Monday, March 17, 2014 - Mean, Median, Mode, Range, Outlier, Dot (Line) Plot, and Histograms
Bell work - Complete problems 1-5. Refresh your memory of central tendency (mean, median, mode and range) using your graphic organizer from Friday, the PowerPoint, and slides from the Brainpop video.
The data set included 12 sample test scores.
To find the median, order the numbers from least to greatest. Find the value in the middle where half of the numbers to the left are smaller and half of the numbers to the right are larger. If there are two middle numbers, the median is the arithmetic mean of the two middle numbers.
To find the range, subtract the smallest value from the largest value in a set of data.
To find the mean, find the sum of the values in the data set, then, divide the sum by the number of values in the data set.
To find the mode, list the value(s) that occur most often. If there is more than one value occurring the same number of times more than the other values, then both are modes. There is no mode when all the values occur an equal # of times.
Classwork - Using data from your class from the Brainpop Quiz, construct a dot plot. Do this on "The Dot Plot Thickens." Find the mean, median, mode, range, and outlier(s) (if any) for both sets of data. The data for your class can be found below.
Homework - Completed problems 1-4 from "What is it like to live under a carpet?" Show organized work: Set up, Substitute, and Solve
***The following graded assignments were returned today: "GADOE TASK: Finding Surface Area" and "Surface Area Practice - Set E and/or F." Please see the keys below.
Tuesday, March 18, 2014 - Box and Whisker Plots
Bell work - Complete problems 6-10. Homework was checked during bell work - Organized work for #1-4 of "What is it Like to Live Under a Carpet?". Solutions reviewed and work shown by students in class: #1: 416 m, #2: 210 square centimeters, #3: 47 kilometers, #4: 170 diagonals.
Classwork - Students completed guided notes on graphing box plots using the following worksheet and PowerPoint.
|File Size:||95 kb|
Homework - Complete #5-8 of "What is it Like to Live Under a Carpet?". Complete classwork: "The Dot Plot Thickens" and "Box Plot" notes. Please see Monday samples of each period's guided practice for "The Dot Plot Thickens." Please follow the PowerPoint posted above to complete "Box Plot" notes.
Wednesday, March 19, 2014 - Dot Plots vs. Box and Whisker Plots
Bell work - Complete problems 11-15.
11. The mean for this set of data is 3.25 or approximately 3. Find the sum of all the values: 0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,3,3,3,3,4,4,4,6,8,10,13,14. Then, divide the sum of 91 by the total number of values in the set, which is 28. 28 households were surveyed and are represented on the dot (line) plot.
The median is 2. Half of 28 values is 14. Therefore, 14 values will be to the left of the median and 14 values will be to the right. You can count the n
The mode is 1 because its frequency of 6 is greater than all the frequencies of the other numbers.
The range is 14. Subtract the highest value in the data set by the lowest.
There are no outliers. The closest value(s) that could be considered outliers would be 13 and 14. A more significant difference is needed.
12. Possible questions: How many more households have 1 pet than 3 pets? Answer: Two more households have 1 pet than 3. What fraction of the households have less than 4 pets? Answer: 20/28 or 5/7. How would the mean change if the 3 households with four pets had 8 pets instead? Answer: The average would increase.
13. Using the box plot, you can only identify the median and range, which is 155 and 130 respectively. You cannot find the mean or mode because you would need all values from the data set and the box plot only shows you 5 values - lower extreme, lower quartile, median, upper quartile, and upper extreme.
14. The first quartile (lower) is 130. The third quartile (upper) is 175.
15. The interquartile range is 45. Subtract 130 from 175 to get this range.
Classwork - Student samples from bell work and homework were presented, viewed over the projector, and discussed. Remember the Order of Operations: Parenthesis, Exponents, Multiply or Divide (from left to right, whichever comes first), Add or Subtract (from left to right, whichever comes first). "The Dot Plot Thickens" and "Box Plot" notes were checked for completion. Individual feedback was given to each student regarding their work. Finish these assignments tonight along with homework.
Homework - Complete all problems 1-7 of "Where Can You See the World's Biggest Rock Group?" Show organized work: Set up (the equation), Substitute (the values for each variable), and Solve (using the Order of Operations). Check out solutions for last night's homework.
|File Size:||42 kb|
Thursday, March 20, 2014 - Analyzing Trends with Dot Plots and Box and Whisker Plots
Bell work - Complete #16-20 posted below. Bell work will be collected Friday after completing #1-25. Completion of homework was checked and we will review solutions on Friday.
16. The mean can be find by dividing the sum of the values by the number of families represented in the dot plot.
0 + 3(1) + 5(2) + 4(3) + 2(5) + 6 + 7 + 8 = 68
68/21 = 3.2
The mean or average number of televisions owned
by families on this city block is 3.
The median or middle value in this set is 3. The mode or number with the greatest frequency is 2. The range of the data is 8. There are no outliers.
17. Most of the data leans towards the lower values staying in between 1 and 4 televisions. As the number of televisions increase, the number of families with larger numbers of televisions decrease.
18. The lower extreme value is 0. The upper extreme value is 75. The median is 30. The lower quartile is 10 and the upper quartile is 70.
19. A large interquartile range (IR) means the data is more spread out. A small IR means the values are close to each other. In this data set, the values are spread out - from 10 to 70 minutes.
20. The least number of data you would need is 5. You would need a lower and upper extreme value, median, and first and third quartile. Possible data set where these 5 values remained reflected in the box plot shown:
0, 5, 10, 11, 12, 30, 50, 65, 70, 71, 75
The key is to make sure there is an equal number of data on either side of the median, and then on both sides of the first and third quartiles.
In the data set below, look at how the interquartile range (IR) is affected when the third quartile is changed to 35. The IR is now 25 showing that the values in the middle are close together.
0, 5, 10, 11, 12, 30, 32, 35, 35, 40, 75
Classwork - Students received guided practice on constructing box plots using "Box and Whisker Plots Set 1." They had list the data set in order from least to greatest. Then, identify the median, lower quartile, upper quartile, and interquartile range. Examples are attached below.
|File Size:||578 kb|
Homework - Complete #1-5 of "Box and Whisker Plots Set 2."
Statistics Test has been postponed until Tuesday or Wednesday of next week.
Friday, March 21, 2014 - Box and Whisker Plots and Mean Absolute Deviation
Bell work - Complete problems 21-25. Work was collected after solutions were shared and discussed.
25. Dot plots display all values in a data set which allows you to see frequency and trends. The shape of the data shows that more students study 2-3 hours after school. As the data reaches towards both extremes (0 and 5) the number of students that study for that amount of time is significantly smaller. The mean, mode, median, range, and outliers can be determined from a dot plot. Box plots are great for displaying range between the lower and upper extremes and the quartiles. It shows you the spread of the data. You cannot find the mode, mean, or outliers from this type of graph.
24. The interquartile range tells you how spread out your data is in the middle. A low interquartile range means the data is close together. A large interquartile range means the data is more spread out.
Classwork - Homework from last night was checked. For extra practice use "Box and Whisker Plots Set 3 and 4" to match the box plots with their corresponding data set. The keys are posted below. The box plot solutions are in order for each set for problems 1-10. If you want, print and cut out the box plots, mix them up, then match them with their data set.
Classwork (continued) - Mean Absolute Deviation (MAD) was introduced. Students completed notes using the following video. Follow the link to see the video and use it to complete the notes and/or you can click on the completed notes.
|File Size:||499 kb|
The following assignments were checked and graded for the week: (1)The Dot Plot Thickens, (2)What is it like to live under a carpet?, (3)Where Can You See the World's Biggest Rock Group?, (4)Box Plot Notes, (5)Box and Whisker Plot Practice Set 1 or 2 #1-5, and (6)Bell Work #1-25.