Glencoe Math Accelerated, Student Edition
Glencoe Math Accelerated, Student Edition
1st Edition
ISBN: 9780076637980
Author: McGraw-Hill Glencoe
Publisher: MCG
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Chapter 10.2, Problem 6IP
To determine

To Find: To find the measures of variability and outliers if any of the given data.

Expert Solution & Answer
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Answer to Problem 6IP

The answer is

  Range=22,Inter-quartilerange=7.75,Variance=39.61andStandarddeviation=6.29

And no outlier exists for the given set of data.

Explanation of Solution

Given information:Number of volunteer hours per month.

Formula used:

  ForRange=HighestvalueLowestvalueFor Inter-Quartile Range=Q3Q1For Variance=i=1n(xi)2nx¯2For Standard Deviation=VarianceForOutliers:DataValue<Q11.5(IQR)orDataValue>Q3+1.5(IQR)

Calculation:

Since, the given data is 38, 43, 36, 37, 32, 37, 29, and 51.

Arranging the data in ascending order

29, 32, 36, 37, 37, 38, 43, 51

Now, the range of the given data is

  Range=5129=22

Also, first and third quartile are

  Q1=(n+14)thobservationQ1=(8+14)thobservationQ1=(94)thobservationQ1=(2.25)thobservationQ1=2ndobservation+0.25(3rdobservation2ndobservation)Q1=32+0.25(3632)Q1=32+2=34

and

  Q3=3(n+14)thobservationQ3=3(8+14)thobservationQ3=3(94)thobservationQ3=(6.75)thobservationQ3=6thobservation+0.75(7thobservation6thobservation)Q3=38+0.75(4338)Q3=38+3.75=41.75

Thus, Inter-quartile range is Q3Q1=41.7534=7.75

Calculation of Mean and Variance

  Mean=SumofallobservationsNumberofobservationsMean=29+32+36+37+37+38+43+518Mean=3038Mean=37.875Variance=i=1n(xi)2nx¯2,wherei=1nxi2n=(29)2+(32)2+(36)2+(37)2+(37)2+(38)2+(43)2+(51)28i=1nxi2n=841+1024+1296+1369+1369+1444+1849+26018i=1nxi2n=117938=1474.125Now,Variance=1474.125(37.875)2Variance=1474.1251434.516Variance=39.61

Calculation of standard deviation

  Standard Deviation=VarianceStandardDeviation=39.61StandardDeviation=6.29

Calculation of Outliers

  DataValue<Q11.5(Interquartilerange)DataValue<341.5×7.75DataValue<3411.625DataValue<22.375

Which is not exist in the given set of data, also

  DataValue>Q3+1.5(Interquartilerange)Data Value>41.75+1.5×7.75DataValue>41.75+11.625DataValue>53.375

No value exists in the given data

Hence, the required measure of variability is

  Range=22,Inter-quartilerange=7.75,Variance=39.61andStandarddeviation=6.29

And no outlier exists for the given set of data.

Chapter 10 Solutions

Glencoe Math Accelerated, Student Edition

Ch. 10.1 - Prob. 11IPCh. 10.1 - Prob. 12IPCh. 10.1 - Prob. 13IPCh. 10.1 - Prob. 14IPCh. 10.1 - Prob. 15IPCh. 10.1 - Prob. 16HPCh. 10.1 - Prob. 17HPCh. 10.1 - Prob. 18HPCh. 10.1 - Prob. 19HPCh. 10.1 - Prob. 20HPCh. 10.1 - Prob. 21HPCh. 10.1 - Prob. 22STPCh. 10.1 - Prob. 23STPCh. 10.1 - Prob. 24STPCh. 10.1 - Prob. 25STPCh. 10.1 - Prob. 26CCRCh. 10.1 - Prob. 27CCRCh. 10.1 - Prob. 28CCRCh. 10.1 - Prob. 29CCRCh. 10.1 - Prob. 30CCRCh. 10.1 - Prob. 31CCRCh. 10.1 - Prob. 32CCRCh. 10.1 - Prob. 33CCRCh. 10.1 - Prob. 34CCRCh. 10.1 - Prob. 35CCRCh. 10.2 - Prob. 1GPCh. 10.2 - Prob. 2GPCh. 10.2 - Prob. 3GPCh. 10.2 - Prob. 4IPCh. 10.2 - Prob. 5IPCh. 10.2 - Prob. 6IPCh. 10.2 - Prob. 7IPCh. 10.2 - Prob. 8IPCh. 10.2 - Prob. 9IPCh. 10.2 - Prob. 10IPCh. 10.2 - Prob. 11IPCh. 10.2 - Prob. 12HPCh. 10.2 - Prob. 13HPCh. 10.2 - Prob. 14HPCh. 10.2 - Prob. 15HPCh. 10.2 - Prob. 16HPCh. 10.2 - Prob. 17HPCh. 10.2 - Prob. 18STPCh. 10.2 - Prob. 19STPCh. 10.2 - Prob. 20STPCh. 10.2 - Prob. 21STPCh. 10.2 - Prob. 22CCRCh. 10.2 - Prob. 23CCRCh. 10.2 - Prob. 24CCRCh. 10.2 - Prob. 25CCRCh. 10.2 - Prob. 26CCRCh. 10.2 - Prob. 27CCRCh. 10.2 - Prob. 28CCRCh. 10.2 - Prob. 29CCRCh. 10.2 - Prob. 30CCRCh. 10.2 - Prob. 31CCRCh. 10.2 - Prob. 32CCRCh. 10.2 - Prob. 33CCRCh. 10.3 - Prob. 1GPCh. 10.3 - Prob. 2GPCh. 10.3 - Prob. 3IPCh. 10.3 - Prob. 4IPCh. 10.3 - Prob. 5IPCh. 10.3 - Prob. 6IPCh. 10.3 - Prob. 7IPCh. 10.3 - Prob. 8IPCh. 10.3 - Prob. 9IPCh. 10.3 - Prob. 10IPCh. 10.3 - Prob. 11HPCh. 10.3 - Prob. 12HPCh. 10.3 - Prob. 13HPCh. 10.3 - Prob. 14HPCh. 10.3 - Prob. 15STPCh. 10.3 - Prob. 16STPCh. 10.3 - Prob. 17STPCh. 10.3 - Prob. 18STPCh. 10.3 - Prob. 19CCRCh. 10.3 - Prob. 20CCRCh. 10.3 - Prob. 21CCRCh. 10.3 - Prob. 22CCRCh. 10.3 - Prob. 23CCRCh. 10.3 - Prob. 24CCRCh. 10.3 - Prob. 25CCRCh. 10.4 - Prob. 1GPCh. 10.4 - Prob. 2GPCh. 10.4 - Prob. 3IPCh. 10.4 - Prob. 4IPCh. 10.4 - Prob. 5IPCh. 10.4 - Prob. 6IPCh. 10.4 - Prob. 7IPCh. 10.4 - Prob. 8IPCh. 10.4 - Prob. 9IPCh. 10.4 - Prob. 10IPCh. 10.4 - Prob. 11HPCh. 10.4 - Prob. 12HPCh. 10.4 - Prob. 13HPCh. 10.4 - Prob. 14HPCh. 10.4 - Prob. 15STPCh. 10.4 - Prob. 16STPCh. 10.4 - Prob. 17CCRCh. 10.4 - Prob. 18CCRCh. 10.4 - Prob. 19CCRCh. 10.4 - Prob. 20CCRCh. 10.4 - Prob. 21CCRCh. 10.4 - Prob. 22CCRCh. 10.4 - Prob. 23CCRCh. 10.4 - Prob. 24CCRCh. 10.4 - Prob. 25CCRCh. 10.4 - Prob. 26CCRCh. 10.4 - Prob. 27CCRCh. 10.5 - Prob. 1GPCh. 10.5 - Prob. 2GPCh. 10.5 - Prob. 3GPCh. 10.5 - Prob. 4GPCh. 10.5 - Prob. 5IPCh. 10.5 - Prob. 6IPCh. 10.5 - Prob. 7IPCh. 10.5 - Prob. 8IPCh. 10.5 - Prob. 9IPCh. 10.5 - Prob. 10IPCh. 10.5 - Prob. 11IPCh. 10.5 - Prob. 12IPCh. 10.5 - Prob. 13IPCh. 10.5 - Prob. 14IPCh. 10.5 - Prob. 15IPCh. 10.5 - Prob. 16IPCh. 10.5 - Prob. 17HPCh. 10.5 - Prob. 18HPCh. 10.5 - Prob. 19HPCh. 10.5 - Prob. 20HPCh. 10.5 - Prob. 21STPCh. 10.5 - Prob. 22STPCh. 10.5 - Prob. 23STPCh. 10.5 - Prob. 24STPCh. 10.5 - Prob. 25CCRCh. 10.5 - Prob. 26CCRCh. 10.5 - Prob. 27CCRCh. 10.5 - Prob. 28CCRCh. 10.5 - Prob. 29CCRCh. 10.5 - Prob. 30CCRCh. 10.5 - Prob. 31CCRCh. 10.5 - Prob. 32CCRCh. 10.5 - Prob. 33CCRCh. 10.5 - Prob. 34CCRCh. 10.5 - Prob. 35CCRCh. 10.6 - Prob. 1GPCh. 10.6 - Prob. 2GPCh. 10.6 - Prob. 3GPCh. 10.6 - Prob. 4GPCh. 10.6 - Prob. 5GPCh. 10.6 - Prob. 6GPCh. 10.6 - Prob. 7GPCh. 10.6 - Prob. 8GPCh. 10.6 - Prob. 9GPCh. 10.6 - Prob. 10GPCh. 10.6 - Prob. 11GPCh. 10.6 - Prob. 12IPCh. 10.6 - Prob. 13IPCh. 10.6 - Prob. 14IPCh. 10.6 - Prob. 15IPCh. 10.6 - Prob. 16IPCh. 10.6 - Prob. 17IPCh. 10.6 - Prob. 18IPCh. 10.6 - Prob. 19IPCh. 10.6 - Prob. 20IPCh. 10.6 - Prob. 21IPCh. 10.6 - Prob. 22IPCh. 10.6 - Prob. 23IPCh. 10.6 - Prob. 24IPCh. 10.6 - Prob. 25IPCh. 10.6 - Prob. 26IPCh. 10.6 - Prob. 27IPCh. 10.6 - Prob. 28IPCh. 10.6 - Prob. 29IPCh. 10.6 - Prob. 30IPCh. 10.6 - Prob. 31IPCh. 10.6 - Prob. 32IPCh. 10.6 - Prob. 33IPCh. 10.6 - Prob. 34IPCh. 10.6 - Prob. 35IPCh. 10.6 - Prob. 36IPCh. 10.6 - Prob. 37IPCh. 10.6 - Prob. 38IPCh. 10.6 - Prob. 39IPCh. 10.6 - Prob. 40IPCh. 10.6 - Prob. 41HPCh. 10.6 - Prob. 42HPCh. 10.6 - Prob. 43HPCh. 10.6 - Prob. 44HPCh. 10.6 - Prob. 45STPCh. 10.6 - Prob. 46STPCh. 10.6 - Prob. 47STPCh. 10.6 - Prob. 48STPCh. 10.6 - Prob. 49CCRCh. 10.6 - Prob. 50CCRCh. 10.6 - Prob. 51CCRCh. 10.6 - Prob. 52CCRCh. 10.6 - Prob. 53CCRCh. 10.6 - Prob. 54CCRCh. 10.6 - Prob. 55CCRCh. 10.6 - Prob. 56CCRCh. 10.6 - Prob. 57CCRCh. 10.6 - Prob. 58CCRCh. 10.6 - Prob. 59CCRCh. 10.7 - Prob. 1GPCh. 10.7 - Prob. 2GPCh. 10.7 - Prob. 3GPCh. 10.7 - Prob. 4GPCh. 10.7 - Prob. 5IPCh. 10.7 - Prob. 6IPCh. 10.7 - Prob. 7IPCh. 10.7 - Prob. 8IPCh. 10.7 - Prob. 9IPCh. 10.7 - Prob. 10IPCh. 10.7 - Prob. 11IPCh. 10.7 - Prob. 12IPCh. 10.7 - Prob. 13IPCh. 10.7 - Prob. 14IPCh. 10.7 - Prob. 15HPCh. 10.7 - Prob. 16HPCh. 10.7 - Prob. 17HPCh. 10.7 - Prob. 18STPCh. 10.7 - Prob. 19STPCh. 10.7 - Prob. 20STPCh. 10.7 - Prob. 21STPCh. 10.7 - Prob. 22CCRCh. 10.7 - Prob. 23CCRCh. 10.7 - Prob. 24CCRCh. 10.7 - Prob. 25CCRCh. 10.7 - Prob. 26CCRCh. 10.7 - Prob. 27CCRCh. 10.7 - Prob. 28CCRCh. 10.7 - Prob. 29CCRCh. 10.7 - Prob. 30CCRCh. 10.7 - Prob. 31CCRCh. 10.7 - Prob. 32CCRCh. 10.7 - Prob. 33CCRCh. 10.7 - Prob. 34CCRCh. 10.7 - Prob. 35CCRCh. 10.7 - Prob. 36CCRCh. 10.7 - Prob. 37CCRCh. 10.7 - Prob. 38CCRCh. 10.8 - Prob. 1GPCh. 10.8 - Prob. 2GPCh. 10.8 - Prob. 3GPCh. 10.8 - Prob. 4GPCh. 10.8 - Prob. 5GPCh. 10.8 - Prob. 6IPCh. 10.8 - Prob. 7IPCh. 10.8 - Prob. 8IPCh. 10.8 - Prob. 9IPCh. 10.8 - Prob. 10IPCh. 10.8 - Prob. 11IPCh. 10.8 - Prob. 12IPCh. 10.8 - Prob. 13IPCh. 10.8 - Prob. 14IPCh. 10.8 - Prob. 15IPCh. 10.8 - Prob. 16IPCh. 10.8 - Prob. 17IPCh. 10.8 - Prob. 18HPCh. 10.8 - Prob. 19HPCh. 10.8 - Prob. 20HPCh. 10.8 - Prob. 21HPCh. 10.8 - Prob. 22HPCh. 10.8 - Prob. 23STPCh. 10.8 - Prob. 24STPCh. 10.8 - Prob. 25STPCh. 10.8 - Prob. 26STPCh. 10.8 - Prob. 27CCRCh. 10.8 - Prob. 28CCRCh. 10.8 - Prob. 29CCRCh. 10.8 - Prob. 30CCRCh. 10.8 - Prob. 31CCRCh. 10.8 - Prob. 32CCRCh. 10.8 - Prob. 33CCRCh. 10.8 - Prob. 34CCRCh. 10.8 - Prob. 35CCRCh. 10.8 - Prob. 36CCRCh. 10 - Prob. 1CRCh. 10 - Prob. 2CRCh. 10 - Prob. 3CRCh. 10 - Prob. 4CRCh. 10 - Prob. 5CRCh. 10 - Prob. 6CRCh. 10 - Prob. 7CRCh. 10 - Prob. 8CRCh. 10 - Prob. 9CRCh. 10 - Prob. 10CRCh. 10 - Prob. 11CRCh. 10 - Prob. 12CRCh. 10 - Prob. 13CRCh. 10 - Prob. 14CRCh. 10 - Prob. 15CRCh. 10 - Prob. 16CRCh. 10 - Prob. 17CRCh. 10 - Prob. 18CRCh. 10 - Prob. 19CRCh. 10 - Prob. 20CRCh. 10 - Prob. 21CRCh. 10 - Prob. 22CRCh. 10 - Prob. 23CRCh. 10 - Prob. 24CRCh. 10 - Prob. 25CRCh. 10 - Prob. 26CRCh. 10 - Prob. 27CRCh. 10 - Prob. 28CRCh. 10 - Prob. 29CRCh. 10 - Prob. 30CR
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