
11. 11.  A veterinarian keeps records of the weights of puppies in ounces: {4.1, 3.8, 5.0, 4.6, 5.6, 4.7, 11.6}  Mean- 5.6  Median- 4.7  Range- 7.8  Mode- n/a How would you explain the range and its connection to the data set? The range for the weights of puppies in ounces is 7.8 This shows the difference between the largest weight of the puppy and the puppy with the lowest weight.
12. 12.  Commuting The local newspaper conducted a telephone survey of commuters to see how they get to work each day. The responses were: commuter rail, 22;bus, 17; subway, 18; walking, 15; car, 224  Mean w/ outlier- 59.2 Mean w/o outlier- 74  Median w/ outlier- 18 Median w/o outlier- 17.5  Range w/ outlier- 209 Range w/o outlier- 7 What facts can you gather about the outlier? Which Central Tendency will most likely be affected by the outlier? 224 commuters get to work each day by car. Central tendencies such as Mean, Median, and Range. The outlier makes the mean and median inaccurate, So you must drop the outlier.
13. 13.  SNOWFALL A weather station keeps records of how many inches of snow fall each week: {9, 2, 0, 3, 0, 2, 1, 2, 3, 1}  Mean- 2.3  Median- 2 What would happen to your decision if we had a blizzard and added 24 inches to the above data set?  Mean- 4.27  Median- 2 24 would be the outlier of the data set and with the outlier it will make the mean and median inaccurate
14. 14.  SALES A supermarket keeps records of how many boxes of cereal are sold each in a week: {12, 9, 11, 14, 19, 49, 18} Based on the above information, which cereal makes the most \$ ? The cereal that makes the most money in each week is the cereal that sells 18 boxes a week. I found this out using mean because this shows the average of cereal boxes being sold each week.
15. 15.  ELECTIONS A city councilman keeps track of the number of votes he receives in each district: {68, 66, 58, 59, 61, 62, 67} If you ran against the city councilman and wanted to beat him, what voting numbers would you want to see? If I was to run against the city councilman and wanted to beat him I would like to see the numbers 68, 66, and 67
16. 16.  BODYBUILDING A bodybuilder keeps track of how many sets of each exercise he performs each day: { 9, 8, 6, 5, 11, 7, 10}. Which measure of central tendency best represents the data? Justify your answer. Then find the measure.  Mean: 5, 6, 7, 8, 9, 10, 11= 56/7=8 I would use mean to best represent this data because if your trying to find how much he exercises a day you would use mean to find the average.
17. 17.  Property taxes A landlord is keeping track of what he pays each month in property taxes so he can budget accordingly. For the first half of the year, the tax bills were 256, 256, 274, 256, 256, and 274. Which measure of central tendency best represents the data? Justify your answer. Then find the measure.  The best central tendency the represents this data is mean.  256+256+256+256+256+274+274=1572/6= 262