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Data Analysis and Statistics

Data Analysis and Statistics. When you have to interpret information, follow these steps:. Understand the title of the graph Read the labels Analyze pictures Recognize scales Look for trends Use only the information on the graph, don’t use personal knowledge or opinions.

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Data Analysis and Statistics

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  1. Data Analysis and Statistics

  2. When you have to interpret information, follow these steps: • Understand the title of the graph • Read the labels • Analyze pictures • Recognize scales • Look for trends • Use only the information on the graph, don’t use personal knowledge or opinions

  3. Measure of Central Tendency • Median • Mode • Mean

  4. the sum or the data values the number of data values in the data set Mean • Average of the data values • Influenced by outliers • Mean is equal to

  5. Median • Middle value of a data set • Average of the two middle values • Not influenced by outliers • Based on relative size of data set, not on the actual values

  6. Mode • Value that occurs most frequently • Can be one, more than one, or no mode • Only appropriate measure of central tendency for data that is strictly nonnumeric • Based on relative frequency rather than all the values in the set

  7. Richard has participated in eight track meets so far this season. His running times for the 440-meter race have been 73, 63, 68, 64, 69, 61, 66, and 64 seconds. What is Richard’s median running time for the eight meets? • 64 seconds • 65 seconds • 66 seconds • 66.5 seconds

  8. First put the numbers in order. 61, 63, 64, 64, 66, 68, 69, 73 Since there is no middle, average 64 and 66. • 64 seconds • 65 seconds • 66 seconds • 66.5 seconds

  9. Measure of Dispersion • Range • Standard deviation • Variance

  10. Range • Difference between maximum value and minimum value • Should have the same units as those of the data values from the data set

  11. Standard Deviation • A measure of the dispersion of a set of data from its mean. The more spread apart the data is, the higher the deviation. • Standard deviation can also be calculated as the square root of the variance.

  12. Variance • Square of the standard deviation of the population.

  13. Regression • Correlation coefficient • The closer is to 1, the more perfect is the linear relationship between x and y. • If r is close to zero, there is little or no linear relationship.

  14. Normal Distributions • 68-95-99.7 Rule • 68% of the values are within 1 standard deviation of the mean • 95% of the values are within 2 standard deviations of the mean • 99.7% of the values are within 3 standard deviations of the mean

  15. The lifetime of a certain type of disposable razor is normally distributed with a mean of 16.8 shavings and a standard deviation of 2.4 shavings. What percentage of disposable razors of this type will last more than 19.2 shavings? • 2.5% • 16% • 34% • 68%

  16. First you need to find the z-score for 19.2. The z-score is 1. Therefore, 19.2 is 1 standard deviation above the mean. Now find the percentage of the normal distribution that is 1 standard deviation above the mean. If we were to look at the normal curve we would see that from 16.8 – 2.4 to 16.8 + 2.4 there is 68% of the data. Which means the remaining 32% of the graph contains the rest of the data. However, because the graph is symmetric, half of the 32% is below 16.8 – 2.4. Therefore, 16% is above 16.8 + 2.4. • 2.5% • 16% • 34% • 68%

  17. Z-Score • Number of standard deviations away from the mean

  18. Other Key Words • Quartiles ~ four portions • Skewness ~ lopsidedness • Positively skewed (longer tail to the right) • Negatively skewed (longer tail to the left)

  19. Donna scored at the 75th percentile on a multiple-choice history exam. The best interpretation of this information is that • Donna answered 75% of the questions on the test correctly • Only 25% of the other students did worse on the test than did Donna • Donna answered 75 questions correctly • Donna did as well as or better than 75% of the students who took the exam

  20. The 75th percentile is a value at or below which 75% of the data fall. Therefore, the best interpretation of Donna’s score is that she did as well as or better than 75% of the students who took the exam. • Donna answered 75% of the questions on the test correctly • Only 25% of the other students did worse on the test than did Donna • Donna answered 75 questions correctly • Donna did as well as or better than 75% of the students who took the exam

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