A Statistics Teacher Gave Her Class a 15 Point Quiz

question 17

Essay

A statistics teacher gave her class a 15 point quiz. The summary statistics for the students'
scores are shown in the table. $$\begin{array} { | c | c | } \hline \bar { x } & 10.95 \text { points } \\\hline s & 2.481 \text { points } \\\hline \text { min } & 4 \\\hline \text { Q1 } & 9.5 \\\hline \text { median } & 12 \\\hline \text { Q3 } & 12 \\\hline \max & 15 \\\hline\end{array}$$
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:

Chaos Theory

A field of study in mathematics and science that deals with complex systems whose behavior is highly sensitive to slight changes in conditions, leading to unpredictability.

Unknowable Complexity

A term describing situations or systems that are so complex they cannot be fully understood or predicted.

Random Patterns

Patterns that have no predictable order or sequence, appearing without any systematic arrangement.

Scientific Management

A management theory that examines and combines different work processes to enhance economic effectiveness and increase worker productivity.