Researchers recruited a sample group of older adults and a sample group of younger adults for a study on memory. Their ages are below. Older adults: Younger adults:Age Age2 Age Age250 2500 22 48472 5184 24 57664 4096 30 90078 6084 21 44155 3025 26 67684 7056 28 78467 4489 27 72965 4225 19 36170 4900 32 1024 Calculate the mean, range, variance, and standard deviation for the ages of each group.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Researchers recruited a sample group of older adults and a sample group of younger adults for a study on memory. Their ages are below.

Older adults:                                      Younger adults:
Age        Age²                                      Age        Age²
50           2500                                       22           484
72           5184                                       24           576
64           4096                                       30           900
78           6084                                       21           441
55           3025                                       26           676
84           7056                                       28           784
67           4489                                       27           729
65           4225                                       19           361
70           4900                                       32           1024

Calculate the mean, range, variance, and standard deviation for the ages of each group.

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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