Question

71,74,81,78,67,69,64 The interquartile range of the new dataset is ____ it changed by ____

Answer 1

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

1. **Sort the dataset**:
\[
64, 67, 69, 71, 74, 78, 81
\]

2. **Find the median (Q2)**:
- The dataset has 7 numbers. The median (middle value) is the 4th number:
\[
Q2 = 71
\]

3. **Find the first quartile (Q1)**:
- Q1 is the median of the first half of the data (numbers before the median):
\[
64, 67, 69 \quad \text{(first half)}
\]
- The median of these three numbers (the second number) is:
\[
Q1 = 67
\]

4. **Find the third quartile (Q3)**:
- Q3 is the median of the second half of the data (numbers after the median):
\[
74, 78, 81 \quad \text{(second half)}
\]
- The median of these three numbers (the second number) is:
\[
Q3 = 78
\]

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

Now, regarding the statement "it changed by ____", we would need a previous dataset to compare the current IQR of 11 with that of the previous dataset.

If you have a previous dataset or the previous IQR value, please provide that so we can calculate the change.