Find the IQR for the smolt data.

Question

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 smolt's skin is a measure of the smolt's readiness for the migration. Here are the reflectances, in percents, for a sample of 50 smolts. 57.6 54.9 63.4 57.0 54.8 42.2 63.5 55.6 33.5 63.2 58.4 42.2 56.1 47.9 56.2 56.0 38.9 49.6 42.2 45.7 69.1 50.5 53.1 38.2 60.3 49.2 42.7 44.6 46.4 44.3 58.8 42.2 47.5 47.8 69.3 46.7 68.1 42.7 45.6 47.2 59.6 37.9 53.9 43.2 51.4 64.4 43.9 42.7 50.8 43.8 (a)

Answer 1

Step 1: Order the data from smallest to largest left to right.

 

Step 2: Count in from smallest and biggest numbers 13 numbers.

 

The 13th number in from the left is Q1

 

The 13th number in from the right is Q3

 

Q3-Q1 =IQR

 

We are basically finding the median of the lower half and the median of the upper half of data and then just subtracting the two medians. The lower half median is called quartile 1 and the upper median is called quartile 3.