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4. Standard Deviation and Variance
A teacher recorded the scores on two different quizzes from her statistics class.
The histograms below display the quiz scores, out of 10 points, for each of the 36
students.
Frequency
2
1
7
Frequency
1
4
6
5
0
0 1 2
4
5 6 7 8 9 10 11
Quiz 1 scores
2 3
4 5 6 7 8 9 10 11
Quiz 2 scores
(a) Which quiz, Quiz 1 or Quiz 2, has a larger standard deviation? Explain.
(b) The students took two more quizzes. Quiz 3 was difficult for the students, with
most students scoring low, and Quiz 4 was easy for the students, with most
students scoring high. Each quiz had 10 possible total points. Describe how the
standard deviations for both quizzes might be similar or different, and draw
possible histograms for each quiz.
(c) For their fifth quiz, every student received the same score. What is the standard
deviation for Quiz 5? Explain.
