The annual earnings (in dollars) of 35 randomly selected microbiologists are shown in the data table. Use the data to (a) find the sample mean, (b) find the sample standard deviation, and (c) construct a 98% confidence interval for the population mean.100,48180,50077,49268,13751,15467,84494,59565,771 78,91373,90344,54387,26560,85657,43554,82077,763 47,47798,52581,06192,85663,65074,36450,81160,577 91,15583,67580,48663,96373,79256,78047,04088,929 75,94361,49182,415 (a) Find the sample mean. x=(Type an integer or decimal rounded to two decimal places as needed.)

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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Chapter10: Statistics

Section10.4: Distributions Of Data

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The annual earnings (in dollars) of 35 randomly selected microbiologists are shown in the data table. Use the data to (a) find the sample mean, (b) find the sample standard deviation, and (c) construct a 98% confidence interval for the population mean.

100,481	80,500	77,492	68,137	51,154	67,844	94,595	65,771
78,913	73,903	44,543	87,265	60,856	57,435	54,820	77,763
47,477	98,525	81,061	92,856	63,650	74,364	50,811	60,577
91,155	83,675	80,486	63,963	73,792	56,780	47,040	88,929
75,943	61,491	82,415

(a) Find the sample mean.

(Type an integer or decimal rounded to two decimal places as needed.)

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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