The image you've uploaded presents a question involving statistical data analysis. Let's break it down and solve each part step by step. Here's the data set provided:

Data (sorted):
38, 40, 41, 45, 48, 48, 50, 50, 51, 51, 52, 52, 53, 54, 54, 55, 55, 55, 56, 57, 58, 59, 59, 59, 62, 62, 63, 64, 65, 66, 67, 69, 69, 71, 77, 78, 78, 79, 79, 79

Part a: Median Number of Calls

The median is the middle value in the ordered data set. Since there are 40 values, the median is the average of the 20th and 21st values.

Part b: First and Third Quartiles

• The first quartile $Q_1$ is the median of the lower half of the data (first 20 values).
• The third quartile $Q_3$ is the median of the upper half of the data (last 20 values).

Part c: First Decile (10th percentile) and Ninth Decile (90th percentile)

• The first decile $D_1$ represents the 10th percentile (approximately the 4th value in the data set).
• The ninth decile $D_9$ represents the 90th percentile (approximately the 36th value).

Part d: 33rd Percentile

The 33rd percentile corresponds to 0.33 times the number of data points, so it's around the 14th value.

Let me calculate these now.Here are the results for each part of the exercise:

• a. Median number of calls: 57.5
• b. First quartile (Q1): 51.75
  Third quartile (Q3): 66.25
• c. First decile (D1, 10th percentile): 47.7
  Ninth decile (D9, 90th percentile): 78.0
• d. 33rd percentile: 53.87

Would you like further explanation or have any questions about these calculations?

Here are 5 related questions to extend your understanding:

1. How would you calculate the interquartile range (IQR)?
2. What is the significance of deciles in statistical data analysis?
3. How can you use percentiles to interpret data distribution?
4. Can you determine the outliers in this data set using quartiles?
5. How would you compute the mean and mode for this data?

Tip: Percentiles help compare individual data points with the entire distribution by showing what percentage of the data falls below a certain value.