Given data is 54, 59, 35, 41, 46, 25, 47, 60, 54, 46, 49, 46, 41, 34, 22
Arranging it in increasing order:
22 25 34 35 41 41 46 46 46 47 49 54 54 59 60
Number of data items, n=15.
Finding Median, First Quartile, and Third Quartile
[tex] Finding\;\;median\\M=\frac{n+1}{2}th\;\;term =\frac{15+1}{2}=8th\;\;term\;\; i.e. \;\;46 [/tex]
22 25 34 35 41 41 46 46 46 47 49 54 54 59 60
Now finding First Quartile from set: 22 25 34 35 41 41 46
Q₁ = middle term i.e. 35
Now finding Third Quartile from set: 46 47 49 54 54 59 60
Q₃ = middle term i.e. 54
So we have Q₁ = 35, M = 46, and Q₃ = 54. Lower bound is 22 and Upper bound is 60.
While drawing the given data on number line and marking First quartile, Median, Third quartile on number line. We can clearly observe that option A matches with given data points.
Hence, option A i.e. Box-plot A is the correct choice.
