Exam 3: Descriptive Measures

Provide an appropriate response. -Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if it is at least three standard deviations above or Below the mean. Round the z-score to one decimal place, if necessary. A time for the 100 meter sprint of 20.2 seconds at a school where the mean time for the 100 meter Sprint is 17.5 seconds and the standard deviation is 2.1 seconds.

Roughly speaking, the standard deviation indicates how far, on average, the observations are from the mean. Do you think that for the data set below the standard deviation will give a good indication of the typical deviation from the mean? $2,3,4,4,5,5,6,6,100$ What drawback of the standard deviation is illustrated by this example?

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that usedfor the observations. -Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores. 52 15 48 27 12 42 68

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations. -The normal monthly precipitation (in inches)for August is listed for 12 different U.S. cities. 3.5 1.6 2.4 3.7 4.1 3.9 1.0 3.6 4.2 3.4 3.7 2.2

Find the median for the given sample data. -The weights (in ounces)of 21 cookies are shown. 0.61 1.07 0.73 1.62 0.68 0.68 1.41 1.07 1.53 0.99 0.61 1.28 1.19 0.70 0.47 1.28 0.68 1.19 1.72 0.68 0.56

Without calculating the standard deviation, compare the standard deviation for the following data sets. (Note: All data sets have a mean of 30.)Which do you expect to have the largest standard deviation and which do you expect to have the smallest standard deviation? Explain your answers in terms of the formula $s = \sqrt { \frac { \sum ( x - \bar { x } ) ^ { 2 } } { n - 1 } }$ Data set 1: 30, 30, 30, 30, 30, 30, 30, 30, 30, 30 Data set 2: 20, 25, 25, 30, 30, 30, 30, 35, 35, 40 Date set $3 : 20,20,20,25,25,35,35,40,40,40$

Find the median for the given sample data. -6, 7, 23, 21, 30, 46

A meteorological office keeps records of the annual precipitation in different cities. For one city, the mean annual precipitation is 34.5 and the standard deviation of the annual precipitation amounts is 5.1. Let x represent the annual precipitation in that city. Determine the z-score for an annual Precipitation in that city of 21.6 inches. Round your final answer to two decimal places.

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that usedfor the observations. -The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m)are listed below. 0.559 0.189 0.527 0.183 0.3 0.316 0.657

Provide an appropriate response. -A company's raw-data sample of weekly salaries (in dollars)is shown below. 230 340 320 590 780 980 600 350 500 450 460 290 470 400 490 580 570 890 680 410 860 540 530 690 A frequency distribution of this data set is presented below, with a third column showing the class midpoints. Salary Frequency f Midpoint x 200 -under 300 2 250 300 -under 400 3 350 400 -under 500 6 450 500 -under 600 6 550 600 -under 700 3 650 700 -under 800 1 750 800 -under 900 2 850 900 -under 1000 1 950

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that usedfor the observations. -496, 598, 503, 528, 565, 601, 576, 543

Construct and interpret a boxplot or a modified boxplot as specified. -The highest temperatures ever recorded (in °F)in 32 different U.S. states are shown below. Construct a boxplot for the data. 100 100 105 105 106 106 107 107 109 110 110 112 112 112 113 113 115 115 116 117 118 118 118 118 118 119 120 121 122 125 128 134

Draw one boxplot to illustrate bell-shaped data, another for uniform data, and a third for skewed data.

Determine the quartile or interquartile range as specified. -The test scores of 19 students are listed below. Find the third quartile, Q3 . 36 45 49 53 55 56 59 61 62 65 69 70 74 78 84 87 89 93 98

Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place thanthat used for the observations. -Frank's Furniture employees earned the following amounts last week: \ 399.89 \ 186.46 \ 308.25 \ 331.59 \ 449.13 \ 342.34 \ 193.69 \ 411.78 \ 472.69 What was the mean amount earned by an employee last week? Round your answer to the nearest cent.

Determine the quartile or interquartile range as specified. -The weekly salaries (in dollars)of sixteen government workers are listed below. Find the third quartile, $\mathrm { Q } _ { 3 } .$ 492 773 545 843 506 750 609 820 663 890 450 579 704 473 632 527

Use the empirical rule to solve the problem. -The amount of Jen's monthly phone bill has a roughly bell-shaped distribution with a mean of $57 and a standard deviation of $9. What percentage of her phone bills are between $30 and $84?

The empirical rule and Chebyshev's rule both relate the percent of data points to the number of standard deviations above or below the mean. What is the significant difference between the two and why do the percents for $\pm 2$ SD and $\pm 3$ SD differ so much?

A population consists of 100 professional gymnasts and 100 professional basketball players. For this group, the average height is 70 inches. However, most of the gymnasts are between 57 and 61 inches tall while most of the basketball players are between 78 and 82 inches tall. For this group, observations far from the mean are more common than observations close to the mean. Describe what a boxplot for the heights of this group would look like. Discuss, in particular, the lengths of the whiskers relative to the width of the box and explain your reasoning.

The data set below consists of the scores of 15 students on a quiz. For this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? Explain your thinking. 90 90 91 91 89 90 89 91 91 90 60 90 89 90 91