This is our last week focusing on statistics, with the Unit 3 test next Tuesday, December 17. In the previous three lessons, students learned about the range and interquartile range. Through these lessons, students built an understanding of maximum, minimum, Q1 and Q3. Throughout the unit students have also been learning about the median. These are the five components of the five-number summary that is required to create a box plot. Furthermore, in the previous lesson, students learned how to create and analyze box plots. On Tuesday, students will compare numerical data using box plots. Going forward, students will build on their usage of graphs to compare data through the use of histograms. Vocabulary: Box Plot: A graph that uses a rectangle to represent the middle 50% of a set of data and “whiskers” at both ends to represent the remainder of the data. Five-Number Summary: Minimum Lower Quartile (Q1) Median Upper Quartile (Q3) Maximum After we finish comparing box plots, we will get MAD on Wednesday! That is, we will calculate the Median Absolute Deviation! Students have used the interquartile range which describes the variability of a set. Another way to describe the variability of a set is to use its mean absolute deviation. The mean absolute deviation of a set is the average distance between each data value and the mean. To find the MAD: 1. Find the mean of the data. 2. What is the distance between each data value and the mean. That is, find the absolute value of the difference between each data value and the mean. 3. Find the average of those differences. We will watch this short instructional video: http://learnzillion.com/lessons/539-summarize-the-spread-of-data-using-range-and-mean-absolute-deviation and then work some problems in class. On Thursday, we will explore another way to record data - the STEM AND LEAF PLOT. We will watch a video... http://www.mathplayground.com/howto_stemleaf.html (7:02) In a stem-and-leaf plot, the data is organized from least to greatest. The digits of the least place value usually form the leaves, and the next place-value digits form the stems. A special table where each data value is split into a "leaf" (usually the last digit) and a "stem" (the other digits). Like in this example: "32" is split into "3" (stem) and "2" (leaf). The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values. The "stem" is used to group the scores and each "leaf" indicates the individual scores within each group. On Friday, my daughter graduates from UGA! This proud mama will be there as another product of Douglas County Schools receives her degree. The substitute will work through HISTOGRAMS with the students. Below is an information sheet explaining the differences between bar graphs and histograms. A HISTOGRAM displays data from a frequency table. A histogram has one bar for each interval. The length of a bar indicates the frequency of the interval. There is no space between bars because there are no gaps between intervals. Because the intervals of a histogram have equal size, the bars have equal width.Through all of the lessons this week, we will bring all of our learning together. Students should be developing a firm understanding of statistical questions, measures of center and spread, and how to create numerous graphs. This is perhaps the ultimate goal in any statistical study: the ability to take a real life data set, and determine what it is telling you based on the shape of the data set, and the context it was collected. The students will hold this lesson with them for the rest of their lives, whether it be something as simple as video game statistics, all the way to understanding newspaper articles and statistics that they come across in all aspects of life. Lesson Vocabulary: Measure of center: A measure of center is one single number that represents the entire data set as a whole. Nominal: A nominal data set includes elements that cannot be put in order. Ordinal: An ordinal data set includes elements that can be put in numerical order.
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April 2015
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