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Chapter 3: Numerically S ummarizing D ata

Chapter 3: Numerically S ummarizing D ata. Section 3.1: Measures of Central Tendency; i.e., Where is the dataset centered? Section 3.2: Measures of Dispersion; i.e., How spread out is the dataset?. Mean Sample mean (“x bar ”, ) Population mean (“mu ”, μ , a parameter) Median Mode.

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Chapter 3: Numerically S ummarizing D ata

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  1. Chapter 3: Numerically Summarizing Data • Section 3.1: Measures of Central Tendency; i.e., Where is the dataset centered? • Section 3.2: Measures of Dispersion; i.e., How spread out is the dataset?

  2. Mean • Sample mean (“x bar”, ) • Population mean (“mu”, μ, a parameter) • Median • Mode

  3. Given the data:2, 2, 9, 4, 8 Question 1: Mean = ? • 2 (B) 4 (C) 5 (D) 9 Question 2: Mode = ? (A)2 (B) 4 (C) 5 (D) 9 Question 3: Median = ? (A)2 (B) 4 (C) 5 (D) 9

  4. Given the data:2, 2, 9, 4, 8, 9 Question 1: Median = ? • 4 (B) 5.66 (C) 6 (D) There is no median Question 2: Mode = ? (A)2 (B) 6 (C) 2 & 9 (D) There is no mode

  5. The shape of this distribution is? • Symmetric • Skewed Left • Skewed Right • Bimodal

  6. Which one is true for these data? • median = mean • median < mean • median > mean • None are true

  7. Why do economists typically use median instead of mean when discussing income or home prices? • It’s a tradition in economics. • The median uses every data point. • The median is resistant to extreme values. • The median is easier to calculate.

  8. Which statistic is most appropriate for qualitative data? • Mean • Median • Mode • None of the above are ever appropriate.

  9. What can cause bimodal data? • Sampling data from two different symmetric populations as though they were one population. • Simple chance • Missing data • Too much data.

  10. Common measures of dispersion • Range • Standard deviation (sd) • Sample sd: s • Population sd: σ • Variance:

  11. Given the data:2, 2, 9, 4, 8 Range=? (A) 2 (B) 6 (C) 7 (D) 9 S = ? (A) 0 (B) 3.3 (C) 8.8 (D) 11

  12. Using the data: 7, 7, 7, 7, 7 The standard deviation = ?

  13. 34 • The interval (26,34), including 26 and 34. • The interval (34,26), including 26 and 34. • Both B and C.

  14. Suppose the mean test score on an exam for a very large number of students was 80 with a sd of 5. Assume the scores were distributed according to a bell-shaped distribution. Which one of the following is false? • About 68% of the scores were between 75 and 85. • About 99.7% of the scores were between 70 and 90. • About half the scores were below 80. • About 13.5% of the scores were between 85 and 90.

  15. Empirical Rule gives us some rough use of the SD value • Uses the “normal distribution” • 68% • 95% • 99.7%

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