Section 3.2 HW
Find the population variance and standard deviation: 6, 15, 27, 33, 39 (Type an integer or a decimal. Round to one decimal place as needed.) A. s^2 = ___________ A.1 σ^2 = ________________ Choose the correct answer below. Fill in the answer box to complete your choice. (Round to one decimal place as needed.) B. σ = ___________ B.1 s = ____________
A. s^2 = ___________ A.1 σ^2 = 144 B. σ = 12 B.1 s = ____________
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 17. Use the empirical rule to determine the following. (Type an integer or a decimal.) (a) What percentage of people has an IQ score between 83 and 117? (b) What percentage of people has an IQ score less than 49 or greater than 151? (c) What percentage of people has an IQ score greater than 117?
(a) 68 % (b) 0.3 % (c) 16 %
A certain standardized test math scores have a bell-shaped distribution with a mean of 520 and a standard deviation of 119. Complete parts (a) through (c). (Round to one decimal place as needed.) (a) What percentage of standardized test scores is between 163 and 877 ? (b) What percentage of standardized test scores is less than 163 or greater than 877? (c) What percentage of standardized test scores is greater than 758?
(a) 99.7 % (b) 0.3 % (c) 2.5 %
Match the histograms on the right to the summary statistics given. Number Mean Median St.Dev I 57 57 1.9 II 66 66 9 III 57 57 10 IV 57 57 18 (a) (b) (c) (d)
(a) I (b) II (c) III (d) IV
The standard deviation is used in conjunction with the __(a)____ to numerically describe distributions that are bell shaped. The ___(b)___ measures the center of the distribution, while the standard deviation measures the ___(c)___ of the distribution.
(a) mean (b) mean (c) spread
Compute the range and sample standard deviation for strength of the concrete (in psi): 3940, 4120, 3100, 3200, 2960, 3860, 4120, 4030 (a) The range is _________ psi. (b) s = _______ psi (Round to one decimal place asneeded.)
(a) range: 1160 (b): sample st. dev. : 491.8
The following data represent the flight time (in minutes) of a random sample of seven flights from one city to another city. 282, 268, 258, 264, 255, 261, 267 Compute the range and sample standard deviation of flight time. (a) The range of flight time is __________ minutes. (b) The sample standard deviation of flight time is ___________ minutes. (Type an integer or decimal rounded to one decimal place as needed.)
(a) range: 27 (b) sample st. dev. : 8.8
Find the sample variance and standard deviation: 8, 49, 14, 51, 34, 28, 32, 32, 32, 31 (Round to two decimal places as needed.) A. sigma squared = _______________ s^2 = ___________ A.1 s squared = ______________ σ^2 = ________________ Choose the correct answer below. Fill in the answer box to complete your choice. (Round to one decimal place as needed.) B. s = ___________ B.1 σ = ____________
A. sigma squared = _______________ s^2 = 173.66 A.1 s squared = ______________ σ^2 = ________________ B. s = 13.2 B.1 σ = ____________
Find the sample variance and standard deviation: 20, 15, 4, 10, 8 (Type an integer or a decimal. Round to one decimal place as needed.) A. sigma squared = _______________ σ^2 = ___________ A.1 s squared = ______________ s^2 = ________________ Choose the correct answer below. Fill in the answer box to complete your choice. (Round to one decimal place as needed.) B. σ = ___________ B.1 s = ____________
A. sigma squared = _______________ σ^2 = ________ A.1 s squared = ______________ s^2 = 38.8 B. σ = _________ B.1 s = 6.2
Which histogram depicts a higher standard deviation? Histogram A: Freq. : 1, 2, 6, 7, 8, 9, 7, 7, 3, 1 Histogram B: Frequency: 2, 2, 2, 6, 9, 8, 5, 4, 3 A. Histogram b depicts the higher standard deviation, since it is more bell shaped. B. Histogram a depicts the higher standard deviation, because the bars are higher than the average bar in b. C. Histogram b depicts the higher standard deviation, because the distribution has more dispersion. D. Histogram a depicts the higher standard deviation, because the distribution has more dispersion.
C. Histogram b depicts the higher standard deviation, because the distribution has more dispersion.
The sum of the deviations about the mean always equals _____________________
Zero
True or False: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure. A. True, because the standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed. B. False, because the standard deviation measures the spread of the distribution, not the dispersion of the distribution. C. True, because the standard deviation is the difference between the largest and smallest observation. When the standard deviation is larger, there is more distance between the largest and smallest observation, and therefore, more dispersion in the distribution. D. False, because the larger the standard deviation is, the less dispersion the distribution has.
A. True, because the standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.