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 3.1, Problem 25E
To determine

To find:

The mean hourly wage for the given data.

Expert Solution & Answer
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Answer to Problem 25E

Solution:

The mean hourly wage for the given data is $10.20.

Explanation of Solution

Given information:

Hourly Wage at First Job (in Dollars)
Class Frequency
7.508.49 12
8.509.49 50
9.5010.49 48
10.5011.49 45
11.5012.49 34

Definition:

The weighted mean is the mean of a data set in which each data value in the set does not hold the same relative importance.

Formula used:

When upper limit of the first class is not equal to lower limit of second class.

Class mid point is calculated.

The formulae to calculate class mid point is,

Class mid-point =upperlimitofclass+lowerlimitofclass2

Calculation:

Compute the class mid-point of each class.

For the class 7.50-8.49,

Class mid‐point=upper limit of class+lower limit of class2 =7.50+8.492 =7.995

For the class 8.50-9.49,

Class mid‐point=upper limit of class+lower limit of class2 =8.50+9.492 =8.995

For the class 9.50-10.49,

Class mid‐point=upper limit of class+lower limit of class2 =9.50+10.492 =9.995

For the class 10.50-11.49,

Class mid‐point=upper limit of class+lower limit of class2 =10.50+11.492 =10.995

For the class 11.50-12.49,

Class mid‐point=upper limit of class+lower limit of class2 =11.50+12.492 =11.995

Construct the table class mid-point.

Age at time of First Marriage (in Years)
Class Mid-point Frequency
7.508.49 7.995 12
8.509.49 8.995 50
9.5010.49 9.995 48
10.5011.49 10.995 45
11.5012.49 11.995 34

Table 1

Formula used:

The formula to calculate the weighted mean of set of data is,

WeightedMean(x¯)=w1x1+w2x2+...+wnxnw1+w2+...+wn =i=1n(wixi)i=1nwi

Where, xi is the ith data value and wi is the weight of the ith data value and n is the total number of collection.

Calculation:

Substitute. 7.995,8.995,9.995,10.995,11.995 for x1,x2,x3,x4,x5 and 12,50,48,45,34 for w1,w2,w3,w4,w5 respectively in the formula.

WeightedMean(x¯)=w1x1+w2x2+...+wnxnw1+w2+...+wn=(7.995×12)+(8.995×50)+(9.995×48)+(10.995×45)+(11.995×34)12+45+50+48+34=95.94+449.75+479.76+494.775+407.83189=10.20

The mean hourly wage for the given data is $10.20.

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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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