Calculate the interquartile range of the data set.

Question

{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 \( \boxed{4} \).