Question 1176961: 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?
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.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Organize the Data**
First, we need to order the distances from least to greatest:
1, 2, 2, 2, 3, 3, 4, 4, 6, 8, 10, 11, 14, 15, 17, 20
**2. Find the Five-Number Summary**
* **Minimum:** The smallest value (1)
* **First Quartile (Q1):** The median of the lower half of the data (3)
* **Median (Q2):** The middle value of the data (5)
* **Third Quartile (Q3):** The median of the upper half of the data (12.5)
* **Maximum:** The largest value (20)
**3. Create the Box and Whisker Plot**
* Draw a number line that includes the range of your data (from 1 to 20).
* Draw a box from Q1 (3) to Q3 (12.5).
* Draw a vertical line inside the box at the median (5).
* Draw whiskers (lines) from the box to the minimum (1) and maximum (20).
**Interpretation of the Box and Whisker Plot**
* **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.
* **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.
* **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.
* **Outliers:** The plot doesn't show any outliers (unusually distant values). All the data points fall within the whiskers.
**Insights for the Shop Owner**
* **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.
* **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.
* **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.
**Limitations**
* The box and whisker plot doesn't show the number of customers at each distance, only the spread and quartiles of the data.
* The data set is relatively small (only 16 customers), so the plot may not be fully representative of the entire customer base.
Let me know if you want to dive deeper into any specific aspect of the plot or its implications for the shop owner!
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