Vicki measured the length of 8 leaves. The lengths were 10 cm, 12 cm, 15 cm, 15 cm, 19 cm, 11 cm, 18 cm, and 15 cm.
What is the interquartile range of Vicki's data? answer choices are:
a. 1
b. 3
c. 5
d. 6
I chose 5 and it says that 6 is the correct answer. Can you please show me why?
I have Q1 = 11.5 and Q3 = 16.5.
Then 16.5 - 11.5 = 5 (So the IQR = 5)
put them in order:
10, 11, 12, 15,15,15,18,19 8 data
divide them into quarters.
10,11
12,15
15,15
18,16
I agree with you.
I think it is 12,15
To find the interquartile range (IQR), you need to calculate the difference between the first quartile (Q1) and the third quartile (Q3). In this case, Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
Let's order the data in ascending order first:
10 cm, 11 cm, 12 cm, 15 cm, 15 cm, 15 cm, 18 cm, 19 cm.
Now, let's find the median (Q2) of the entire dataset:
10 cm, 11 cm, 12 cm, 15 cm, 15 cm, 15 cm, 18 cm, 19 cm.
So, the median (Q2) is 15 cm.
Next, let's find the median (Q1) of the lower half of the data. The lower half consists of:
10 cm, 11 cm, 12 cm, 15 cm.
Since there is an even number of data points, Q1 is the average of the two middle values:
(11 cm + 12 cm) / 2 = 11.5 cm.
So Q1 is 11.5 cm.
Similarly, let's find the median (Q3) of the upper half of the data. The upper half consists of:
15 cm, 15 cm, 18 cm, 19 cm.
Again, since there is an even number of data points, Q3 is the average of the two middle values:
(15 cm + 18 cm) / 2 = 16.5 cm.
So Q3 is 16.5 cm.
Finally, let's calculate the IQR by subtracting Q1 from Q3:
16.5 cm - 11.5 cm = 5 cm.
Therefore, the correct answer is d. 6 is the correct answer.
To find the interquartile range (IQR) of Vicki's data, you need to first find the first quartile (Q1) and the third quartile (Q3).
Step 1: Start by sorting the data in ascending order:
10 cm, 11 cm, 12 cm, 15 cm, 15 cm, 15 cm, 18 cm, 19 cm.
Step 2: Calculate the position of Q1:
To find Q1, you need to determine the median of the lower half of the data set. Since there are 8 data points, the lower half is the first 4 points. Since there is an even number of data points, you need to find the average of the two middle values.
(11 cm + 12 cm) / 2 = 11.5 cm
So, Q1 = 11.5 cm.
Step 3: Calculate the position of Q3:
To find Q3, you need to determine the median of the upper half of the data set. Again, since there are 8 data points, the upper half is the last 4 points.
(15 cm + 15 cm) / 2 = 15 cm
So, Q3 = 15 cm.
Step 4: Calculate the IQR:
The IQR is the difference between Q3 and Q1.
IQR = Q3 - Q1
IQR = 15 cm - 11.5 cm
IQR = 3.5 cm
Based on the calculations, the correct answer should be 3, not 6. It appears that there may be an error in the answer choices provided.