DECEMBER 2, 2013 MATH 010: 10.1 & 10.2 STATISTICS.

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DECEMBER 2, 2013 MATH 010: 10.1 & 10.2 STATISTICS

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 =

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 = 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.

FREQUENCY DISTRIBUTION ClassesFrequency

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

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.

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 = 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)

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

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

BOX-AND-WHISKERS PLOT Smallest value Largest value Q1Q3 Median Need to know how to create box-and-whiskers plots with any given set of data

WHAT BOX PLOTS TELL YOU

CORRELATION (NOT IN BOOK) A correlation is a relationship between two variables. (poll)(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)(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)(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.

HOW STRONG IS THE CORRELATION?

CORRELATION DOES NOT IMPLY CAUSATION!

QUIZ 1.Interpret the box plot below. What does it say about the distribution of test scores? 2.Find the mean, median, and mode of this set: {0, 1, 2, 2, 3, 3, 3, 4} 3.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?