Chapter 3 - Chapter 3 KVANLI PAVUR KEELING Click to edit...

Info icon This preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Click to edit Master subtitle style 3/13/11 Chapter 3 – Data Summary Using Descriptive Measures KVANLI PAVUR KEELING
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3/13/11 Chapter Objectives v At the completion of this chapter, you should be able to define and use the following four measures: ∙ Measures of Central Tendency: Mean, Median, Mode and Midrange ∙ Measures of Variation: Range, Standard Deviation, Variance, and
Image of page 2
3/13/11 Chapter Objectives - Continued v At the completion of this chapter, you should be able to define and use the following measures: ∙ Measures of Position: Percentiles, Quartiles, and z-scores ∙ Measures of Shape: Skewness and
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3/13/11 Measures of Central Tendency v These are: • mean • median • midrange • mode These determine where the “middle” of the sample is; that is, a “typical” value The mode is that value that occurs the most often
Image of page 4
3/13/11 Central Tendency Calculation v Example: v Consider a sample consisting of the number of purchased textbooks this semester for 5 randomly selected students v The sample values are {6, 9, 7, 23, 5} Here, the sample size is n = 5
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3/13/11 The Sample Mean v The sample mean is the sample average v Our sample: {6, 9, 7, 23, 5} v The sample mean is books v The symbol for the sample mean is v So, = 10 0 . 10 5 5 23 7 9 6 = + + + + X X Read as “x bar”
Image of page 6
3/13/11 The Sample Median v Median (Md) is the center of the ordered array v 2 steps to find the Md. v 1st step: put the values in order from smallest to largest v For our sample, this would be {5, 6, 7, 9, 23} v 2nd step: Consider n is odd or even. th n + 2 1 Here, this would be the 3rd value
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3/13/11 The Sample Median – n is Even v IF n is even , the median is the average of the middle two values Consider this sample: {2, 4, 8, 12, 16, 18} (n = 6) v Here, Md = books v In general for n even, Md is the average of the 10 2 12 8 = + th n 2
Image of page 8
3/13/11 The Sample Midrange v The midrange is the average of lowest (L) and highest (H) sample values v The symbol for the midrange is Mr v Mr = v The textbook sample is {6, 9, 7, 23, 5} 2 H L + 14 2 23 5 = + This is H This is L
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3/13/11 The Sample Mode v The mode ( Mo ) is that value that occurs more than once and the most often in the sample. v For the textbook example, there is no mode since there are no repeat values v If there is a 2-way tie, you state that the modes are ____ and ____ v For continuous data, don’t bother looking for a mode
Image of page 10
3/13/11 More on the Sample Mode v If your company manufactures clothing , the sample mode is more likely to be of interest rather than the other three measures of central tendency v Example: Your company manufactures hats v The statistic of interest in a sample of head sizes would be the most popular head size since we should manufacture more hats of that size v The mean (say, 6.82), median and midrange
Image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3/13/11 Outlier v In statistics, an outlier is an observation that is numerically distant from the rest of the data.
Image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern