The following data are the ages (in years) of 24 doctors in a medical group.

30

41

37

46

41

46

53

60

48

37

44

39

Send data to calculator

38

54

31

51

51

44

51

45

44

65

67

57

Send data to Excel)

Construct a box-and-whisker plot (sometimes called a boxplot) by adjusting the *. Use the to plot outliers, if any.

To construct a box-and-whisker plot (boxplot) for the ages of 24 doctors, follow these steps:

1. **Arrange the data in ascending order**:
   
   The given ages are:
   
   \[
   30, 31, 37, 37, 38, 39, 41, 41, 44, 44, 44, 45, 46, 46, 48, 51, 51, 51, 53, 54, 57, 60, 65, 67
   \]

2. **Identify the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum**:
   
   - **Minimum**: \( 30 \)
   - **Q1 (first quartile)**: The 25th percentile. For 24 data points, the position is \(\frac{24}{4} = 6\). The 6th number in the sorted list is \(39\).
   - **Median (Q2)**: The 50th percentile. For 24 data points, the median is the average of the 12th and 13th data points: \( \frac{45 + 46}{2} = 45.5 \).
   - **Q3 (third quartile)**: The 75th percentile. The 18th number in the sorted list is \(51\).
   - **Maximum**: \( 67 \)
   
3. **Find the interquartile range (IQR)**:

   \[
   IQR = Q3 - Q1 = 51 - 39 = 12
   \]
   
4. **Determine outliers**:

   Outliers are any values outside the range \([Q1 - 1.5 \times IQR, Q3 + 1.5 \times IQR]\).

   - Lower bound: \( Q1 - 1.5 \times IQR = 39 - 1.5 \times 12 = 21 \)
   - Upper bound: \( Q3 + 1.5 \times IQR = 51 + 1.5 \times 12 = 69 \)

   Since the data falls between \(30\) and \(67\), there are no outliers.

5. **Boxplot Construction**:

   The key elements for your boxplot are:
   - Minimum: 30
   - Q1: 39
   - Median: 45.5
   - Q3: 51
   - Maximum: 67

Would you like a visualization of this boxplot? I can also send this to Excel or create the graph here. Let me know!

---

Do you have any questions, or would you like more details? Here are 5 related questions to explore:

1. How is the IQR used to identify outliers in a dataset?
2. What happens to a boxplot when there are outliers?
3. Can the median be affected by outliers? Why or why not?
4. What is the significance of the range in statistical data?
5. How do quartiles help in understanding the distribution of data?

**Tip**: Always ensure that your data is sorted before calculating quartiles and constructing a boxplot.

The following data are the ages (in years) of 24 doctors in a medical group. 30, 41, 37, 46, 41, 46, 53, 60, 48, 37, 44, 39, Send data to calculator 38, 54, 31, 51, 51, 44, 51, 45, 44, 65, 67, 57, Send data to Excel. Construct a box-and-whisker plot (sometimes called a boxplot) by adjusting the *. Use the to plot outliers, if any.

This solution demonstrates how to construct a box-and-whisker plot for the ages of 24 doctors. It covers identifying the quartiles (Q1, Q2, Q3), interquartile range (IQR), and determining if any outliers exist. Learn step-by-step how to find the median, quartiles, and calculate the IQR. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation