What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? We have the following data from Florence Nightingale’s writingAge Range (yr)20-2930-3940-4950-5960-6970-7980+Midpoint x24.534.544.554.564.574.584.5Percantage of Nurses5.7%9.7%19.5%29.2%25.0%9.1%1.8% Using the age midpoints x and the percentage of nurses, do we have a valid probability distribution? ExplainUse a histogram to graph the probability distribution of part (a).Compute the expected age (mean) of a nurse.Compute the standard deviation for ages of nurses.What is the probability that a British nurse selected at random was younger than 60?

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Description: What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? We have the following data from Florence Nightingale’s writingAge Range (yr)20-2930-3940-4950-5960-6970-7980+Midpoint x24.534.544.554.564.574.584.5Percantag

x p(x) xp(x) (x-xbar)^2 (x-xbar)^2p(x) 24.5 0.057 1.3965 856.1476 48.80041 34.5 0.097 3.3465…

Answered: Using the age midpoints x and the…

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What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? We have the following data from Florence Nightingale’s writing

Age Range (yr)	20-29	30-39	40-49	50-59	60-69	70-79	80+
Midpoint x	24.5	34.5	44.5	54.5	64.5	74.5	84.5
Percantage of Nurses	5.7%	9.7%	19.5%	29.2%	25.0%	9.1%	1.8%

Using the age midpoints x and the percentage of nurses, do we have a valid probability distribution? Explain
Use a histogram to graph the probability distribution of part (a).
Compute the expected age (mean) of a nurse.
Compute the standard deviation for ages of nurses.
What is the probability that a British nurse selected at random was younger than 60?

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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Working

x	p(x)	xp(x)	(x-xbar)^2	(x-xbar)^2p(x)
24.5	0.057	1.3965	856.1476	48.80041
34.5	0.097	3.3465	370.9476	35.98192
44.5	0.195	8.6775	85.7476	16.72078
54.5	0.292	15.914	0.5476	0.159899
64.5	0.25	16.125	115.3476	28.8369
74.5	0.091	6.7795	430.1476	39.14343
84.5	0.018	1.521	944.9476	17.00906
		53.76		186.6524

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