Question
The average temperature in December in Washington DC from 1993 the 1998 are given as a data set 38,1,44,2,35,643,0,41,0,44.4 . Find the interquartile range of the data set express your answer as a decimal rounded to the nearest 10th.
Answers
GPT-4o mini
To find the interquartile range (IQR) of the given data set, we first need to organize the data in ascending order and then calculate the first quartile (Q1) and the third quartile (Q3).
The given data set is:
38, 1, 44, 2, 35, 643, 0, 41, 0, 44.4
**Step 1: Organize the data in ascending order**
Arranging the data:
0, 0, 1, 2, 35, 38, 41, 44, 44.4, 643
**Step 2: Calculate Q1 and Q3**
- **Finding Q1 (the first quartile)**:
Q1 is the median of the first half of the data (the lower half).
Lower half: 0, 0, 1, 2, 35
The median of this lower half (5 numbers) is the 3rd number:
Q1 = 1
- **Finding Q3 (the third quartile)**:
Q3 is the median of the second half of the data (the upper half).
Upper half: 38, 41, 44, 44.4, 643
The median of this upper half (5 numbers) is the 3rd number:
Q3 = 44
**Step 3: Calculate the interquartile range (IQR)**
IQR = Q3 - Q1
IQR = 44 - 1 = 43
So, the interquartile range of the data set is **43.0** (rounded to the nearest tenth).
The given data set is:
38, 1, 44, 2, 35, 643, 0, 41, 0, 44.4
**Step 1: Organize the data in ascending order**
Arranging the data:
0, 0, 1, 2, 35, 38, 41, 44, 44.4, 643
**Step 2: Calculate Q1 and Q3**
- **Finding Q1 (the first quartile)**:
Q1 is the median of the first half of the data (the lower half).
Lower half: 0, 0, 1, 2, 35
The median of this lower half (5 numbers) is the 3rd number:
Q1 = 1
- **Finding Q3 (the third quartile)**:
Q3 is the median of the second half of the data (the upper half).
Upper half: 38, 41, 44, 44.4, 643
The median of this upper half (5 numbers) is the 3rd number:
Q3 = 44
**Step 3: Calculate the interquartile range (IQR)**
IQR = Q3 - Q1
IQR = 44 - 1 = 43
So, the interquartile range of the data set is **43.0** (rounded to the nearest tenth).