Math 243 Quiz 1 Solutions: Descriptive Statistics and Z-scores - Prof. Hao Wang, Quizzes of Probability and Statistics

The solutions to quiz 1 of math 243, focusing on descriptive statistics and z-scores. Topics covered include identifying skewed distributions, calculating z-scores, and interpreting the five number summary. Students will learn how to determine the skewness of a distribution, understand the relationship between the mean and median for skewed distributions, and calculate z-scores to compare data points to a distribution.

Typology: Quizzes

Pre 2010

Uploaded on 09/17/2009

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Quiz 1 Name solutions
Math 243 GTF
April 3, 2009 Disc. Time
1. Suppose we are analyzing data on the yearly incomes of people living in Eugene. Which of the
following best describes the distribution?
(a) ๎˜‡
๎˜†
๎˜„
๎˜…
Skewed right
(b) Skewed left
(c) Symmetric
(d) None of the above
2. The distribution of heights of NBA players is skewed left. If we were to calculate the mean
and median, which of the following would we expect to find?
(a) The mean to be significantly greater than the median.
(b) ๎˜‡
๎˜†
๎˜„
๎˜…
The mean to be significantly less than the median.
(c) The mean to be approximately equal to the median.
(d) None of the above
3. The average adult American consumes 3700 calories per day. If caloric intake of adults in
America is approximately normally distributed with a standard deviation of 250 calories, and
Dan Wang eats 4500 calories per day, what is the z-score of his caloric intake?
z=4500 โˆ’3700
250 = 3.2
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Quiz 1 Name solutions Math 243 GTF April 3, 2009 Disc. Time

  1. Suppose we are analyzing data on the yearly incomes of people living in Eugene. Which of the following best describes the distribution?

(a)

Skewed right (b) Skewed left (c) Symmetric (d) None of the above

  1. The distribution of heights of NBA players is skewed left. If we were to calculate the mean and median, which of the following would we expect to find?

(a) The mean to be significantly greater than the median. (b)

The mean to be significantly less than the median. (c) The mean to be approximately equal to the median. (d) None of the above

  1. The average adult American consumes 3700 calories per day. If caloric intake of adults in America is approximately normally distributed with a standard deviation of 250 calories, and Dan Wang eats 4500 calories per day, what is the z-score of his caloric intake?

z =

  1. The Bayside Tigers football team had the following final scores for their games over the last 2 years.

(a) Make a stem plot of these data. 0 3 3 7 1 4 2 1 1 7 3 2 5 5 4 2 2 5 5 8 9 9 5 6 6 3 7 0 (b) Calculate the five number summary of these data.

min = 3, Q 1 = 21, median = 38. 5 , Q 3 = 48. 5 , max = 70

(c) Is 70 an outlier? No.