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## 5-Minute Check on Activity 7-2

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**5-Minute Check on Activity 7-2**• What were the graphs examined in the last lesson? • What type of graph was the Age-Gender Population graph? • Are pie-charts the same as a relative frequency chart? • What is a pareto chart? Bar graphs and pie charts Back to back bar graphs Yes; the both add up to 100% Pareto charts list s the bars in percentage order from highest to lowest Click the mouse button or press the Space Bar to display the answers.**Activity 7 - 3**The Class Survey**Objectives**• Organize data with frequency tables, dotplots, and histograms • Organize data using stem-and-leaf plots**Vocabulary**• Frequency – the number of occurrences of each data value • Dotplot – a graph that represent each occurrence of a data value with a dot • Frequency Distributions – show how the data is distributed over all possible values • Classes – are frequency intervals (grouped data) • Class width – how wide a class is (upper limit – lower limit) • Stem – the digit or group of digits with the greatest place value • Leaf – the remaining digits**Activity**Decisions that are made in business, government, education, engineering, medicine, and many other professions depend on analyzing collections of data. As a result, data analysis has become an important topic in many mathematics classes. In this activity, you will collect and organize data from your class.**Activity cont**Fill in the requested data on the board:**Activity cont**Using the data collected on the board, determine the following characteristics of your class: • Most common number of siblings (mode) • Average number of miles from school (mean) • More females or males in class (mode) • The most hours studied last night (max)**Activity cont**Draw dot plots of the four categories of data Siblings Homework Miles from School Gender**TI-83 Graph Support**• 2nd “Y=“ gets into STAT PLOT where we find six graph types supported • Dot plot • Line Plot • Histogram • Boxplot with outliers marked • Boxplot without outliers marked • Normality Plot • To graph things we need the values entered into the list variables L1, L2, etc • Zoom – 9 (ZoomStat) will do the windowing for us**Histograms**• Histograms break the range of data values into classes and displays the count or % of observations that fall into that class • Divide the range of data into equal-width classes • Count the observations in each class: “frequency” • Draw bars to represent classes: height = frequency • Bars should touch (unlike bar graphs).**Histogram versus Bar Chart**HistogramBar Chart • variables quantitativecategorical • bar space no spacespaces between**Categorical Data Example**Physical Therapist’s Rehabilitation Sample**Categorical Data**• Items are placed into one of several groups, intervals or categories (to be counted) • Typical graphs of categorical data: • Pie Charts; emphasizes each category’s relation to the whole • Bar Charts; emphasizes each category’s relation with other categories Bar Chart Pie Chart**Charts for Both Data Types**Relative Frequency Chart Pareto Chart Cumulative Frequency Chart**Quantitative Data**• Quantitative Variable: • Values are numeric - arithmetic computation makes sense (average, etc.) • Distributions list the values and number of times the variable takes on that value • Displays: • Dotplots • Stemplots • Histograms • Boxplots**Dot Plot**• Small datasets with a small range (max-min) can be easily displayed using a dotplot • Draw and label a number line from min to max • Place one dot per observation above its value • Stack multiple observations evenly • First type of graph under STATPLOT 34 values ranging from 0 to 8**Stem Plots**• A stemplot gives a quick picture of the shape of a distribution while including the numerical values • Separate each observation into a stem and a leafeg. 14g -> 1|4 256 -> 25|6 32.9oz -> 32|9 • Write stems in a vertical column and draw a vertical line to the right of the column • Write each leaf to the right of its stem • Note: • Stemplots do not work well for large data sets • Not available on calculator**Stem & Leaf Plots Example**Given the following values, draw a stem and leaf plot 20, 32, 45, 44, 26, 37, 51, 29, 34, 32, 25, 41, 56 Ages Occurrences ------------------------------------------------------------------ 2 | 0, 6, 9, 5 | 3 | 2, 3, 4, 2 | 4 | 5, 4, 1 | 5 | 1, 6**Splitting Stems**• Double the number of stems, writing 0-4 after the first and 5-9 after second.**Back-to-Back Stemplots**• Back-to-Back Stemplots: Compare datasets Example1.4, pages 42-43 of YMS Literacy Rates in Islamic Nations**Example 2**The ages (measured by last birthday) of the employees of Dewey, Cheatum and Howe are listed below. • Construct a stem graph of the ages • Construct a back-to-back comparing the offices • Construct a histogram of the ages Office A Office B**Example 2a: Stem and Leaf**Ages of Personnel 2 0, 1, 2, 6, 8, 8, 3 0, 1, 1, 2, 3, 5, 6, 7, 8, 9, 9, 4 2, 2, 5, 7, 8, 9, 9,**Example 2b: Back-to-Back Stem**Office A: Ages of Personnel Office B: Ages of Personnel 20, 8 3 2, 3, 5, 6, 7, 8, 45, 7, 8, 9, 1, 2, 6, 8 0, 1, 1, 9, 9 2, 2, 9**Example 2c: Histogram**8 n = 24 k = √24 ≈ 4.9 so pick k = 5 w = (49 – 20)/5 = 29/5 ≈ 5.8 6 KrangeNr 1 20 – 25 3 2 26 – 31 6 3 32 – 37 5 4 38 – 43 5 5 44 – 49 5 6 4 Numbers of Personnel 2 20-25 32-37 44-49 26-31 38-43 Ages**Summary and Homework**• Summary • Frequency Distribution describes how frequently each data value occurs: • Listed in a frequency table • Visually depicted in a dot-plot or histogram • Grouped histograms are useful for wide range of data by dividing groups in equal-width intervals • Stem-and-leaf organizes data by splitting each data value into two parts (usually tens digit and singles digit) • Homework • pg 811-814; problems 2, 3, 7