Question

Listed below are amounts of strontium-90 (in millibecquerels, or mBq) in a simple random sample of baby teeth obtained from residents in a region born after 1979. Use the given data to construct a boxplot and identify the 5-number summary. 121 122 126 131 133 135 136 139 142 144 146 146 148 149 150 157 158 159 162 168 Find the 5-number summary of the data set above.

Answer 1

The given observations in the ascending order are :

121 122 126 131 133 135 136 139 142 144 146 146 148 149 150 157 158 159 162 168

Total number of observations = n = 20

The 5-number summary includes minimum, 1^st quartile (Q₁), median, 3^rd quartile (Q₃) and maximum.

Minimum = 121

Q₁ = ((n + 1) / 4)^th observation

      = 5.25^th observation

      = 5^th observation + (6^th observation - 5^th observation) * 0.25

      = 133 + (135 - 133) * 0.25

      = 133.5

1^st Quartile = 133.5

Median = ((n + 1) / 2)^th observation

             = 10.5^th observation

             = (10^th observation + 11^th observation) / 2

             = (144 + 146) / 2

             = 145

Median = 145

Q₃ = (3 * (n + 1) / 4)^th observation

      = 15.75^th observation

      = 15^th observation + (16^th observation - 15^th observation) * 0.75

      = 150 + (157 - 150) * 0.75

      = 155.25

3^rd Quartile = 155.25

Maximum = 168

The boxplot is given below.