STATS CHAP 3.2
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 18. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 82 and 118? (b) What percentage of people has an IQ score less than 82 or greater than 118? (c) What percentage of people has an IQ score greater than 118?
A.68 B. 32 C. 16
The standard deviation can be negative.
FALSE
The standard deviation is a resistant measure of spread.
FALSE
An insurance company crashed four cars in succession at 5 miles per hour. The cost of repair for each of the four crashes was $418, $461, $420, $217. Compute the range of the data.
The range is $244
Is a measure of 26 inches "far away" from a mean of 16 inches? As someone with knowledge of statistics, you answer "it depends" and request the standard deviation of the underlying data. (a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 26 inches from 16 inches? (b) Is 26 inches far away from a mean of 16 inches? (c) Suppose the standard deviation of the underlying data is 7 inches. Is 26 inches far away from a mean of 16 inches?
(a) 26 inches is 55 standard deviation(s) away from 16 inches. B. Yes, because 26 inches is more than more than 2 standard deviations away from 16 inches. C. No, because 26inches is less than less than 2 standard deviations away from 16 inches.
If a variable has a distribution that is bell-shaped with mean 25 and standard deviation 4, then according to the Empirical Rule, 99.7% of the data will lie between which values?
13 TO 37
Find the sample standard deviation for the given data. 22, 14, 2, 8, 11
7.4
Find the sample variance and standard deviation. 17 11 5 9 10 Choose the correct answer below. Fill in the answer box to complete your choice.
A. 18.8 B. 4.3
The data set below on the left represents the annual rate of return (in percent) of eight randomly sampled bond mutual funds, and the data set below on the right represents the annual rate of return (in percent) of eight randomly sampled stock mutual funds. Use the information in the table below to complete parts (a) through (d).Then complete part (e). (a) Determine the mean and standard deviation of each data set. (b) Based only on the standard deviation,_____ (c) What proportion of the bond mutual funds are within one standard deviation of the mean? (d) The coefficient of variation, CV, is defined as the ratio of the standard deviation to the mean of a data set. CV=standard deviation/ mean The CV allows for a comparison in spread by describing the amount of spread per unit mean. Compute the CV for both data sets. What is the CV of the data set for bond mutual funds? (e) In the table below, the data set on the left has the heights of students measured in inches, while the data set on the right has the same students' heights measured in centimeters. For each data set, determine the mean and the standard deviation. Draw a conclusion about the spread using the standard deviation, then find the coefficient of variation for both data sets. What is true of the coefficient of variation?
A. 2.275 0.669 7.913 0.903 B. STOCK MUTUAL C. 0.625 0.625 D. 0.294 0.114 BOND MUTUAL E. 70.625 3.292 179.388 8.362 0.047 0.047 When converting units of measure, the coefficient of variation is unchanged.
Find the sample variance and standard deviation.
A. 237.56 B. 15.4
The weight of an organ in adult males has a bell-shaped distribution with a mean of 325 grams and a standard deviation of 25 grams. Use the empirical rule to determine the following. (a) About 99.7% of organs will be between what weights? (b) What percentage of organs weighs between 300 grams and 350 grams? (c) What percentage of organs weighs less than 300 grams or more than 350 grams? (d) What percentage of organs weighs between 250 grams and 375 grams?
A. 250-400 B.68 C.100-68=32 D. 97.35
Blocking refers to the idea that the variability in a variable can be reduced by segmenting the data by some other variable. The data in the accompanying table represent the recumbent length (in centimeters) of a sample of 10 males and 10 females who are 40 months of age. Complete parts (a) through (d). (a) Determine the standard deviation of recumbent length for all 20 observations. b) Determine the standard deviation of recumbent length for the males. (c) Determine the standard deviation of recumbent length for the females. d) What effect does blocking by gender have on the standard deviation of recumbent length for each gender?
A. 6.06 B. 5.49 C. 5.59 D. The standard deviation is lower for each group than it is for the groups combined.
The following data represent the weights (in grams) of a random sample of 50 candies. (a) Determine the sample standard deviation weight. b) On the basis of the histogram on the right, comment on the appropriateness of using the empirical rule to make any general statements about the weights of the candies. (c) Use the Empirical Rule to determine the percentage of candies with weights between 0.7 and 0.98 gram. Hint: (d) Determine the actual percentage of candies that weigh between 0.7 and 0.98 gram, inclusive. (e) Use the Empirical Rule to determine the percentage of candies with weights more than 0.91gram. (f) Determine the actual percentage of candies that weigh more than 0.91 gram.
A. STATCRUNCH 0.07 g B. The histogram is bell-shaped so the empirical rule can be used. C. 95% D. 16% E. 16%
Complete the following statement about the Empirical Rule.
According to the Empirical Rule, if a distribution is bell-shaped, then approximately 68% of the data will lie within 1 standard deviation of the mean; approximately 95% of the data will lie within 2 standard deviations of the mean; approximately 99.7% of the data will lie within 3 standard deviations of the mean.
What can be said about a set of data with a standard deviation of 0?
All the observations are the same value.
Over the past 10 years, five mutual funds all had the same mean rate of return. The standard deviations for each of the five mutual funds are shown below. Capital Investment: 6.8%; Vanity: 10.6%; Global Advisor: 8.7%; International Equities: 9.1%; Nomad: 11.4% Which mutual fund was least consistent in rate of return?
NOMAD
Stocks may be categorized by sectors. The accompanying data represent the one-year rate of return (in percent) for a sample of consumer cyclical stocks and industrial stocks for a 12-month period. Note: Consumer cyclical stocks include restaurants and retailers. Industrial stocks include manufacturers and shipping companies. Complete parts (a) through (c) below. (a) Draw a relative frequency histogram for each sector using a lower class limit for the first class of −50 and a class width of 10. Which sector appears to have more dispersion? Choose the correct relative frequency histogram for consumer cyclical stocks. Choose the correct relative frequency histogram for industrial stocks. (b) Determine the mean and median rate of return for each sector. Which sector has the higher mean rate of return? Which sector has the higher median rate of return? (c) Determine the standard deviation rate of return for each sector. In finance, the standard deviation rate of return is called risk. Typically, an investor "pays" for a higher return by accepting more risk. Is the investor paying for higher returns for these sectors?
The industrial sector appears to have more dispersion. B. 7.994 3.7 15.442 10.6 The industrial sector has the higher mean rate of return, and the industrial sector has the higher median rate of return. 20.949 23.832 The investor is paying for a higher return for the sector with the higher median rate of return
The following data for a random sample of banks in two cities represent the ATM fees for using another bank's ATM. Compute the range and sample standard deviation for ATM fees for each city. Which city has the most dispersion based on range? Which city has more dispersion based on the standard deviation? City A City B 1.50 2.50 1.00 1.00 1.50 1.00 1.50 0.00 1.50 2.00 Which city has the most dispersion based on range? Which city has the most dispersion based on standard deviation?
The range for city A is $0.5 The range for city B is $2.5 The standard deviation for city A is $0.22 The standard deviation for city B is $0.97 City B, because it has a higher range. City B, because it has a higher standard deviation.
An insurance company crashed four cars in succession at 5 miles per hour. The cost of repair for each of the four crashes was $428, $467, $404, $211 . Compute the range, sample variance, and sample standard deviation cost of repair.
The range is $256 s2=12995 dollar s=$113.99
Find the population standard deviation for the given data. 7, 11, 21, 24,
The standard deviation is 7.69
In a statistics class, the standard deviation of the heights of all students was 4.1 inches. The standard deviation of the heights of males was 3.3 inches and the standard deviation of females was 3.2 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately?
The standard deviation of the entire class is more than the standard deviation of the males and females considered separately because the distribution of the entire class has more dispersion.
The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "flipped" classroom. Complete parts (a) through (c) below. (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? (b) Which course has more dispersion in exam scores using the sample standard deviation as the measure of dispersion? (c) Suppose the score of 59.6 in the traditional course was incorrectly recorded as 596. How does this affect the range? How does this affect the standard deviation? What property does this illustrate?
The traditional course has a range of 28.7 while the "flipped" course has a range of 27.92 The traditional course has more dispersion. The traditional course has a standard deviation of 8.618 while the "flipped" course has a standard deviation of 7.559 The traditional course has more dispersion The range is now 539.6 The standard deviation is now 145.326 Neither the range nor the standard deviation is resistant.
The following data for a random sample of banks in two cities represent the ATM fees for using another bank's ATM. Compute the sample variance for ATM fees for each city. City A City B 1.00 2.25 1.00 1.25 1.50 1.75 1.50 0.00 1.50 2.00
The variance for city A is $0.075 The variance for city B is $0.8
The following data for a random sample of banks in two cities represent the ATM fees for using another bank's ATM. Compute the sample variance for ATM fees for each city. City A City B 1.25 2.00 1.00 1.50 1.50 1.75 1.00 0.00 1.00 2.00
The variance for city A is $0.05 The variance for city B is $0.7
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.
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.
The sum of the deviations about the mean always equals
ZERO
