Below are data collected by a researcher who measured the number of hours college students spend interactingwith social media:X3344558Calculate the mean for the sample AND explain what the number tells you (how do you interpret this statistic?)Calculate the standard deviation AND explain what the number tells you (how do you interpret this statistic?)Using z-scores and the unit normal table, calculate the probability of spending 6 hours or MORE interactingwith social media [ p (x > 6)|

Answered: Below are data collected by a…

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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Below are data collected by a researcher who measured the number of hours college students spend interacting
with social media:
X
3
3
4
4
5
5
8
Calculate the mean for the sample AND explain what the number tells you (how do you interpret this statistic?)
Calculate the standard deviation AND explain what the number tells you (how do you interpret this statistic?)
Using z-scores and the unit normal table, calculate the probability of spending 6 hours or MORE interacting
with social media [ p (x > 6)|

Expert Solution

Step 1

From the provided data the mean and standard deviation are computed as,

$M e a n = x = \frac{\sum_{i} x_{i}}{n} = \frac{36}{10} = 3.6$

Thus, the mean is 3.6 which implies that on an average college student spends 3.6 hours interacting with social media.

$S \tan d a r d d e v i a t i o n = s = \sqrt{\frac{\sum_{i} {(x_{i} - \bar{x})}^{2}}{n - 1}} = \sqrt{\frac{{(0 - 3.6)}^{2} + {(2 - 3.6)}^{2} + {(2 - 3.6)}^{2} + {(3 - 3.6)}^{2} {+ (3 - 3.6)}^{2} + {(4 - 3.6)}^{2} {(4 - 3.6)}^{2} + {(5 - 3.6)}^{2} {(5 - 3.6)}^{2} + {(8 - 3.6)}^{2}}{10 - 1}} = \sqrt{4.711111} = 2.170509$

Thus, standard deviation is, 2.170509, which implies the average distance between the data points and the mean. There is an average variation of 2.1705 hours from the mean.

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