High School

Select the correct answer.

The high temperatures at a park for 10 days are: 40, 42, 41, 41, 43, 43, 44, 45, 44, and 45 degrees Fahrenheit. What is the interquartile range of the data?

A. 4.5
B. 5.5
C. 3.5
D. 5
E. 4
F. 3
G. 6.5
H. 6

Answer :

To find the interquartile range (IQR) of the given data set, we need to follow these steps:

1. Organize the Data:
Start by arranging the temperatures in ascending order:
40, 41, 41, 42, 43, 43, 44, 44, 45, 45.

2. Find the Median (Q2):
The median is the middle number in an ordered data set. Since we have 10 numbers, the median will be the average of the 5th and 6th numbers:
[tex]\[
Q2 = \frac{43 + 43}{2} = 43
\][/tex]

3. Divide the Data into Lower and Upper Halves:
The lower half consists of the numbers before the median:
40, 41, 41, 42, 43.
The upper half consists of the numbers after the median:
43, 44, 44, 45, 45.

4. Find Q1 (First Quartile):
The first quartile is the median of the lower half. Since there are 5 numbers, the median is the 3rd number:
[tex]\[
Q1 = 41
\][/tex]

5. Find Q3 (Third Quartile):
The third quartile is the median of the upper half. Similarly, with 5 numbers, the median is the 3rd number:
[tex]\[
Q3 = 44
\][/tex]

6. Calculate the Interquartile Range (IQR):
The interquartile range is the difference between Q3 and Q1:
[tex]\[
IQR = Q3 - Q1 = 44 - 41 = 3
\][/tex]

Therefore, the interquartile range of the data set is 3.