Answer with explanation:
Lowest Variate in distribution =10
Largest Variate in distribution =45
Range =Maximum Variate - Minimum Variate
= 45 -10
=35
→First Quartile
[tex]Q_{1}=15[/tex]
→Median =Q= 25
→Third Quartile
[tex]Q_{3}=40[/tex]
IQR=Inter Quartile Range
[tex]=Q_{3}-Q_{1}\\\\=40-15\\\\=25[/tex]
To calculate Outliers
[tex]\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[/tex]
→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.
