document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176961>Question 1176961</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A shop owner took information from customers about how many miles they lived from his store: 14,6,3,2,4,15,11,8,17,2,1,3,4,10,2,20 Draw a box and whisker plot?<BR>\n" );
document.write( "Discuss this information shown on the box and whisker plot as it relates to the information the owner was looking for ie: distance his customers travelled to get to his store. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850545 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Organize the Data**\r<BR>\n" );
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document.write( "First, we need to order the distances from least to greatest:\r<BR>\n" );
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document.write( "1, 2, 2, 2, 3, 3, 4, 4, 6, 8, 10, 11, 14, 15, 17, 20\r<BR>\n" );
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document.write( "**2. Find the Five-Number Summary**\r<BR>\n" );
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document.write( "* **Minimum:** The smallest value (1)<BR>\n" );
document.write( "* **First Quartile (Q1):** The median of the lower half of the data (3)<BR>\n" );
document.write( "* **Median (Q2):** The middle value of the data (5)<BR>\n" );
document.write( "* **Third Quartile (Q3):** The median of the upper half of the data (12.5)<BR>\n" );
document.write( "* **Maximum:** The largest value (20)\r<BR>\n" );
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document.write( "**3. Create the Box and Whisker Plot**\r<BR>\n" );
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document.write( "* Draw a number line that includes the range of your data (from 1 to 20).<BR>\n" );
document.write( "* Draw a box from Q1 (3) to Q3 (12.5).<BR>\n" );
document.write( "* Draw a vertical line inside the box at the median (5).<BR>\n" );
document.write( "* Draw whiskers (lines) from the box to the minimum (1) and maximum (20).\r<BR>\n" );
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document.write( "**Interpretation of the Box and Whisker Plot**\r<BR>\n" );
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document.write( "* **Spread:** The plot visually shows the spread of the data. We can see that the distances customers travel vary quite a bit, from just 1 mile to 20 miles.<BR>\n" );
document.write( "* **Median:** The line inside the box represents the median distance traveled, which is 5 miles. This means that half of the customers travel 5 miles or less to reach the store.<BR>\n" );
document.write( "* **Interquartile Range (IQR):** The box itself represents the interquartile range, which contains the middle 50% of the data. In this case, the IQR is from 3 to 12.5 miles, indicating that a significant portion of the customers travel within this range.<BR>\n" );
document.write( "* **Outliers:** The plot doesn't show any outliers (unusually distant values). All the data points fall within the whiskers.\r<BR>\n" );
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document.write( "**Insights for the Shop Owner**\r<BR>\n" );
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document.write( "* **Customer Reach:** The plot helps the owner understand how far customers are willing to travel to visit the store. Most customers seem to come from within a 12.5-mile radius.<BR>\n" );
document.write( "* **Marketing:** The owner could use this information to target marketing efforts. For example, they might focus on areas within a 5-mile radius where most of their customers live.<BR>\n" );
document.write( "* **Delivery Service:** If the owner is considering offering a delivery service, the plot shows that most customers are located within a reasonable distance for deliveries.\r<BR>\n" );
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document.write( "**Limitations**\r<BR>\n" );
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document.write( "* The box and whisker plot doesn't show the number of customers at each distance, only the spread and quartiles of the data.<BR>\n" );
document.write( "* The data set is relatively small (only 16 customers), so the plot may not be fully representative of the entire customer base.\r<BR>\n" );
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document.write( "Let me know if you want to dive deeper into any specific aspect of the plot or its implications for the shop owner! </SPAN>\n" );
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