A Statistics Teacher Gave Her Class a 15 Point Quiz

question 22

Essay

A statistics teacher gave her class a 15 point quiz. The summary statistics for the students'scores are shown in the table at the right.

$\begin{array}{|c|c|}\hline\bar{X} & 10.95 \text {points} \\\hline\text { s} & 2.481 \text {points }\\\hline \text {min} & 4 \\\hline \text {Q1} & 9.5 \\\hline \text {median} & 12 \\\hline \text {Q3 }& 12 \\\hline \text {max } & 15 \\\hline\end{array}$

a. Notice that the median score and the third quartile are the same. Explain how this can be.
b. One student's parent heaped praise on him for scoring 13, saying it was an amazing score. Comment on whether that praise is deserved using the summary statistics as support.
c. To convert these raw scores to a score out of 100, the teacher multiplies each score by six,then adds 10. (We can debate the wisdom of such a strategy later!). What is the median converted score? And the IQR?
d. What are the mean and standard deviation of the converted test scores?

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Definitions:

Cross-Cutting Relations

A geological principle stating that any geologic feature that cuts across another feature must be younger than the feature it cuts.

Inclusions

Pieces of one rock unit that are enclosed within another rock unit, often used in geology to determine the relative age of rock layers.

Original Horizontality

A principle stating that sedimentary rocks are deposited in horizontal or nearly horizontal layers under the action of gravity.

Superposition

A principle that states in an undisturbed sequence of rocks, layers of rock were deposited in order from bottom to top according to their age, with the oldest at the bottom and the youngest at the top.