Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Essential Question: How do you compare measures of central tendency and dispersion? Before we start… The data shown below represents the weights (in pounds) of 9 dogs at a kennel. Write the data in order from least to greatest 32, 12, 15, 25, 18, 40, 18, 29, 27 What data value occurs most? Which weight is in the middle when the data is listed in order? What are the measures of central tendency? They are used to represent a typical number in a data set. Mean Median Mode What is the mean? The average of a numerical data set. Add up all the data points and divide by the number of data. 𝒙 is the symbol for mean. What is the median? The middle number when the values are written in numerical order. If there is an even number of values, the median is the mean of the two middle values. What is the mode? The value that occurs most frequently. No mode One mode More than one mode What should you choose the measure of central tendency? Type When Best Used Mean The data sets have no outliers Median The data set has outliers, but there are no big gaps in the middle of the data Mode The data set has many repeated numbers The data shown below represents the weights (in pounds) of 9 dogs at a kennel. Which measure of central tendency best represents the data? 32, 12, 15, 25, 18, 40, 18, 29, 27 The heights (in feet) of 8 waterfalls in the state of Washington are listed below. Which measure of central tendency best represents the data? 1000, 1000, 1181, 1191, 1200, 1268, 1328, 2584 The lengths (in miles) of the 10 longest rivers in the U.S. are listed below. Which measure of central tendency best represents the data? 1290, 1310, 1420, 1450, 1460, 1900, 1900, 1980, 2340, 2540 Archmont High School is collecting recyclable paper as a fundraiser to buy some benches for the courtyard. The newspapers are gathered into 5-inche bundles. Ms. Sato counted the bundles received each Friday for the first quarter of the school year. Which measure of central tendency best represents the data? 15, 12, 14, 15, 18, 15, 13, 14, 13, 12 A sub shop adds a new bread to its menu. To see if they should keep it, the manager counts how many orders of that bread type are taken each day. Which measure of central tendency best represents the data? 10, 16, 14, 13, 17, 15, 18, 16, 19 What is a measure of dispersion? It describes the dispersion, or spread, of data. Range Mean Absolute Deviation What is the range? The difference of the greatest value and the least value. Gives the length of the interval containing the data. What is the mean absolute deviation? Gives the average variation of the data from the mean. You find the average of how far away each data value is from the mean of the set. Mean Absolute Deviation Formula x1 x x2 x ... xn x n How do you find the mean absolute deviation? • Find the mean. • Find the distance between each data point and the mean. • Add the distances up. • Divide by the number of values in the data set. Marketing Each person that visited the Comic Book Shoppe’s web site was asked to enter the number of times each month they buy a comic book. They received the following responses one day: 2, 2, 3, 4, 14 Find the range and the mean absolute deviation. Dances The prom committee kept count of how many tickets it sold each day during lunch: 12, 32, 36, 41, 22, 47, 51, 33, 37, 49 Find the range and the mean absolute deviation. Financial Literacy Mike is waiting tables at the Pizza Pan Restaurant. He is keeping track of the tips that he receives each hour. 20, 31, 24, 22, 35, 12 Find the range and the mean absolute deviation. Parties Dalila kept an account of what each cousin spent on their grandmother’s birthday party: 25, 24, 36, 28, 34, 25, 17 Find the range and the mean absolute deviation. How do you compare measures of… Central tendency? To find which measure best represents most of the data. Dispersion? To find which data set covers a wider interval. Mean Median Mode Range Mean Absolute Deviation How do you compare measures of central tendency and dispersion? Ticket Out the Door Find the mean, median, mode, range and mean absolute deviation of the data. 13, 16, 19, 20, 22, 25, 30, 31