Question

The mass of a whiffle ball varies, usually between 40 and 50 grams. You decide to gather a random sample of whiffle balls and record the mass of each. Your data is displayed in the table below. (Units are grams.) 45.7 44.4 49.2 46.2 45.4 50 46.2 43.3 42 Checksum: 412.4 You would like to describe the variability in whiffle ball mass from your sample. You decide to make several calculations describing the "spread" of the data set. Find the following: a) range b) IQR c) sample standard deviation d) Interpret the standard deviation in this context.

Answer 1

a) Range:
Range = Highest value - Lowest value

Thus,

b) IQR:
IQR = Q₃ - Q₁
First of all, arrange the data in ascending order.
42, 43.3, 44.4, 45.4, 45.7, 46.2, 46.2, 49.2, 50
Then, Q₁ = 44.4 and Q₃ = 46.2

c) Sample Standard Deviation:

Thus,

d) Interpretation of Standard deviation:
Standard deviation here shows that approximately 2.6 units variation or dispersion exists from the mean or expected value.
It can also be interpreted as the variability of the population data