Question

what is the interquartile range iqr of the data set represented by this box plot apex. 3,14,25,37,49

A)11
B)23
C)12
D)49

Answer 1

To determine the interquartile range (IQR) from the given data set represented by the box plot, we first need to identify the quartiles.

Given the data set: 3, 14, 25, 37, 49.

1. **Find Q1 (the first quartile)**: This is the median of the first half of the data. The first half of the data is 3, 14 (the numbers before the overall median).
- Q1 = (3 + 14) / 2 = 8.5

2. **Find Q3 (the third quartile)**: This is the median of the second half of the data. The second half of the data is 37, 49 (the numbers after the overall median).
- Q3 = (37 + 49) / 2 = 43

3. **Calculate the IQR**:
- IQR = Q3 - Q1
- IQR = 43 - 8.5 = 34.5

However, upon checking, it seems that Q1 and Q3 were calculated incorrectly. The actual quartiles for the dataset of 5 numbers is determined differently:

- The median (Q2) in this case is 25 (the middle number).
- Q1 (the median of the lower half, which contains 3, 14) is simply 14.
- Q3 (the median of the upper half, which contains 37, 49) is simply 37.

Now, calculate the correct IQR:
- IQR = Q3 - Q1 = 37 - 14 = 23.

Thus, the correct answer from the options provided is:

**B) 23**.