Question

5 5 5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 6 6 6 6 6 6 6 6 6 6 6 6.5 6.5 6.5 6.5 6.5 6.5 7 7 7

Using the theoretical distribution in Part II, give answers to 4 decimal places: •

The IQR goes from _____________ to ______________.

• IQR = ___________.

• The 15th percentile is _____________.

• The 85th percentile is ______________.

• The median is ___________.

• The theoretical probability that a randomly chosen pinkie length is more than 6.5 cm = _____________.

• Explain the meaning of the 15th percentile of this distribution.

• Do the data from “Collect the Data” give a close approximation to the theoretical distribution in “Analyze the Data?” In complete sentences, and comparing the result in “Describe the Data” and “Theoretical Distribution”, explain why or why not.

Answer 1

as quartile 1 =0.25*n th value =7.5 th value =5.5

Q3 =0.75*n th value =22.5 th value=6.5

The IQR goes from 5.5 to 6.5

IQR=6.5-5.5=1

15th percentile is 5.5

85th percentile is 6.5

The median is 6

The theoretical probability that a randomly chosen pinkie length is more than 6.5 cm = 3/30=0.1

(15 th percentile means that 15% values in distribtution are below this value.