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q 37 provide graph of both a and b with data not solve also seprate graph of a and b




Here are the two requested graphs:

1. **First and Third Quartiles (Q1 and Q3)**:
   - The top graph shows the cumulative frequency distribution with Q1 and Q3 marked.
   - Q1 (the first quartile) corresponds to an age of approximately **36.00 years**, and Q3 (the third quartile) corresponds to an age of approximately **45.75 years**.

2. **Central 50% of Age Limits**:
   - The bottom graph displays the age distribution of workers with the central 50% of workers falling between **36.00 years** (Q1) and **45.75 years** (Q3), indicated by the red and green vertical lines.

Would you like any further details or adjustments to the graphs?

Here are five related questions:
1. How would you calculate the interquartile range (IQR) from Q1 and Q3?
2. How can you interpret the spread of ages within the central 50% range?
3. What insights can you derive from comparing Q1 and Q3 to the total age distribution?
4. How would the quartiles change if the data distribution were more uniform?
5. Can the same method of interpolation be used for other percentiles?

**Tip:** The interquartile range (IQR) is a useful measure of statistical dispersion and is calculated as \( IQR = Q3 - Q1 \).

For the data given, find graphically (a) the first and third quartiles and (b) the central 50% limit of the age.

Learn how to calculate the first and third quartiles for a given age distribution of workers, along with the central 50% limit. This problem explores key statistical concepts like cumulative frequency and quartile interpolation.

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