Question

Calculate the interquartile range of the data set.
{7, 3, 10, 8, 4, 1, 8, 6, 5, 8}

answers below:
4
5
6
7

Answer 1

To calculate the interquartile range (IQR) of the data set \{7, 3, 10, 8, 4, 1, 8, 6, 5, 8\}, follow these steps:

1. **Sort the Data**: First, we need to sort the data in ascending order.
- Sorted data: \{1, 3, 4, 5, 6, 7, 8, 8, 8, 10\}

2. **Determine the Quartiles**:
- The median (Q2) is the middle value. Since there are 10 values (an even number), the median is the average of the 5th and 6th values.
\[
Q2 = \frac{6 + 7}{2} = 6.5
\]

- To find the first quartile (Q1), look at the lower half of the data (the first 5 numbers): \{1, 3, 4, 5, 6\}. The median of this set (Q1) is the 3rd value:
\[
Q1 = 4
\]

- To find the third quartile (Q3), look at the upper half of the data (the last 5 numbers): \{7, 8, 8, 8, 10\}. The median of this set (Q3) is the 3rd value:
\[
Q3 = 8
\]

3. **Calculate the Interquartile Range (IQR)**:
\[
IQR = Q3 - Q1 = 8 - 4 = 4
\]

Thus, the interquartile range of the data set is \( \boxed{4} \).