To find the interquartile range (IQR) of the weights of the 10 students, follow these detailed steps:
1. List the weights:
The given weights are 88, 89, 90, 87, 86, 90, 89, 88, 87, and 90.
2. Sort the weights in ascending order:
Arranging these weights in increasing order, we get:
[tex]\[
86, 87, 87, 88, 88, 89, 89, 90, 90, 90
\][/tex]
3. Determine the median of the entire dataset:
The median is the middle value that separates the higher half from the lower half. Since there are 10 weights (an even number), the median is the average of the 5th and 6th values.
[tex]\[
\text{Median} = \frac{88 + 89}{2} = 88.5
\][/tex]
4. Find the first quartile (Q1):
Q1 is the median of the lower half of the dataset. The lower half consists of the first 5 values:
[tex]\[
86, 87, 87, 88, 88
\][/tex]
The median of these values (Q1) is the 3rd value (since there are 5 values):
[tex]\[
Q1 = 87.0
\][/tex]
5. Find the third quartile (Q3):
Q3 is the median of the upper half of the dataset. The upper half consists of the last 5 values:
[tex]\[
89, 89, 90, 90, 90
\][/tex]
The median of these values (Q3) is the 3rd value (since there are 5 values):
[tex]\[
Q3 = 90.0
\][/tex]
6. Calculate the interquartile range (IQR):
The IQR is the difference between the third quartile (Q3) and the first quartile (Q1):
[tex]\[
\text{IQR} = Q3 - Q1 = 90.0 - 87.0 = 3.0
\][/tex]
Therefore, the interquartile range of the weights is 3.
The correct option is O3.
