Question

W 15. Dissolving Rates of Vitamins A student wanted to know whether Centrum vitamins dissolve faster than the corresponding generic brand. The student used vinegar as a proxy for stomach acid and measured the time (in minutes) it took for a vitamin to completely dissolve. The results are shown next. Centrum Generic Brand 2.73 3.07 3.30 3.35 3.12 6.57 6.23 6.17 7.17 5.77 2.95 2.15 2.67 2.80 2.25 6.73 5.78 5.38 5.25 5.55 2.60 2.57 4.02 3.02 2.15 5.50 6.50 7.42 6.47 6.30 3.03 3.53 2.63 2.30 2.73 6.33 7.42 5.57 6.35 5.92 3.92 2.38 3.25 4.003.63 5.35 7.25 7.58 6.50 4.97 3.02 4.17 4.33 3.85 2.23 7.13 5.98 6.60 5.03 7.18 Source: Amanda A. Sindewald, student at Joliet Junior College (a) Draw side-by-side boxplots for each vitamin type. (b) Which vitamin type has more dispersion? (c) Which vitamin type appears to dissolve faster?

Answer 1

Solution:-

a.) Boxplot for Centrum:-

From the above box plot we can Observe (Approximately):-

Q₁=2.6, Median(Q₂ )=3, Q₃=3.5

So, Interquartile range (IQR)=(Q₃-Q₁)=0.9

Box plot for Generic Brands:-

From the above box plot we can Observe (Approximately):-

Q₁=5.6, Median(Q₂ )=6.3, Q₃=6.8

So, Interquartile range (IQR)=(Q₃-Q₁)=1.2

b.) ans:- from the part (a.)

IQR for Centrum=0.9

IQR for Generic Brands=1.2

so, here

IQR(Generic Brands)>IQR(Centrum)

Hence, Generic Brands has more Dispersion.

Note:-there are another type of dispersion like-Standard deviation and Variance, so we can also find dispersion on that ways.

c.)ans-

Mean time for Centrum=3.05 Min

mean time for Generic brands=6.265 Min

Hence, Centrum will Dissolve Faster.