Chapter 2 Test Review
Use the histogram below to approximate the median heart rate of adults in the gym.
70
Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these.
skewed right
Find the mean, median, and mode of the data.
= 70; median = 69; mode = 67
Use the grouped data formulas to find the indicated mean or standard deviation. For the following data set, approximate the sample standard deviation.
3.85
The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be considered unusual.
3647 g
The data below represent the alcohol-related driving fatalities, in thousands, in the United States over a 20-year period. Use a time series chart to display the data. Describe any trends shown.
It appears the number of alcohol-related fatalities is gradually declining
Use the given frequency distribution to find the (a) class width. (b) class midpoints of the first class. (c) class boundaries of the first class.
(a) 3(b) 51(c) 49.5-52.5
Find the sample standard deviation. 15 42 53 7 9 12 14 28 47
17.8
Use the histogram below to approximate the mean heart rate of adults in the gym.
70.8
For the dot plot below, what is the maximum and what is the minimum entry?
max: 17; min: 12
The mean score of a competency test is 73, with a standard deviation of 4. Use the Empirical Rule to find the percentage of scores between 69 and 77. (Assume the data set has a bell-shaped distribution.)
68%
A student receives test scores of 62, 83, and 91. The student's final exam score is 88 and homework score is 76. Each test is worth 20% of the final grade, the final exam is 25% of the final grade, and the homework grade is 15% of the final grade. What is the student's mean score in the class?
80.6
Use the maximum and minimum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits. min = 1, max = 30, 6 classes
Class width = 5, Lower class limits: 1, 6, 11, 16, 21, 26; Upper class limits: 5, 10, 15, 20, 25, 30
Approximate the mean of the frequency distribution.
6
A random sample of 30 high school students is selected. Each student is asked how many hours he or she spent on the Internet during the previous week. The results are shown in the histogram. Estimate the sample mean.
7.9 hr
Sample annual salaries (in thousands of dollars) for public elementary school teachers are listed. Find the sample standard deviation. 18.6 22.9 29.5 35.5 12.6 23.3
8.04
Explain the difference between class limits and class boundaries.
Class limits determine which numbers can belong to that class. Class boundaries are the numbers that separate classes without forming gaps between them.
Here are the batting averages of Sammy Sosa and Barry Bonds for 13 recent years. Which player is more consistent? Explain your reasoning.
Sosa: mean = 0.279 and s = 0.033; Bonds: mean = 0.312 and s = 0.027.Bonds is more consistent since his standard deviation is less.
In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed below. a) If a constant value k is added to each value, how will the standard deviation be affected? b) If each value is multiplied by a constant k, how will the standard deviation be affected? 1.1 5.2 3.6 5.0 4.8 1.8 2.2 52 1.5 0.8
The standard deviation will not be affected
Use the relative frequency histogram toa) identify the class with the greatest, and the class with the least, relative frequency.b) approximate the greatest and least relative frequencies.c) approximate the relative frequency of the fifth class.
a) Class with greatest relative frequency: 105-115 mm Hg Class with least relative frequency: 145-155 mm Hgb) Greatest relative frequency ≈ 0.35Least relative frequency ≈ 0.03c) Approximately 0.08
The speeds of a random sample of 100 cars are recorded as they pass a highway checkpoint. The results are summarized in the frequency distribution below. Approximate the sample mean.
55.9 mph
Find the sample standard deviation. 2 6 15 9 11 22 1 4 8 19
7.1
The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find the percentile that corresponds to a cholesterol level of 238 milligrams per deciliter. 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265
90th percentile
The mean IQ score of adults is 100, with a standard deviation of 15. Use the Empirical Rule to find the percentage of adults with scores between 70 and 130. (Assume the data set has a bell-shaped distribution.)
95%
For the stem-and-leaf plot below, find the range of the data set.
34
In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed below. Compute the range, standard deviation and variance of the data 1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8
range = 4.4, s = 1.8, s2 = 3.324
What is the difference between using μ and to represent a mean?
μ represents a population mean and x-bar represents a sample mean.
Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Compare the variation in heights to the variation in weights of thirteen-year old girls. The heights (in inches) and weights (in pounds) of nine randomly selected thirteen-year old girls are listed below.
Heights: 4.3%Weights: 17.4%There is substantially more variation in the weights than in the heights of the girls
Find the mean, median, and mode of the following numbers: 96 99 92 96 89 97 96 90 91 94
mean 94, median 95, mode 96
Grade points are assigned as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Grades are weighted according to credit hours. If a student receives an A in a four-credit class, a D in a two-credit class, a B in a three-credit class and a C in a three-credit class, what is the student's grade point average?
2.75
The numbers of runs batted in that Sammy Sosa hit in the first 15 years of his major league baseball career are listed below. Find the mean and median number of runs batted in. Round the mean to the nearest whole number.
mean: 97; median 103
The numbers of home runs that Sammy Sosa hit in the first 15 years of his major league baseball career are listed below. Make a stem-and-leaf plot for this data. What can you conclude about the data?
Most of these years he hit 36 or more home runs.
In a random sample, 10 students were asked to compute the distance they travel one way to school to the nearest tenth of a mile. The data is listed below. Compute the coefficient of variation. 1.1 5.2 3.6 5.0 4.8 1.8 2.2 5.2 1.5 0.8
coefficient of variation = (1.82 / 3.12) × 100% = 58.3%
Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class had a mean of 69 with a standard deviation of 3.7. Suppose a student gets a 59 on the history test and a 55 on the physics test. Calculate the z-score for each test. On which test did the student perform better?
history z-score = -4.44; physics z-score = -3.78; The student performed better on the physics test
Use the data to identify any outliers. 38 43 55 65 66 68 70 73 74 76 80 82 87 90 99
38, 43
The scores of the top ten finishers in a recent golf tournament are listed below. Find the median score. 67 67 68 71 72 72 72 72 73 76
72
The mean score of a competency test is 82, with a standard deviation of 2. Between what two values do about 99.7% of the values lie? (Assume the data set has a bell-shaped distribution.)
Between 76 and 88
The test scores of 30 students are listed below. Find the five-number summary. 31 41 45 48 52 55 56 58 63 65 67 67 69 70 70 74 75 78 79 79 80 81 83 85 85 87 90 92 95 99
Min = 31, Q1 = 58, Q2 = 72, Q3 = 83, Max = 99
On a recent Statistics test, the scores were 15, 66, 66, 81, 82, 83, 85, 88, 90, 92, 93, and 95. Is the mean a good representation of the center of data? If not, why?
No, the mean is not a good representation of the center. The mean score is 78, and 9 of the scores are better than this.
Use the box-and-whisker plot below to determine which statement is accurate.
One half of the cholesterol levels are between 180 and 211.
A study was conducted to determine how people get jobs. Four hundred subjects were randomly selected and the results are listed below.
Online Services 31%, Networking 26%, Executive Search Firms 18%, Newspaper Want Ads 17%, Mailing 8%