Answer:
B
Step-by-step explanation:
Option B) The IQR is the best measure of variability and equals 4, is the appropriate answer.
Step-by-step explanation:
The range (highest value minus lowest value) is a measure of variability, but it can be sensitive to outliers, which are extreme values that are significantly different from the other values. In this case, the highest value (19) is significantly different from the other values, so the range would not be the best measure of variability.
The mean (average) is also a measure of variability, but it can also be sensitive to outliers. In this case, the mean would be approximately 11.0, but again, the value of 19 is significantly different from the other values, so the mean would not be the best measure of variability.
The median (middle value) is a more robust measure of variability, as it is not affected by outliers. In this case, the median is 10, which gives some indication of the typical or central value of the data.
The interquartile range (IQR) is another robust measure of variability, which is defined as the difference between the third quartile (Q3) and the first quartile (Q1). The quartiles divide the data into quarters, so that 25% of the data falls below Q1, 50% falls below the median, and 75% falls below Q3. In this case, Q1 is 7 and Q3 is 11, so the IQR is 11 - 7 = 4. The IQR gives some indication of the spread of the middle 50% of the data, and is not affected by outliers. Therefore, the appropriate measure of variability for this data is the IQR, and its value is 4.