Answer:
IQR = 11
Explanation:
- Before we're able to find the IQR, we'll first need to find the median (Q2) and the lower and upper quartiles (Q1 and Q3).
- We must find the median because finding it will allow us to find the lower and upper quartiles, which are the two values we need to find the IQR.
Finding the median:
- First. we need to arrange the data in ascending numerical order.
Thus, the data in ascending numerical order is:
52, 54, 57, 58, 61, 63, 63, 65, 68, 69, 71.
- The median lies in the middle of the data.
- Since there are 11 values in the data set, the median will have 5 values to the left and right of it.
Thus, the median is 63.
Finding Q1:
To find Q1, we find the middle term of all the values below 63.
Since there are two 63s, we find the middle term of 52, 54, 57, 58, and 61.
Because 57 lies in the middle, 57 is Q1.
Finding Q3:
To find Q3, we find the middle term of all the values above 63.
Now we include the other 63 since it's above the median and find the middle term of 63, 65, 68, 69, and 71.
Because 68 lies in the middle, 68 is Q3.
Finding the IQR:
The IQR is the difference of Q3 and Q1.
Since Q1 = 57 and Q3 = 68, we can find the IQR by subtracting 57 from 68:
IQR = 68 - 57
IQR = 11
Therefore, the IQR = 11.