Children of First Ladies This list represents the number of children for the first six “first ladies” of the United States. (Source: 2009 World Almanac and Book of Facts) a. Find the mean number of children, rounding to the nearest tenth. Interpret the mean in this context. b. According to eh.net/encyclopedia, women living around 1800 tended to have between 7 and 8 children. How does the mean of these first ladies compare to that? c. Which of the first ladies listed here had the number of children that is farthest from the mean and therefore contributes most to the standard deviation? d. Find the standard deviation, rounding to the nearest tenth.

Children of First Ladies This list represents the number of children for the first six “first ladies” of the United States. (Source: 2009 World Almanac and Book of Facts) a. Find the mean number of children, rounding to the nearest tenth. Interpret the mean in this context. b. According to eh.net/encyclopedia, women living around 1800 tended to have between 7 and 8 children. How does the mean of these first ladies compare to that? c. Which of the first ladies listed here had the number of children that is farthest from the mean and therefore contributes most to the standard deviation? d. Find the standard deviation, rounding to the nearest tenth.

Children of First Ladies This list represents the number of children for the first six “first ladies” of the United States. (Source: 2009 World Almanac and Book of Facts)

a. Find the mean number of children, rounding to the nearest tenth. Interpret the mean in this context.

b. According to eh.net/encyclopedia, women living around 1800 tended to have between 7 and 8 children. How does the mean of these first ladies compare to that?

c. Which of the first ladies listed here had the number of children that is farthest from the mean and therefore contributes most to the standard deviation?

d. Find the standard deviation, rounding to the nearest tenth.

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 + ...

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