Question

3 the data set and some summary statistics are listed.
11.5 12.3 13.5 15.6 16.7 17.2 18.4 19 19.5 21.5

• mean: 16.52
• standard deviation: 3.11
• median: 16.95
• iqr: 5.5

a. how does adding 5 to each of the values in the data set affect the shape of
the distribution?

b. how does adding 5 to each of the values in the data set affect the measures
of center?

c. how does adding 5 to each of the values in the data set affect the measures
of variability?

Explanation:

a. Adding 5 to each value shifts the distribution right but doesn’t change its shape (e.g., symmetry, skewness).
b. Measures of center (mean, median) increase by 5, as they are affected by additive shifts.
c. Measures of variability (standard deviation, IQR) remain unchanged, as they depend on value differences, not their magnitudes.

Answer:

a. It does not change the shape of the distribution.
b. It increases each measure of center by 5.
c. It does not change the measures of variability.