1. Statistics
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2. 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.
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3. 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.
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4. 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
= 25
25 divided by 5 = 5
The mean is 5
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5. 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
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6. 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
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7. Averaging Grades
Lowest 55 60 75 80 83 93
Highest
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8. 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
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9. 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
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10. 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
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11. Real Life
If these were your math grades, what would you learn by analyzing them?
The mean was In order to raise your grades, you would have to make higher than an 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.
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12. 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.
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13. 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
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14. 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
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15. Coefficient of Variation
Expresses the SD as a percentage
CV = standard deviation / mean * 100
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16. 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
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17. 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
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18. Interquartile Range Q3-Q1 Shows the range within the inner medians
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19. Five-number summary Includes:
lowest value, Q1, median, Q2, and highest value
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20. Write down the following numbers55 60 42 90 33 78 67 54
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21. Compute the following Median and Mean Q3 and Q1 Interquartile range
Lowest value
Highest value
Variance and Standard Deviation of Sample
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