Question

what is the interquartile range of the dataset {71,74,81,78,67,69,64}

Answer 1

To find the interquartile range (IQR) of the dataset {71, 74, 81, 78, 67, 69, 64}, follow these steps:

1. **Sort the data**: First, we need to arrange the data in ascending order.
\[
\{64, 67, 69, 71, 74, 78, 81\}
\]

2. **Find the quartiles**:
- The median (Q2) of the dataset is the middle value. Since there are 7 data points, the median is the 4th value.
\[
Q2 = 71
\]

- To find the first quartile (Q1), we look at the lower half of the data: {64, 67, 69}. The median of this lower half is the second value (67).
\[
Q1 = 67
\]

- To find the third quartile (Q3), we look at the upper half of the data: {74, 78, 81}. The median of this upper half is the second value (78).
\[
Q3 = 78
\]

3. **Calculate the interquartile range**:
\[
IQR = Q3 - Q1 = 78 - 67 = 11
\]

Thus, the interquartile range of the dataset is **11**.