Learning Plan 09. Question 1. Question 2. Question 3. Question 4. What is the difference between the highest and lowest data values in a data set?

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1 Learning Plan 09 Question 1 What is the difference between the highest and lowest data values in a data set? The difference is called range. (p. 794) Question 2 Measures of Dispersion. Read the answer on page 794. Question 3 Find the range for the group of data items. 10, 11, 12, 13, 14 Highest - Lowest = 4 Question 4 Find the range for the group of data items. 22, 22, 24, 24, 26, 26 Highest - Lowest = 4 1

2 Question 5 A group of data items and their mean is given. 6, 10, 14, 24, 36, 54; Mean = 24 a. Find the deviation from the mean for each of the data items. b. Find the sum of the deviations in part (a). Subtract the mean from each data value = 14 = 10 = 0 = = 18 The sum of the deviations: = 0 Question 6 Find a. the mean; b. the deviation from the mean for each data item; c. the sum of the deviations in part (b) = 30 85, 95, 90, 85, 100 a. Mean = b. = = = = = = 9 c = 0 2

3 Questions 7, 8, 9, 11 Find the standard deviation for the group of data items. Round answers to two decimal places. 1, 2, 3, 4, 5 Mean = = 3 Data item Deviation: Data item Mean (Deviation) 2 : (Data item Mean)^ = 2 ( 2) 2 = = 1 ( 1) 2 = = 0 (0) 2 = = = = 2 (2) 2 = 4 (Data item Mean) 2 = = 10 (Data Item Mean)2 Standard Deviation = = 10 n Question 10 If you have a group of numbers and you add the same number to each of your numbers, the mean will increase by that number, but the standard deviation will stay the same, because the new numbers will be as far from the new mean as the old ones from the old mean. 3

4 Question 12 Women s heights average 62 inches with a standard deviation of 2.2 inches in a certain study. Use the rule to determine the typical ranges of the women s heights. In what range will approximately the middle 95% of the women s heights lie? Start from the middle (62) and add 2.2 twice, then subtract 2.2 twice. 4

5 Questions 13, 14 A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. Question 15 Women s average height is 65 inches and the standard deviation is 2.5 inches. Find the height 2 standard deviations above average = 70 Computing z-scores A z-score describes how many standard deviations a data item in a normal distribution lies above or below the mean. The z-score can be obtained using z score = data item mean standard deviation. Data items above the mean have positive z-scores. Data items below the mean have negative z-scores. The z-score for the mean is 0. Question 16 The average score on an IQ test is 100 with a standard deviation of 15 points. If you scored 120 on the IQ test, what would be your z-score? (Round to the nearest hundredth). z score = data item mean standard deviation = = = =

6 Questions 17, 18 A set of data items is normally distributed with a mean of 60 and a standard deviation of 8. Convert 68 to a z-score. z score = data item mean standard deviation z 68 = = 8 8 = 1 Question 19 Scores on a dental anxiety scale range from 0 (no anxiety) to 20 (extreme anxiety). The scores are normally distributed with a mean of 11 and a standard deviation of 4. Find the z-score on this dental anxiety scale. 19 z score = data item mean standard deviation = = 8 4 = 2 Question 20 A survey was done of parents with children under five. Seven hundred eighty-four parents were surveyed on their children s eating habits and fast food. What would be the margin of error? 1 n 100% = 1 100% 3.57% 784 6

7 Question 21 A random sample of 2296 college students were asked their major. The top five responses and the percentage of students who named each of the top five majors are shown in the graph. a. Find the margin of error, to the nearest tenth of a percent, for the survey. b. Write the statement about the percentage of students whose major in math. (follow the example on pages ) a. 1 n 100% = 1 100% % 2296 b. From the graph, math represents 20%. 20% 2.1% = 17.9% 20% + 2.1% = 22.1% We can be 95% confident that between 17.9% and 22.1% of students in the population are majoring in math. 7

8 Question 22 Using a random sample of 3535 TV households, Acme Media Statistics found that 58.9% watched the final episode of When Will It End? c. Find the margin of error. (Round to the nearest hundredth). d. Write the statement about the percentage of TV households in the population who tuned into the final episode of When Will It End? (follow the example on pages ) c. 1 n 100% = 1 100% % 3535 d. 58.9% 1.68% = 57.22% 58.9% % = 60.58% We can be 95% confident that between 57.22% and 60.58% of students in the population are majoring in math. Question 23 z-score Find the answer on page 806. Question 24 Negative z-score Find the answer on page 806. Question 25 Quartiles Find the answer on page

9 Question 26 The scores on a test are normally distributed with a mean of 80 and a standard deviation of 16. What is the score that is 1 standard deviation below the mean? Because it is 1 standard deviation below, you have to subtract = 64 Question 27 The scores on a test are normally distributed with a mean of 150 and a standard deviation of 30. What is the score that is 3 standard deviations below the mean? Because it is 3 standard deviations below, you have to subtract 30 three times. Or you can also do it this way: = = 60 Question 28 The scores on a test are normally distributed with a mean of 200 and a standard deviation of 10. What is the score that is 1 1 standard deviations above the mean? 2 Because it is above, you have to add = = = = 215 9

10 Question 29 The average number of chocolate chips in a particular brand of chocolate chip chewy cookie is 19. The standard deviation is 2.6. Assuming that the number of chocolate chips per cookie is normally distributed, what percentage of cookies would have between 13.8 and 24.2 chips? To reach to 13.8 and 24.2, you have to subtract 2.6 twice, then add 2.6 twice. Approximately 95% of the data items fall within 2 standard deviations from the mean. 95% of the cookies. 10

11 Question 30 Not everyone pays the same price for the same model of a car. The figure illustrates a normal distribution for the prices paid for a particular model of a new car. The mean is $18,000 and the standard deviation is $1000. Use the Rule to find what percentage of buyers paid between $15,000 and $21, ,000 is three standard deviations below the mean, and 21,000 is three standard deviations above the mean. Approximately 99.7% of the data items fall within 3 standard deviations from the mean. 11

12 Question 31 Scores on the GRE are normally distributed with a mean of 517 and a standard deviation of 85. Use the Rule to find the percentage of people taking the test who score between 347 and 687. To reach to 347 and 687, you have to subtract 85 twice, then add 85 twice. Approximately 95% of the data items fall within 2 standard deviations from the mean. 12