1 / 14

Central Tendencies: Mean, Median, and Mode

Central Tendencies: Mean, Median, and Mode. Brittany Schultz Veronica Koite. TEKS. (6.10)   Probability and statistics. The student uses statistical representations to analyze data.

velma-combs
Télécharger la présentation

Central Tendencies: Mean, Median, and Mode

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Central Tendencies:Mean, Median, and Mode Brittany Schultz Veronica Koite

  2. TEKS (6.10)  Probability and statistics. The student uses statistical representations to analyze data. (B)  identify mean (using concrete objects and pictorial models), median, mode, and range of a set of data; (6.1)  Number, operation, and quantitative reasoning. The student represents and uses rational numbers in a variety of equivalent forms. (C) use integers to represent real-life situations; (6.11)  Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. (B)  use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

  3. NCTM Standards • Find, use, and interpret measures of center and spread, including mean and interquartile range • Build new mathematical knowledge through problem solving • Solve problems that arise in mathematics and in other contexts • Apply and adapt a variety of appropriate strategies to solve problems • Monitor and reflect on the process of mathematical problem solving

  4. Research into Practice: Teaching Statistics Research • When working with mean: • Students perform lower when the term mean is used. • Students see the mean as a computational rather than a conceptual act. • Only 16% of students can find a missing piece of data when given the average and all other data entries. • When working with median: • Less than 50% can find the median of a set of data listed in order from least to greatest. • Performance is even less when the data is reported in non numerical order of in a table. In these instances many students choose the value that is in the center of a table or list. • When working with mode: • Students identified the greatest number in the list as “the most” instead of the most frequently occurring piece of data. • Over 1/3 do not know what a mode is. • Only ¼ can correctly identify the mode of a list of data.

  5. Research into Practice: Teaching Statistics Research into Practice • Link concrete experience to procedures. • Give students the opportunity to develop language. • Give students a variety of problem types. • Use problems that represent the data in various forms. • Have students collect and summarize their own data. • Use a calculator for weighted-mean problems.

  6. Mean and Median: Are they really so easy? • The NAEP reports that many students do not understand statistical terms such as mean, median, mode, and range. • There is evidence that they can compute the mean when asked for the average. • This study focused on 3 problems asking students to find the mean and median in various ways.

  7. Mean and Median: Are they really so easy? Problem #2 • Only 1/5 of 8th grade students and 1/3 of 12th grade students answered correctly. • The most common wrong answer was 55. Which means that students were confused not only about mean and median but also were unable to interpret information in graphical form.

  8. Science Sampler: Mean, Median, Mode, and Range • Research shows that when students work hands-on, their learning is more meaningful. • Students can collect data in science class and calculate the central tendencies in math class. • The process of calculating can also be hands-on by recording each set of data on an index card. • Mean – Set cards next to each other and add the data up. Then divide by the number of cards. • Median – Place cards in order from least to greatest and remove one card from each end until only one is left. • Mode – Stack cards with the same data together to find which stack is the most.

  9. Conclusion • Students need to be aware of technical terms so that they can perform the correct calculations. • To increase students’ understanding, create hands-on activities that allow for concrete experiences. • Allow for deeper understanding of concepts by giving students a variety of problems and data in a variety of formats.

  10. Problem 1 Mr. Bloom made a collection of minerals and fossils from Big Sandy Creek. On his first trip, 14% of his specimens were fossils. On his second trip, 13% of his specimens were fossils. On his third trip, 21% were fossils. On his fourth and final trip, 9% of his specimens were fossils. What was the average percent of his daily collection that consisted of minerals?

  11. Problem #1 Solution Understand the Problem: We know that only either fossils or minerals were found on each day. We know the percentage of fossils that was found for each day. We must find the average percentage of mineral that was found over his four trips.  Make a Plan: To find the percentages of minerals that were found each day we will use the known information of percentages of fossils found. After we find the percentages of minerals we can find our mean.  Carry out Plan: First, we need to find out what percentage of our findings are minerals on each trip. • For the first trip, we know that 14% of his findings were fossils and that the rest would be minerals. So we would subtract 100 - 14= 86% minerals • On the second trip, 13% of his findings were fossils. So 100 - 13= 87% minerals. • On the third trip, 21% of his findings were fossils. So 100 - 21= 79% minerals • On his final trip, 9% of his findings were fossils. So 100 - 9= 91% minerals.   Then we find the average of these numbers. 86+87+79+91= 261. 261/4= 85.75%.  Look back and Check: We can find the average of the percentage of fossils and subtract it from 100. This should give us the same number we calculated from our plan. 14+13+21+9= 14.25. Then we take this value and subtract it from 100. 100-14.25= 85.75.

  12. Problem 2 Nathaniel’s daily average in his math class is an 86. If five of his six grades are 77, 92, 85, 77, 93, what is the other daily grade? What is the median and mode of his set of grades? 

  13. Problem #2 Solution Understand the problem: We know the average of 6 grades is 86. We are given 5 of those grades and must find the 6th grade. Make a plan: We will work backwards to solve for the total points and then subtract the given grades from this total to find the missing grade. Carry out the plan: If we work backwards we will multiply the average of 86 by 6, so that we can undo the division that found the mean. 86 * 6 = 516. This is the total that all six grades must add up to. If we add up the given grades, the total is 77+92+85+77+93 = 424. To find the missing grade, we subtract this from the total points we found. 516-424 = 92. So the missing grade is 92. Look back: To check this problem, we can take our new grade and work forwards to see if we obtain the average that was given. So, first we add up all grades, 77+92+85+77+93+92 = 516. Then, divide that total by the number of grades, 516/6 = 86. This was the average we were originally given, so our answer is valid.

  14. References • Jones, P. (December 2007). Mean, median, mode, and range. Science Scope, 31(4), 59. Retrieved April 23, 2008, from WILSON database. • Lappan, G. (1988, January 1). Research into Practice: Teaching Statistics: Mean, Median, and Mode. Arithmetic Teacher, 35(7), 25. (ERIC Document Reproduction Service No. EJ367976) Retrieved April 25, 2008, from ERIC database. • NCTM. (2004). In Standards for Grades 6–8. Retrieved Apr. 24, 2008, from http://standards.nctm.org/document/chapter6/index.htm • Polya, G. (1988). How to Solve It. Princeton, NJ: Princeton University Press. • Texas Education Agency, (2001). In Texas Essential Knowledge and Skills. Retrieved Apr. 24, 2008, from http://www.tea.state.tx.us/rules/tac/ chapter111/ch111b.html#111.22 • Zawojewski, J. S., et. al. (March 2000). Mean and median: are they really so easy?. Mathematics Teaching in the Middle School. 5(7), 436-40. Retrieved April 23, 2008 from WILSON database.

More Related