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Chapter 16

Chapter 16. 16.1 – Statistics Organizing Data 16.2 – Measures of Central Tendency 16.3 – Measures of Variation. Stem-and-Leaf Plots. Stem and Leaf. ASTRONAUTS Display the data shown in a stem-and-leaf plot. Step 1 Find the least and the greatest number. 54. 77. Stem-and-Leaf Plots.

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Chapter 16

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  1. Chapter 16 16.1 – Statistics Organizing Data 16.2 – Measures of Central Tendency 16.3 – Measures of Variation

  2. Stem-and-Leaf Plots Stem and Leaf ASTRONAUTS Display the data shown in a stem-and-leaf plot. Step 1 Find the least and the greatest number. 54 77

  3. Stem-and-Leaf Plots ASTRONAUTS Display the data shown in a stem-and-leaf plot. 54 77 Step 2 Draw a vertical line and write the stems from 5 to 7 to the left of the line.

  4. Stem-and-Leaf Plots ASTRONAUTS Display the data shown in a stem-and-leaf plot. Step 3 Write the leaves to the right of the line, with the corresponding stem. Stem and Leaf Diagram

  5. Stem-and-Leaf Plots ASTRONAUTS Display the data shown in a stem-and-leaf plot. Step 4 Rearrange the leaves so they are ordered from least to greatest. Ranked Stem and Leaf Plot

  6. Frequency Distribution Slides Frequency Distributions

  7. Box-and-Whisker Plots

  8. Step 1 Find the least and greatest number. Then draw a number line that covers the range of the data.

  9. Step 2 Find the median, the extremes, and the upper and lower quartiles. Mark these points above the number line. Lower Extreme Lower Quartile : Lower hinge Median Upper Quartile : Upper hinge Upper Extreme

  10. Step 3 Draw a box and the whiskers.

  11. Find the mean, median, mode, variance, mean deviation, and standard deviation of the following data

  12. Find the mean, median, mode, variance, mean deviation, and standard deviation of the following data

  13. HW #16.1-3Pg 692-693 3, 9, 10-13Pg 698-699 3, 6, 9-16Pg 702-703 5, 7-10

  14. Chapter 16 16.4 – The Normal Distribution

  15. The heights of 16-year-old girls are not distributed uniformly, or evenly. Many more girls are average height than are very short or very tall. The values are distributed so that they are frequent near the mean, and become more rare and infrequent the farther they are from the mean. The most common distribution with this characteristic is a

  16. Normal curves are symmetric with respect to the vertical line at the mean. The spread of each curve is defined by its standard deviation. Areas under this curve represent probabilities from normal distributions.

  17. When data are distributed in a bell-shaped or normal curve about 68% of the data lie within one standard deviation on either side of the mean, and about 95% lie within two standard deviations of the mean.

  18. Consider the bell-shaped distribution of IQ scores for students in a school. The mean is 100 and the standard deviation is 15. What percent of students in the school would we expect to have IQs between 85 and 115? What percent of the students can we expect to have IQs between 70 and 115?

  19. What percent of the students in the school can we expect to have IQs above 115? What percent of the students in the school can we expect to have IQs in the range from 85 to 145?

  20. The given times of 33 minutes and 57 minutes represent one standard deviation on either side of the mean, So, 68% of the shoppers will spend between 33 an 57 minutes in the supermarket.

  21. According to a survey by the National Center for Health Statistics, the heights of adult men in the United States are normally distributed with a mean of 69 inches and a standard deviation of 2.75 inches. If you randomly choose 1 adult man, what is the probability that all he is 71.75 inches tall or taller?

  22. For example, if a value has a z-score of -2, it is two standard deviations below the mean.

  23. What is the z-score for 46 in a normal distribution whose mean is 44 and whose standard deviation is 2? For this distribution, mean = 44 and Standard Deviation = 2. Thus, 46 is one standard deviation above the mean.

  24. A value is selected randomly from a normal distribution. What is the probability that its z-score is less than -1.46? The probability that a value has a z-score less than -1.46 is equal to the area of the shaded region under the curve. This value is given in Table 7. Table 7 on page 850 gives the probability that a value in the distribution has a z-score that is less than a given value

  25. A student received a score of 56 on a normally distributed standardized test. The test had a mean of 50 and a standard deviation of 5.What is the probability that a randomly selected student achieved a higher score? We need to find the probability that a value greater than 56 is selected from a normal distribution with a mean of 50 and a standard deviation of 5. Look up 1.2 in Table 7. P(Score > 56) = 1-0.8849 = 0.1151 P(Score < 56) = 0.8849

  26. How often would we expect to find an 1Q greater than 142 in a sample of students whose mean 1Q was 110 where the standard deviation was 16?

  27. A company manufactures cover plates for boxes with lengths of 4 inches. Due to variation in the process, the lengths of the plates are normally distributed about a mean of 4 inches with a standard deviation of 0.01 inch. A plate is considered a "reject" if its length is less than 3.98 inches or greater than 4.02 inches.What percent of the production are considered "rejects"?

  28. HW #16.4Pg 708 1-31 Odd, 33-43

  29. Chapter 16 16.5 – Collecting Data Randomness and Bias Objective: Evaluate and select sampling methods. Objective: Describe how to take a stratified random sample.

  30. Objective: Evaluate and select sampling methods. A scientist is studying the weight gain or loss of mice that are given a certain treatment. When choosing mice for the experiment, the scientist reaches into a cage with 30 mice and selects the 5 largest mice in the cage. Is the sample random?

  31. Objective: Evaluate and select sampling methods. Describe how a random sample of 10 individuals might be chosen from a high school graduating class of 202 to receive a gift certificate.

  32. Objective: Evaluate and select sampling methods. Although the processes involved in the development of a random sample guarantee that requirements of equal probability and independence are satisfied, they do not guarantee that the sample drawn will be REPRESENTATIVE

  33. Objective: Evaluate and select sampling methods. A town newsletter is doing an article on high school students. A questionnaire is sent to a random sample of school-aged students. Are the data representative? No. A sample of students from kindergarten through grade 12 would not give results representative of high school students. Even when the sample is restricted to high school students, the data may not be representative. Data might have been collected largely from members of the high school chorus. In this case, the data would most likely be biased. That is, it is likely that the data would be overly influenced by factors that are related to musical interests.

  34. Objective: Evaluate and select sampling methods.

  35. Objective: Describe how to take a stratified random sample. • To draw a representative sample, we may need to divide the population into distinct subgroups, called strata. • Then we can use stratified random sampling to assure that the sample has the same characteristics as the population. • Each member of the population must be placed in one and only one stratum. • A random sample is drawn so that the sample has the same distribution among the strata as the population.

  36. Objective: Describe how to take a stratified random sample. A college has 1260 freshmen, 1176 sophomores, 840 juniors, and 924 seniors. Describe how to take a stratified random sample of 200 students. We would randomly sample 60 freshmen, 56 sophomores, 40 juniors, and 44 seniors.

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