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Math 010: 10.1 & 10.2 statistics

Math 010: 10.1 & 10.2 statistics. December 2, 2013. 10.1 Organizing data. Know how to make a frequency distribution using a set of data. Set of collected scores on Exam #3 (this is our population ): The range is the difference between the least and greatest values in the set 94 - 14 = 80.

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Math 010: 10.1 & 10.2 statistics

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  1. Math 010: 10.1 & 10.2statistics December 2, 2013

  2. 10.1 Organizing data • Know how to make a frequency distribution using a set of data. • Set of collected scores on Exam #3 (this is our population): • The range is the difference between the least and greatest values in the set • 94 - 14 = 80

  3. 10.1 Frequency distribution • Create a frequency distribution with a class width of 8. • To create intervals, add the class width to the lowest value. • 14 + 8 = 22 so first interval is “14-22” • The next intervals are “23-31”, “32-40”, “41-49”, “50-58”, “59-67”, “68-76”, “77-85”, “86-94” • 9 intervals total, so there are 9 classes.

  4. Frequency distribution

  5. histogram • Question: What percentage of students scored between 86 and 94 on the exam? • 24 is the number of total scores (base). 8/24 = 0.333 = 33.3% • Know how to calculate percentages based on a histogram.

  6. What histograms tell you • Histogram A is skewed to the left, so there are more values on the low end of the range. • Histogram B is skewed to the right, so there are more values on the high end of the range. • Histogram C is a normal distribution, which means the values are mostly near the median.

  7. 10.2 types of averages • Mean: Add all values, then divide the sum by the number of values. Sum of values = 1784 • Mean score = 1784 / 24 = 74.333 • Median: Put values in numerical order, then find the value in the middle of the list. • If there is an even number of values, the median is halfway between the two middle values. • Median score = 77 • Mode: The most commonly occurring value. • Mode score = 94(occurs three times)

  8. Which type of average to use? • What does each type of average tell us? • Which average best represents the set of scores? Mean: 74.3 Median: 77 Mode: 94

  9. Box-and-whiskers plot • Know how to make a box-and-whiskers plot. • First find the median (77) • Now, split the list of values in half. • Q1 is the median of the first half. • Even number of values, so Q1 is halfway between 68 and 70. • Q1 = 69 • Q3 is the median of the second half. • Q3 is halfway between 87 and 87 • Q3 = 87

  10. Box-and-whiskers plot Median Largest value Smallest value Q1 Q3 http://math.andyou.com/tools/boxandwhisker.html Need to know how to create box-and-whiskers plots with any given set of data

  11. What box plots tell you

  12. Correlation (not in book) • A correlation is a relationship between two variables. (poll) • A positive correlation means as one variable increases, the other variable increases • Example: There is a positive correlation between gun ownership and homicide rate in a given state. (link) • This means the higher the rate of gun ownership, the higher the homicide rate. • A negative correlation means as one variable increases, the other variable decreases. • Example: There is a negative correlation between couples’ relationship satisfaction and the frequency of texting about relationship problems. (link) • This means if the frequency of texting about relationship problems is higher, relationship satisfaction is lower, and vice versa. • Correlation does NOT imply causation! • Just because there is a relationship between two variables, it does not mean that one caused the other.

  13. How strong is the correlation? • is called the coefficient of determination. • It shows the strength of correlation (how well it can fit into a linear model) • Between 0 (no correlation) and 1 (total correlation) • Relationships are only considered significant when is greater than 0.9

  14. Correlation does not imply causation! • In this example, there is a negative correlation between highway fatality and lemon imports. • is high, so there is a very strong correlation. • Does this mean that if we import more lemons, there will be fewer highway fatalities?

  15. quiz • Interpret the box plot below. What does it say about the distribution of test scores? • Find the mean, median, and mode of this set:{0, 1, 2, 2, 3, 3, 3, 4} • If there is a negative correlation between hours spent in class and level of satisfaction with the course, what does that mean? What is NOT implied?

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