Children’s Heights Mrs. Diaz has two children: a 3-year-old boy 43 inches tall and a 10-year-old girl 57 inches tall. Three-year-old boys have a mean height of 38 inches and a standard deviation of 2 inches, and 10-year-old girls have a mean height of 54.5 inches and a standard deviation of 2.5 inches. Assume the distributions of boys’ and girls’ heights are unimodal and symmetric. Which of Mrs. Diaz’s children is more unusually tall for his or her age and gender? Explain, showing any calculations you perform. (Source: www.kidsgrowth.com)
Children’s Heights Mrs. Diaz has two children: a 3-year-old boy 43 inches tall and a 10-year-old girl 57 inches tall. Three-year-old boys have a mean height of 38 inches and a standard deviation of 2 inches, and 10-year-old girls have a mean height of 54.5 inches and a standard deviation of 2.5 inches. Assume the distributions of boys’ and girls’ heights are unimodal and symmetric. Which of Mrs. Diaz’s children is more unusually tall for his or her age and gender? Explain, showing any calculations you perform. (Source: www.kidsgrowth.com)
Solution Summary: The author identifies the child who is unusually tall for his or her age among the two children of Mrs. Diaz.
Children’s Heights Mrs. Diaz has two children: a 3-year-old boy 43 inches tall and a 10-year-old girl 57 inches tall. Three-year-old boys have a mean height of 38 inches and a standard deviation of 2 inches, and 10-year-old girls have a mean height of 54.5 inches and a standard deviation of 2.5 inches. Assume the distributions of boys’ and girls’ heights are unimodal and symmetric. Which of Mrs. Diaz’s children is more unusually tall for his or her age and gender? Explain, showing any calculations you perform. (Source: www.kidsgrowth.com)
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Introduce yourself and describe a time when you used data in a personal or professional decision. This could be anything from analyzing sales data on the job to making an informed purchasing decision about a home or car.
Describe to Susan how to take a sample of the student population that would not represent the population well.
Describe to Susan how to take a sample of the student population that would represent the population well.
Finally, describe the relationship of a sample to a population and classify your two samples as random, systematic, cluster, stratified, or convenience.
1.2.17. (!) Let G,, be the graph whose vertices are the permutations of (1,..., n}, with
two permutations a₁, ..., a,, and b₁, ..., b, adjacent if they differ by interchanging a pair
of adjacent entries (G3 shown below). Prove that G,, is connected.
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You are planning an experiment to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon. You will use a single test car, adding weights so that its total weight is 3000, 3500, or 4000 pounds. The car will drive on a test track at each weight using each of Amoco, Marathon, and Speedway gasoline. Which is the best way to organize the study?
Start with 3000 pounds and Amoco and run the car on the test track. Then do 3500 and 4000 pounds. Change to Marathon and go through the three weights in order. Then change to Speedway and do the three weights in order once more.
Start with 3000 pounds and Amoco and run the car on the test track. Then change to Marathon and then to Speedway without changing the weight. Then add weights to get 3500 pounds and go through the three gasolines in the same order.Then change to 4000 pounds and do the three gasolines in order again.
Choose a gasoline at random, and run the car with this gasoline at…
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