Concept explainers
To find: mean, variance and standard deviation of the given data. Then find what percent of data lies within one standard deviation of the mean.
Answer to Problem 41E
Mean
Explanation of Solution
Given information:
The data are 389, 332, 295, 280, 280, 272, 311, 365, 411, 446, 606, 699, 874, 975, 1227, 1572, 1673, 1415, 1269 and 1170.
Concept used:
Steps to find Mean
- For returning home press 2nd “MODE (QUIT)”
- Select 2nd “STAT (LIST)”. Go to the right for “MATH”
- choose the third option “mean(”
- Enter the data in L1 and press enter.
Steps to find Standard Deviation
- For returning home press 2nd “MODE (QUIT)”
- Select 2nd “STAT (LIST)”. Go to the right for “MATH”
- choose the seventh option “stdDev(”
- Enter the data in L1 and press enter.
Also,
Calculation:
Arranging the observations are 272, 280, 280, 295, 311, 332, 365, 389, 411, 446, 606, 699, 874, 975, 1170, 1227, 1269, 1415, 1572, 1673
There are 20 observations.
Using the graphing calculator
Mean
Standard deviation
Variance
Approximately mean
Standard deviation
Variance
Values within one standard deviation of mean can be calculated as:
Mean
Mean
From the given data there are 15 data points which lies between 270.71 and 1215.39 so the required percentage can be calculated as
Hence 75% of the data lies within one standard deviation of the mean.
Chapter 13 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning