A certain engineering company hired the following number of Class 1 engineers during the first six months of the past year. (Assume the data represents a sample.)
Number of Month	Engineers Hired
January	1
February	2
March	4
April	2
May	9
June	0
(c)
Compute the first and the third quartiles.
first quartile	
third quartile	
(d)
Compute the z-scores for the months of May and June. (Round your answers to three decimal places.)
May	
June	


To solve this problem, we'll proceed with the following steps:

1. **Compute the first and third quartiles (Q1 and Q3):** 
   - First, sort the data in ascending order.
   - Identify Q1 (the first quartile) and Q3 (the third quartile) using the quartile formulas for a sample data set.

2. **Compute the z-scores for May and June:**
   - Calculate the mean and standard deviation of the data.
   - Use the z-score formula: 

\[
z = \frac{X - \mu}{\sigma}
\]

where:
- \( X \) is the value,
- \( \mu \) is the mean,
- \( \sigma \) is the standard deviation.

Let's perform these calculations step by step.Here are the results:

**(c) First and Third Quartiles:**
- First Quartile (Q1): 1.25
- Third Quartile (Q3): 3.5

**(d) Z-scores for May and June:**
- Z-score for May: 1.861
- Z-score for June: -0.930

These values give insights into how May and June compare to the rest of the data in terms of standard deviations from the mean.

Would you like further details or have any questions? Here are some related questions you might find helpful:

1. How are quartiles calculated for a given data set?
2. What do the first and third quartiles represent in a data set?
3. How can z-scores be used to identify outliers?
4. Why is the standard deviation important when calculating z-scores?
5. How would these quartiles change if another month's data were added?

**Tip:** Quartiles help to understand the distribution of data, showing where the data clusters and how it spreads, while z-scores provide a way to standardize data points relative to the overall data set.

A certain engineering company hired the following number of Class 1 engineers during the first six months of the past year. (Assume the data represents a sample.) Number of Month Engineers Hired: January 1, February 2, March 4, April 2, May 9, June 0. Compute the first and third quartiles. Compute the z-scores for the months of May and June.

Learn how to compute the first and third quartiles and the z-scores for a set of hiring data. This problem covers key concepts in statistics, including quartiles and z-scores, with a step-by-step solution. Suitable for students in Grades 10-12.

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