Statistical Reasoning for everyday life Intro to Probability and Statistics Mr. Spering – Room 113

4.1 Measures of Central Tendency MEAN: The mean is most commonly called the average. It is found by finding a sum of set of values and then dividing by the number of data within that set. MEAN =

4.1 Measures of Central Tendency MEAN: Find the mean of the following data set. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13. MEAN = SUM: 15+13+9+9+7+1+11+10+13+1+13 = 102 MEAN = 102 ∕11 = ≈ 9.3

4.1 Measures of Central Tendency MEDIAN: The median is the value exactly in the middle of the data set (possibly halfway between the middle values of the number of values is even). It is found by first sorting the data ordinally, according to data values and finding the middle value.

4.1 Measures of Central Tendency MEDIAN: Find the median of the following data set. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13. Sort data: 1, 1, 7, 9, 9, 10, 11, 13, 13, 13, 15 Find the middle number: MEDIAN: 10

4.1 Measures of Central Tendency MODE: Most common number in a distribution. {Data set may have one mode, more than one mode, or no mode}

4.1 Measures of Central Tendency MODE: Find the mode of the following data set. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13. Most repeated number? MODE = 13

4.1 Measures of Central Tendency Rounding Rule: State your answers with one more decimal place of precision than is found in the raw data. i.e. Find the mean of 2, 3, 5 is 3⅓, which is 3.3 When in doubt at any other time in class round to the nearest one hundredth of questioned value. i.e. Find index value of reference value 0.15 compared to new value of 1.455 970.00

4.1 Measures of Central Tendency OUTLIER: An outlier in a data set is a value that is much higher or lower than almost all other value. i.e. Is there an outlier? Quiz grades: 9, 9, 9, 9, 8, 9, 9, 7, 10, 10, 11, 10, 8, 9, 9, 10, 3, 7, 8, 8, 9, 10 YES: 3 is much lower than most of the data

4.1 Measures of Central Tendency How does an outlier affect Central Tendency? Measure Takes every value into account? Affected by Outliers? Advantages MEAN Yes Commonly understood, works well with many statistical methods MEDIAN No (remember must count values) No When there are outliers may be more representative of an “average” than the mean MODE Most appropriate for data at the nominal level of measurement

4.1 Measures of Central Tendency WEIGHTED MEAN: A weighted mean accounts for variation in the relative importance of data values. Each data value is assigned a weight, and the weighted mean is: Weighted Mean =

4.1 Measures of Central Tendency WEIGHTED MEAN: Weighted Mean = i.e. Your class average! Classwork/Homework/Participation 20% Quizzes/Tests 80% For example: Classwork/Homework/Participation 14/20 = 70.0% Quizzes/Tests 45/50 = 90.0% Final Average: 0.20(70.0) + 0.80(90.0) = 86%

4.1 Measures of Central Tendency Algebraic Form Definition Sum of all values Mean of an entire population. Weighted Mean Means with More Mathematical Notation

4.1 Measures of Central Tendency GOOD LUCK !!!!!!!

4.1 Measures of Central Tendency What are the mean, median, and mode of the data in the following sample? 7, 16, 1, 16, 13, 16, 11, 16, 9, 15 Mean: 12 Median: 14 Mode: 16

4.1 Measures of Central Tendency HW: pg 154 # 2- 12 all and 21-35 odd