# Chapter 3 Numerically Summarizing Data Insert photo of cover.

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Chapter 3 Numerically Summarizing Data Insert photo of cover

Section 3.3 Measures of Central Tendency and Dispersion from Grouped Data Objectives 1.Approximate the mean of a variable from grouped data 2.Compute the weighted mean 3.Approximate the variance and standard deviation of a variable from grouped data

Objective 1 Approximate the Mean of a Variable from Grouped Data

Hours01-56-1011-1516-2021-2526-3031-35 Frequency01302502301801006050 The National Survey of Student Engagement is a survey that (among other things) asked first year students at liberal arts colleges how much time they spend preparing for class each week. The results from the 2007 survey are summarized below. Approximate the mean number of hours spent preparing for class each week. Source:http://nsse.iub.edu/NSSE_2007_Annual_Report/docs/withhold/NSSE_2007_Annual_Report.pdf EXAMPLEApproximating the Mean from a Relative Frequency Distribution

TimeFrequencyxixi x i f i 0000 1 - 51303.5455 6 - 102508.52125 11 - 1423013.53105 16 - 2018018.53330 21 - 2510023.52350 26 – 306028.51710 31 – 355033.51675

Objective 2 Compute the Weighted Mean

EXAMPLE Computed a Weighted Mean Bob goes the “Buy the Weigh” Nut store and creates his own bridge mix. He combines 1 pound of raisins, 2 pounds of chocolate covered peanuts, and 1.5 pounds of cashews. The raisins cost \$1.25 per pound, the chocolate covered peanuts cost \$3.25 per pound, and the cashews cost \$5.40 per pound. What is the cost per pound of this mix.

Objective 3 Approximate the Variance and Standard Deviation of a Variable from Grouped Data

Hours01-56-1011-1516-2021-2526-3031-35 Frequency01302502301801006050 The National Survey of Student Engagement is a survey that (among other things) asked first year students at liberal arts colleges how much time they spend preparing for class each week. The results from the 2007 survey are summarized below. Approximate the variance and standard deviation number of hours spent preparing for class each week. Source:http://nsse.iub.edu/NSSE_2007_Annual_Report/docs/withhold/NSSE_2007_Annual_Report.pdf EXAMPLEApproximating the Mean from a Relative Frequency Distribution

TimeFrequency x 0 3.5 0 16453.13 00 1 - 5130 6 - 102508.59765.625 11 - 1423013.5359.375 16 - 2018018.52531.25 21 - 2510023.57656.25 26 - 306028.511343.75 31 - 355033.517578.13