Question

Mary measures the weights of five newly hatched pythons in ounces. John converts Mary’s measurements to grams. There are 28.35 grams in an ounce. Here are Mary’s results:

Python 1 2 3 4 5
Mary 1.13 oz 1.02 oz 1.23 oz 1.06 oz 1.16 oz


Show how to calculate the mean and standard deviation of John’s weights.

Answer 1

John first needs to convert these weights in oz to weight in grams by using the conversion weight given

python 1 = 1.13oz = 1.13*28.35 = 32.04 grams

python 2 = 1.02oz = 1.02*28.35 = 28.92 grams

python 3= 1.23oz = 1.23*28.35 = 34.87 grams

python 4 = 1.06oz = 1.06*28.35 = 30.05 grams

python 5 = 1.16oz = 1.16*28.35 = 32.89 grams

Mean of John's weights = sum of all weights/ number of observations = (32.04+28.92+34.87+30.05+32.89)/5 = 31.75 grams

Standard deviation

Step1: Subtract the mean from each observation and take the square

These values are : (32.04-31.75)^2 , (28.92-31.75)^2 , (34.87-31.75)^2 , (30.05-31.75)^2, (32.89-31.75)^2

These values are: 0.0841 , 8.0089, 9.7344, 2.89, 1.2996

Step 2: Sum them and divide by number of observations

This would be =(0.0841+8.0089+9.7344+2.89+1.2996)/5 = 4.4034

Step 3: Take the square root of result in step 2 to get final answer

Std. deviation =
`√(4.4034)`

Std. deviation = 2.098