document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201976>Question 1201976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4.	The following data represent the weekly income distribution of guardians who take care of orphan and vulnerable children in Ethiopia. <BR>\n" );
document.write( "200	150	105	150	300	75	60	75	170	75<BR>\n" );
document.write( "150	100	150	500	100	100	120	80	130	150<BR>\n" );
document.write( "400	100	450	150	100	75	75	75	100	150<BR>\n" );
document.write( "150	150	75	100	100	75	75	50	200	400<BR>\n" );
document.write( "100	100	320	100	100	75	100	100	400	250<BR>\n" );
document.write( "100	100	150	75	75	100	200	200	150	160<BR>\n" );
document.write( "200	120	250	80	75	75	200	150	200	165<BR>\n" );
document.write( "150	160	45	45	300	100	70	170	170	220\r<BR>\n" );
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document.write( "a.	Organize the data into 10 class intervals. <BR>\n" );
document.write( "b.	Draw a histogram, frequency polygon , greater than  and  less than cumulative frequency curve<BR>\n" );
document.write( "c.	Describe the nature of the data<BR>\n" );
document.write( "d.	Determine mean and median and discuss the results<BR>\n" );
document.write( "e.	Determine variance and standard deviation<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836584 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836584\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "Spreadsheet software is strongly recommended for this problem.<BR>\n" );
document.write( "I'm using LibreOffice Calc spreadsheet.\r<BR>\n" );
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document.write( "The sorted data looks like this<BR>\n" );
document.write( "45,45,50,60,70<BR>\n" );
document.write( "75,75,75,75,75<BR>\n" );
document.write( "75,75,75,75,75<BR>\n" );
document.write( "75,75,75,75,80<BR>\n" );
document.write( "80,100,100,100,100<BR>\n" );
document.write( "100,100,100,100,100<BR>\n" );
document.write( "100,100,100,100,100<BR>\n" );
document.write( "100,100,100,100,105<BR>\n" );
document.write( "120,120,130,150,150<BR>\n" );
document.write( "150,150,150,150,150<BR>\n" );
document.write( "150,150,150,150,150<BR>\n" );
document.write( "150,160,160,165,170<BR>\n" );
document.write( "170,170,200,200,200<BR>\n" );
document.write( "200,200,200,200,220<BR>\n" );
document.write( "250,250,300,300,320<BR>\n" );
document.write( "400,400,400,450,500\r<BR>\n" );
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document.write( "The block of numbers has 16 rows and 5 columns<BR>\n" );
document.write( "16*5 = 80 values total\r<BR>\n" );
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document.write( "min = 45<BR>\n" );
document.write( "max = 500<BR>\n" );
document.write( "range = max - min = 500-45 = 455\r<BR>\n" );
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document.write( "Divide this into 10 groups<BR>\n" );
document.write( "455/10 = 45.5\r<BR>\n" );
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document.write( "Each group is about 46 units wide.\r<BR>\n" );
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document.write( "The class intervals are:<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Number</TD><TD >Class Interval</TD></tr><tr><TD >1</TD><TD >45 - 91</TD></tr><tr><TD >2</TD><TD >92 - 138</TD></tr><tr><TD >3</TD><TD >139 - 185</TD></tr><tr><TD >4</TD><TD >186 - 232</TD></tr><tr><TD >5</TD><TD >233 - 279</TD></tr><tr><TD >6</TD><TD >280 - 326</TD></tr><tr><TD >7</TD><TD >327 - 373</TD></tr><tr><TD >8</TD><TD >374 - 420</TD></tr><tr><TD >9</TD><TD >421 - 467</TD></tr><tr><TD >10</TD><TD >468 - 514</TD></tr>\n" );
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document.write( "There are 21 values between 45 and 91<BR>\n" );
document.write( "Those values are: <BR>\n" );
document.write( "45,45,50,60,70<BR>\n" );
document.write( "75,75,75,75,75<BR>\n" );
document.write( "75,75,75,75,75<BR>\n" );
document.write( "75,75,75,75,80<BR>\n" );
document.write( "80\r<BR>\n" );
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document.write( "Repeat the same idea for the other class intervals to get this grouped frequency distribution.<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Class Interval</TD><TD >Frequency</TD></tr><tr><TD >45 - 91</TD><TD >21</TD></tr><tr><TD >92 - 138</TD><TD >22</TD></tr><tr><TD >139 - 185</TD><TD >19</TD></tr><tr><TD >186 - 232</TD><TD >8</TD></tr><tr><TD >233 - 279</TD><TD >2</TD></tr><tr><TD >280 - 326</TD><TD >3</TD></tr><tr><TD >327 - 373</TD><TD >0</TD></tr><tr><TD >374 - 420</TD><TD >3</TD></tr><tr><TD >421 - 467</TD><TD >1</TD></tr><tr><TD >468 - 514</TD><TD >1</TD></tr>\n" );
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document.write( "===========================================================\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Use spreadsheet software to create the histogram. <BR>\n" );
document.write( "This is what it looks like<BR>\n" );
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document.write( "Each bar's height is due to the frequency for that specific class interval.<BR>\n" );
document.write( "Example: There are 21 people in the first class interval, which means the left-most bar is 21 units tall.\r<BR>\n" );
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document.write( "I'll let you do the frequency polygon.\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "Each number mentioned is a positive whole number. <BR>\n" );
document.write( "This data is discrete.\r<BR>\n" );
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document.write( "Midpoints between some values make sense (eg: between 100 and 200), but the midpoint between something like 105.11 and 105.12 does not make sense because any currency has a smallest atomic element.\r<BR>\n" );
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document.write( "Part (d)\r<BR>\n" );
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document.write( "To find the mean, add up the values and divide by n = 80 because that's how many values there are in the set.\r<BR>\n" );
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document.write( "Use the spreadsheet software to quickly add the values up (use the command called \"SUM\")<BR>\n" );
document.write( "The values add 11890\r<BR>\n" );
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document.write( "Then 11890/n = 11890/80 = 148.625 is the arithmetic mean.\r<BR>\n" );
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document.write( "The median is found between slot 40 and 41 (because n/2 = 80/2 = 40)<BR>\n" );
document.write( "The values in these slots are 105 and 120. The midpoint of them is (105+120)/2 = 112.5\r<BR>\n" );
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document.write( "mean = 148.625<BR>\n" );
document.write( "median = 112.5\r<BR>\n" );
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document.write( "The mean and median represent the center of the data distribution. <BR>\n" );
document.write( "Since mean > median in this case, the data is skewed to the right (i.e. positively skewed)\r<BR>\n" );
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document.write( "Right-skewed data occurs when you have large outlier(s).\r<BR>\n" );
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document.write( "Notice that the histogram (in part b) has a tail stretched to the right.\r<BR>\n" );
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document.write( "Part (e)\r<BR>\n" );
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document.write( "Use the spreadsheet software to compute the variance. <BR>\n" );
document.write( "Doing so by hand would be tedious busy-work.\r<BR>\n" );
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document.write( "sample variance = 8887.32594936709 approximately\r<BR>\n" );
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document.write( "sample standard deviation = sqrt(sample variance)<BR>\n" );
document.write( "sample standard deviation = sqrt(8887.32594936709)<BR>\n" );
document.write( "sample standard deviation = 94.2726150553123\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "sample variance = 8887.32594936709 <BR>\n" );
document.write( "sample standard deviation = 94.2726150553123<BR>\n" );
document.write( "Each value is approximate\r<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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