Statistics 5/19/2019

Introduction Using statistics is a helpful way to study different situations. Today I will demonstrate how to find the mean, median, and mode of a set of numbers. 5/19/2019

Topics of Discussion The mean (or average) is found by taking the sum of the numbers and then dividing by how many numbers you added together. The number that occurs most frequently is the mode. When the numbers are arranged in numerical order, the middle one is the median. 5/19/2019

Topic One The mean (or average) is found by adding all the numbers and then dividing by how many numbers you added together. Example: 3,4,5,6,7 3+4+5+6+7= 25 25 divided by 5 = 5 The mean is 5 5/19/2019

Topic Two The number that occurs most frequently is the mode. Example: 2,2,2,4,5,6,7,7,7,7,8 The number that occurs most frequently is 7 The mode is 7 5/19/2019

Topic Three When numbers are arranged in numerical order, the middle one is the median. Example: 3,6,2,5,7 Arrange in order 2,3,5,6,7 The number in the middle is 5 The median is 5 5/19/2019

Averaging Grades Lowest 55 60 75 80 83 93 Highest 5/19/2019

Find The mean of the following set of grades Lowest 55 60 75 80 83 93 Highest First add all the grades together. The total equals 1061 Now divide 1061 by 13 (total grades The answer is 81.61 The mean is 81.61 5/19/2019

Find the median of the following numbers Lowest 55 60 75 80 83 93 Highest The median is the number in the middle of numbers which are in order from least to greatest. If we count from both sides the number in the middle is 83. The median is 83 5/19/2019

Find the mode of the following grades Lowest 55 60 75 80 83 93 Highest The mode is the number which occurs most often. The number which occurs most often is 93 The mode is 93 5/19/2019

Real Life If these were your math grades, what would you learn by analyzing them? The mean was 81.61. In order to raise your grades, you would have to make higher than an 81.61 on the rest of your assignments. The mode was 93 which was your highest grade. You could look at these papers to see why you made this grade the most. The median is a 83. This means that most of your grades were higher than your average. Find your week area and try to improve. 5/19/2019

Real Life Real Life Knowing the mean, median, and mode will help you better understand the scores on your report card. By analyzing the data (grades) you can find your average, the grade you received most often, and the grade in the middle of your subject area. Better understanding your grades may lead to better study habits. 5/19/2019

Range and SD Range of a data set is the highest value minus the lowest value Q1 = lower median Q3 = higher median Standard deviation is the square root of the variance Sx=sample standard deviation Ox=population standard deviation 5/19/2019

Summarizing SD and Variance the SD (and the variance) are basically the same measure of how far a set of values (grades) differs or varies from the mean large SD means their student grades scores are all over the place 5/19/2019

Coefficient of Variation Expresses the SD as a percentage CV = standard deviation / mean * 100 5/19/2019

Mean and SD for grouped data Computer the midpoint of each class (if width is 1-5 then the midpoint is 3) this is called x Count the frequency (f) of each class Mean of grouped data =Sumxf/n 5/19/2019

Weighted Average 83(.4) + 96(.6) .4 + .6 What is the average for a student who has the following grades: Project grade = 88 = 30% of avg Test grade = 81 = 30% of avg Quiz grade = 76 = 20% of avg Homework = 75 = 20% of avg 5/19/2019

Interquartile Range Q3-Q1 Shows the range within the inner medians 5/19/2019

Five-number summary Includes: lowest value, Q1, median, Q2, and highest value 5/19/2019

Write down the following numbers 55 60 42 90 33 78 67 54 5/19/2019

Compute the following Median and Mean Q3 and Q1 Interquartile range Lowest value Highest value Variance and Standard Deviation of Sample 5/19/2019