Beginning Statistics, 2nd Edition
Beginning Statistics, 2nd Edition
2nd Edition
ISBN: 9781932628678
Author: Carolyn Warren; Kimberly Denley; Emily Atchley
Publisher: Hawkes Learning Systems
Question
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Chapter 3.2, Problem 37E
To determine

To find:

The approximate sample variance of gas price corresponding to the given frequency distribution.

Expert Solution & Answer
Check Mark

Answer to Problem 37E

Solution:

The approximate sample variance of gas price corresponding to the given frequency distribution is 0.004.

Explanation of Solution

Given:

The following frequency distribution gives the gas price frequency distribution.

Gas Prices
Price in Dollars per Gallon Frequency
3.553.59 1
3.603.64 3
3.653.69 5
3.703.74 6
3.753.79 2
3.803.84 1

Formula used:

s=n[(fixi2)][(fixi)]2n(n1),

wheren=samplesize,fi=frequencyofclassi,andxi=midpointofclassi.

Class mid-point =upperlimitofclass+lowerlimitofclass2

Sample size=fi=sumoffrequencies.

Variance=s2

Calculation:

Add the frequencies to calculate n.

n=fi=1+3+5+6+2+1=18

Construct the following table to compute the standard deviation corresponding to the given frequency distribution. Use formula of class midpoint to calculate xi in the table.

Class xi fi xi2 fi×xi fi×xi2
3.553.59 3.55+3.592=3.57 1 3.572=12.7449 1×3.57=3.57 1×12.7449=12.7449
3.603.64 3.60+3.642=3.62 3 3.622=13.1044 3×3.62=10.86 3×13.1044=39.3132
3.653.69 3.65+3.692=3.67 5 3.672=13.4689 5×3.67=18.35 5×13.4689=67.3445
3.703.74 3.70+3.742=3.72 6 3.722=13.8384 6×3.72=22.32 6×13.8334=83.0304
3.753.79 3.75+3.792=3.77 2 3.772=14.2129 2×3.77=7.54 2×14.2129=28.4258
3.803.84 3.80+3.842=3.82 1 3.822=14.5924 1×3.82=3.82 1×14.5924=14.5924
n=fi=18 (fixi)=66.46 (fixi2)=245.4512

Substitute 18 for n, 66.46 for (fixi), and 245.4512 for (fixi2) in the given formula to calculate the standard deviation.

s=n[(fixi2)][(fixi)]2n(n1)=18×245.4512(66.46)218×17=1.193080.06

Square the value of s to calculate the variance.

s2=(0.06)2=0.00360.04

The approximate sample variance for the given frequency distribution is 0.004.

Conclusion:

Thus, the approximate sample variance of gas price corresponding to the given frequency distribution is 0.004.

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Chapter 3 Solutions

Beginning Statistics, 2nd Edition

Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.CR - Prob. 1CRCh. 3.CR - Prob. 2CRCh. 3.CR - Prob. 3CRCh. 3.CR - Prob. 4CRCh. 3.CR - Prob. 5CRCh. 3.CR - Prob. 6CRCh. 3.CR - Prob. 7CRCh. 3.CR - Prob. 8CRCh. 3.CR - Prob. 9CRCh. 3.CR - Prob. 10CRCh. 3.CR - Prob. 11CRCh. 3.CR - Prob. 12CRCh. 3.CR - Prob. 13CRCh. 3.CR - Prob. 14CRCh. 3.CR - Prob. 15CRCh. 3.PA - Prob. 1PCh. 3.PA - Prob. 2PCh. 3.PA - Prob. 3PCh. 3.PA - Prob. 4PCh. 3.PA - Prob. 5PCh. 3.PA - Prob. 6PCh. 3.PA - Prob. 7PCh. 3.PA - Prob. 8PCh. 3.PA - Prob. 9PCh. 3.PA - Prob. 10PCh. 3.PB - Prob. 1PCh. 3.PB - Prob. 2PCh. 3.PB - Prob. 3PCh. 3.PB - Prob. 4P
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