Tom observed how many times his dog jumped whenever he met a new person. Use the data set below to determine the interquartile Range for the number of times that Toms dog jumped. 1,1,1,2,2,2,3,3,4,5,5
A. 1.5
B. 4
C. 2.5 My answer
D. 3
your answer is D
you need to know the definition of the interquartile range.
Given an even 2n or odd 2n+1 number of values
first quartile Q1 = median of the n smallest values
third quartile Q3 = median of the n largest values
The interquartile range = Q3-Q1
Your data set (1,1,1,2,2,2,3,3,4,5,5) has 11 = 2*5+1 values
The median of the bottom five is 1
The median of the top five is 4
So the interquartile range is 4-1 = 3
The Interquartile Range (IQR) measures the spread or dispersion of a dataset. To calculate the IQR, we first need to find the first quartile (Q1) and the third quartile (Q3).
To find Q1, we divide the dataset into two halves and find the median of the lower half. In this case, the lower half is 1,1,1,2,2,2. The median of this lower half is 1.5.
To find Q3, we divide the dataset into two halves and find the median of the upper half. In this case, the upper half is 3,3,4,5,5. The median of this upper half is 4.
Now, we can calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 4 - 1.5 = 2.5
Therefore, the correct answer is C. 2.5.
To determine the interquartile range for the number of times Tom's dog jumped, we first need to find the first quartile (Q1) and the third quartile (Q3) of the data set.
1. Arrange the data set in ascending order: 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5.
2. Find the median (Q2) of the data set, which is the middle value. In this case, Q2 is equal to the fifth value, which is 2.
3. Divide the data set into two halves. The first half includes the values lower than Q2, and the second half includes the values greater than Q2.
First Half: 1, 1, 1, 2, 2
Second Half: 2, 3, 3, 4, 5, 5
4. Find the median of the first half (Q1). Since there are an even number of values, take the average of the two middle values, which are 1 and 2. Therefore, Q1 is equal to (1 + 2) / 2 = 1.5.
5. Find the median of the second half (Q3). Again, there are an even number of values, so take the average of the two middle values, which are 3 and 4. Therefore, Q3 is equal to (3 + 4) / 2 = 3.5.
6. Now, we can calculate the interquartile range (IQR). IQR is equal to Q3 minus Q1, so IQR = 3.5 - 1.5 = 2.
Therefore, the correct answer is C. 2.5.