STAT CHAP 3.4
Which of the following are resistant measures of dispersion?
IQR
Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Q1=272.8, Q2=387.9, Q3=529.1
25% of the states have a violent-crime rate that is 272.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 387.9 crimes per 100,000 population or less. 75% of the states have a violent-crime rate that is 529.1 crimes per 100,000 population or less.
In a certain city, the average 20- to 29-year old man is 69.8 inches tall, with a standard deviation of 3.2 inches, while the average 20- to 29-year old woman is 64.5 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75-inch man or a 70-inch woman?
The z-score for the man, 1.63 is larger than the z-score for the woman, 1.45, so he is relatively taller.
The _______ represents the number of standard deviations an observation is from the mean.
Z-SCORE
Explain the meaning of the accompanying percentiles. (a) The 5th percentile of the head circumference of males 3 to 5 months of age in a certain city is 41.5 cm. (b) The 80th percentile of the waist circumference of females 2 years of age in a certain city is 52.7 cm. (c) Anthropometry involves the measurement of the human body. One goal of these measurements is to assess how body measurements may be changing over time. The following table represents the standing height of males aged 20 years or older for various age groups in a certain city in 2015.
5% of 3- to5-month-old males have a head circumference that is 41.5 cm or less 80% of 2-year-old females have a waist circumference that is 52.7 cm or less At each percentile, the heights generally decrease as the age increases. Assuming that an adult male does not grow after age 20, the percentiles imply that adults born in 1990 are generally taller than adults who were born in 1950.
A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one particular customer for the past 20 months. Use the given data to answer parts (a) and (b). (b) Suppose the month in which the customer used 336 minutes was not actually that customer's phone. That particular month the customer did not use their phone at all, so 0 minutes were used. How does changing the observation from 336 to 0 affect the standard deviation and interquartile range? What property does this illustrate? What property does this illustrate? Choose the correct answer below.
a) Determine the standard deviation and interquartile range of the data. s=63.89 IQR=105 (b) The standard deviation increases and the interquartile range is not affected. Resistance
The following graph is an ogive of a standardized test's scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. Complete parts a through c. A. Find and interpret the percentile rank of a test score with a value of 120? B. Find and interpret the percentile rank of a test score with a value of 140 C. What score corresponds to the 10th percentile?
A test score of 120 corresponds to the 50TH percentile rank since this percentage of test scores are less than or equal to a test score with a value of 120. A test score of 140 corresponds to the 90th percentile rank since this percentage of test scores are less than or equal to a test score with a value of 140. The 10th percentile corresponds to a test score of 100
Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Given the quartiles Q1=1.430, Q2=2.975, and Q3=4.460, compute the interquartile range, IQR.
IQR=3.03
Explain the meaning of the following percentiles in parts (a) and (b). (a) The 10th percentile of the weight of males 36 months of age in a certain city is 12.0 kg. (b) The 95th percentile of the length of newborn females in a certain city is 53.8 cm.
10% of36-month-old males weigh 12.0kg orless, and 90% of 36-month-old males weigh more than 12.0 kg 95% of newborn females have a length of 53.8 cm orless, and 5% of newborn females have a length that is more than 53.8 cm
The accompanying data represent the monthly rate of return of a certain company's common stock for the past few years. Complete parts (a) and (b) beloW (a) Determine and interpret the quartiles. (b) Check the data set for outliers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Q1=-0.02 Q2=0.03 Q3=0.095 Of the monthly returns, 25% are less than or equal to the first quartile, 50% are less than or equal to the second quartile, and 75% are less than or equal to the third quartile. The outlier(s) is/are 0.47
The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point? (c) Choose the possible reason(s) for any outlier(s) below. Select all that apply.
A. 3200 B. A C. Data entry error A student with unusually high income A student providing false information
The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine. (a) Compute the z-score corresponding to the individual who obtained 35.9 miles per gallon. Interpret this result. (b) Determine the quartiles. (c) Compute and interpret the interquartile range, IQR. (d) Determine the lower and upper fences. Are there any outliers?
A. 35.9-MEAN/SD =The z-score corresponding to the individual is −0.87 and indicates that the data value is 0.87 standard deviation(s) below the mean. B. Q1=36.9 Q2=38.55 Q3=41 C. The interquartile range is 4.1 mpg. It is the range of the middle 50% of the observations in the data set.
Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile range?
The interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.
In a certain city, the average 20- to 29-year old man is 69.6 inches tall, with a standard deviation of 3.0 inches, while the average 20- to 29-year old woman is 64.5 inches tall, with a standard deviation of 3.8 inches. Who is relatively taller, a 75-inch man or a 70-inch woman? Find the corresponding z-scores. Who is relatively taller, a 75-inch man or a 70-inch woman? Select the correct choice below and fill in the answer boxes to complete your choice.
The z-score for the man, 1.8, is larger than the z-score for the woman, 1.45, so he is relatively taller.
Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years.
What are the quartiles? Q1=1.86 Q2=3.225 Q3=5.09
A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 4 standard deviations from the mean. The quality-control engineer knows that the bolts coming off the assembly line have mean length of 7 cm with a standard deviation of 0.05 cm. For what lengths will a bolt be destroyed?
A bolt will be destroyed if the length is less than 6.8 cm or greater than 7.2 cm.
Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Given the quartiles Q1=2.510, Q2=4.715, and Q3=6.410, determine the lower and upper fences. Are there any outliers, according to this criterion? Are there any outliers in the given data set? What are the outliers? Select the correct choice below and fill in any answer boxes in your choice.
LF=-3.34 UF=11.99 No, all the values are between the lower and upper fences. There are no outliers.
Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. Given the quartiles Q1=1.460, Q2=3.180, and Q3=4.950, determine the lower and upper fences. Are there any outliers, according to this criterion?
LF=-3.775 UF=10.185 No, all the values are between the lower and upper fences. There are no outliers.
Which of the following are resistant measures of central tendency?
MEDIAN
The mean finish time for a yearly amateur auto race was 186.86 minutes with a standard deviation of 0.341 minute. The winning car, driven by Mike, finished in 185.95 minutes. The previous year's race had a mean finishing time of 110.8 with a standard deviation of 0.109 minute. The winning car that year, driven by Rita, finished in 110.48 minutes. Find their respective z-scores. Who had the more convincing victory? Which driver had a more convincing victory?
MIKE: 185.95-186.86= VALUE /SD(0.341) -2.67 -2.94 Rita had a more convincing victory because of a lowerz-score.
Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years. What are the quartiles?
Q1=1.13 Q2=2.87 Q3=4.115
_______ divide data sets in fourths.
QUARTILES
