Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper gave the following distances (in centimeters) at which a bat first detected a nearby insect.61 24 42 56 27 83 52 42 68 34 45 Calculate the sample mean distance at which the bat first detects an insect. (Round your answer to four decimal places.) cmCalculate the sample variance and standard deviation for this data set. (Round your answers to two decimal places.)Variance _____Standard deviation ____ Subtract 10 from each sample observation. For the new set of values, compute the mean. (Round your answer to four decimal places.) cmCalculate the sample variance and standard deviation for the new data set. (Round your answers to two decimal places.)Variance ________ Standard deviation _______

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Description: Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper gave the following distances (in centimeters) at which a bat first detected a nearby insec

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

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ISBN:9780079039897

Author:Carter

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Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper gave the following distances (in centimeters) at which a bat first detected a nearby insect.

61 24 42 56 27 83 52 42 68 34 45

Calculate the sample mean distance at which the bat first detects an insect. (Round your answer to four decimal places.)

Calculate the sample variance and standard deviation for this data set. (Round your answers to two decimal places.)

Variance _____

Standard deviation ____

Subtract 10 from each sample observation. For the new set of values, compute the mean. (Round your answer to four decimal places.)

Calculate the sample variance and standard deviation for the new data set. (Round your answers to two decimal places.)

Variance ________

Standard deviation _______

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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