The problem in the image involves constructing a correct stem-and-leaf plot, calculating quartiles (Q1, Q2, Q3), and finding the interquartile range (IQR) for the given data set:

The recovery times (in days) for 11 individuals are:
$45, 52, 38, 60, 65, 48, 50, 48, 63, 58, 62$

Steps to solve:

1. Stem-and-leaf plot: This type of plot organizes data based on the leading digits (stems) and trailing digits (leaves). Let's sort the data first: $38, 45, 48, 48, 50, 52, 58, 60, 62, 63, 65$

The stems will be the tens digits (3, 4, 5, 6), and the leaves will be the ones digits (units).

• Stem 3: 8
• Stem 4: 5, 8, 8
• Stem 5: 0, 2, 8
• Stem 6: 0, 2, 3, 5

2. Quartiles:

   • Q2 (median) is the middle value of the data set. Since there are 11 values, the 6th value is the median: $Q_2 = 52$
   • Q1 (lower quartile) is the median of the lower half of the data (first 5 values: 38, 45, 48, 48, 50). The middle value of this set is: $Q_1 = 48$
   • Q3 (upper quartile) is the median of the upper half of the data (last 5 values: 58, 60, 62, 63, 65). The middle value of this set is: $Q_3 = 62$

3. Interquartile Range (IQR): $IQR = Q_3 - Q_1 = 62 - 48 = 14$

Answer comparison:

Now, we compare this with the options provided:

• Option A has $Q_1 = 48, Q_2 = 58, Q_3 = 62$, and $IQR = 14$. The stem-and-leaf plot also matches the correct data.
• Therefore, the correct answer is A.

Would you like further details or explanations?

Related Questions:

1. How do you calculate quartiles for larger datasets?
2. What are the advantages of using stem-and-leaf plots?
3. Can the IQR ever be negative, and why?
4. How do outliers affect the quartile calculation?
5. What are other common measures of variability besides IQR?

Tip:

Always sort your data before calculating quartiles or creating stem-and-leaf plots for accuracy.