Answer with explanation:
Lowest Variate in distribution =10
Largest Variate in distribution =45
Range =Maximum Variate - Minimum Variate
= 45 -10
=35
→First Quartile
![Q_{1}=15](https://tex.z-dn.net/?f=Q_%7B1%7D%3D15)
→Median =Q= 25
→Third Quartile
![Q_{3}=40](https://tex.z-dn.net/?f=Q_%7B3%7D%3D40)
IQR=Inter Quartile Range
![=Q_{3}-Q_{1}\\\\=40-15\\\\=25](https://tex.z-dn.net/?f=%3DQ_%7B3%7D-Q_%7B1%7D%5C%5C%5C%5C%3D40-15%5C%5C%5C%5C%3D25)
To calculate Outliers
![\rightarrow Q_{3} + 1.5\times IQR=40 +1.5 \times 25\\\\=40 +3.75\\\\=43.75\\\\\rightarrow Q_{1} - 1.5\times IQR\\\\=15 - 1.5 \times 25\\\\=15 - 3.75\\\\=11.25](https://tex.z-dn.net/?f=%5Crightarrow%20Q_%7B3%7D%20%2B%201.5%5Ctimes%20IQR%3D40%20%2B1.5%20%5Ctimes%2025%5C%5C%5C%5C%3D40%20%2B3.75%5C%5C%5C%5C%3D43.75%5C%5C%5C%5C%5Crightarrow%20Q_%7B1%7D%20-%201.5%5Ctimes%20IQR%5C%5C%5C%5C%3D15%20-%201.5%20%5Ctimes%2025%5C%5C%5C%5C%3D15%20-%203.75%5C%5C%5C%5C%3D11.25)
→Numbers below, 11.25 and numbers above 43.75 are outliers.
So, both , 10 and 45 , are outliers.
Therefore, range is not good measure of variability.
→→I QR , is better measure of Variability.
But , Option A,⇒ Either the IQR or the range are good measures of variability because the distribution has an outlier.