Question

What is the IQR of the annual salaries?
1. 36,700
2. 42,090
3. 47,600
4. 50,620
5. 51,930
6. 53,910
7. 56,630
8. 61,050
9. 61,220

Answer 1

To calculate the Interquartile Range (IQR) of the annual salaries, follow these steps:

1. **Order the Data**: The data is already ordered from lowest to highest:
- 36,700
- 42,090
- 47,600
- 50,620
- 51,930
- 53,910
- 56,630
- 61,050
- 61,220

2. **Determine Quartiles**:
- **Count of values**: There are 9 values.
- **Find the median (Q2)**: The median is the middle value; since there are 9 numbers, the median is the 5th value:
- Median \( Q2 = 51,930 \).

3. **Find Q1 (Lower Quartile)**:
- Q1 is the median of the first half of the data (the first four values):
- Values: 36,700, 42,090, 47,600, 50,620.
- Median of these values (2nd and 3rd elements average):
\[
Q1 = \frac{42,090 + 47,600}{2} = \frac{89,690}{2} = 44,845.
\]

4. **Find Q3 (Upper Quartile)**:
- Q3 is the median of the second half of the data (the last four values):
- Values: 51,930, 53,910, 56,630, 61,050, 61,220.
- Median of these values (7th and 8th elements average):
\[
Q3 = \frac{56,630 + 61,050}{2} = \frac{117,680}{2} = 58,840.
\]

5. **Calculate the IQR**:
- IQR = Q3 - Q1:
\[
IQR = 58,840 - 44,845 = 13,995.
\]

Thus, the Interquartile Range (IQR) of the annual salaries is **13,995**.