Smolts. Smolts are young salmon at a stage when their skin

Problem 1.64

Smolts. Smolts are young salmon at a stage when their skin becomes covered with silvery scales and they start to migrate from freshwater to the sea. The reflectance of a light shined on a smolts skin is a measure of the smolts readiness for the migration. Here are the reflectances, in percents, for a sample of 50 smolts:25 57.6 54.8 63.4 57.0 54.7 42.3 63.6 55.5 33.5 63.3 58.3 42.1 56.1 47.8 56.1 55.9 38.8 49.7 42.3 45.6 69.0 50.4 53.0 38.3 60.4 49.3 42.8 44.5 46.4 44.3 58.9 42.1 47.6 47.9 69.2 46.6 68.1 42.8 45.6 47.3 59.6 37.8 53.9 43.2 51.4 64.5 43.8 42.7 50.9 43.8

(a) Find the mean reflectance for these smolts.

(b) Find the median reflectance for these smolts.

(c) Do you prefer the mean or the median as a measure of center for these data? Give reasons for your preference.

Step by step solution:

Step 1:

(a)

Numerical description of a distribution begins with a measure of its center or average. The two common measures of center are the mean and the median. The mean is the “average value” and the median is the “middle value.”

To find the mean  of a set of observations, add their values and divide by the number of observations. If the n observations are   their mean is

So, the mean reflectance for these smolts is 50.89.