Social Statistics
2/8 (Friday)
Standard Deviation cont’d
Example: Amount of money earned by new immigrants
Sample: 12, 15, 16, 20, 25, 36, 40
Step 1: Find the mean * x̄=164/7 * mean is 23.4
Step 2: Find how much each observation deviates from the mean * 12 - 23.4 = -11.4 * 15 – 23.4 = -8.4 * 16 – 23.4 = -7.4 * 20 – 23.4 = -3.4 * 25 – 23.4 = 1.6 * 36 – 23.4 = 12.6 * 40 – 23.4 = 16.6 * Note: all observations below mean will be negative, all above will be positive
Step 3: Square the deviations * (-11.4)² = 129.96 * (-8.4)² = 70.56 * (-7.4)² = 54.76 * (-3.4)² = 11.56 * (1.6)² = 2.56 * (12.6)² = 158.76 * (16.6)² = 275.56
Step 4: Add them together * 129.96 + 70.56 + 54.76 + 11.56 + 2.56 + 158.76 + 275.56 = 703.72
Steps 5 & 6: * Divide sum from sample size * 703.72/7 = 100.53 * Take square root of the number * √100.53 = 10.03 – round two places out * This means that, on average, the income of new immigrants deviates almost $10.000 from the mean. * This is a relatively large deviation (almost half the mean) * There is a lot of variability in how much new immigrants earn.
The Normal Range * Within 1 standard deviation of the mean * Contains cases considered close to the norm
Variation
* Very similar to standard deviation * Formula: * To calculate variation, square the standard deviation
What do we know? * Distributions – categorizing and graphing frequencies * Central tendency and variability * Conclusions based on what we observe * Example: large standard deviations let us conclude distribution has lots of variability * Now, we will test relationships based on probability
Probability – mathematical measure of the likelihood of an even occurring * Chance of the desired even occurring written in %, proportion, or ration. * 40% chance of rain * Batting average .313 * Probability of a royal flush is
Standard Deviation cont’d
Example: Amount of money earned by new immigrants
Sample: 12, 15, 16, 20, 25, 36, 40
Step 1: Find the mean * x̄=164/7 * mean is 23.4
Step 2: Find how much each observation deviates from the mean * 12 - 23.4 = -11.4 * 15 – 23.4 = -8.4 * 16 – 23.4 = -7.4 * 20 – 23.4 = -3.4 * 25 – 23.4 = 1.6 * 36 – 23.4 = 12.6 * 40 – 23.4 = 16.6 * Note: all observations below mean will be negative, all above will be positive
Step 3: Square the deviations * (-11.4)² = 129.96 * (-8.4)² = 70.56 * (-7.4)² = 54.76 * (-3.4)² = 11.56 * (1.6)² = 2.56 * (12.6)² = 158.76 * (16.6)² = 275.56
Step 4: Add them together * 129.96 + 70.56 + 54.76 + 11.56 + 2.56 + 158.76 + 275.56 = 703.72
Steps 5 & 6: * Divide sum from sample size * 703.72/7 = 100.53 * Take square root of the number * √100.53 = 10.03 – round two places out * This means that, on average, the income of new immigrants deviates almost $10.000 from the mean. * This is a relatively large deviation (almost half the mean) * There is a lot of variability in how much new immigrants earn.
The Normal Range * Within 1 standard deviation of the mean * Contains cases considered close to the norm
Variation
* Very similar to standard deviation * Formula: * To calculate variation, square the standard deviation
What do we know? * Distributions – categorizing and graphing frequencies * Central tendency and variability * Conclusions based on what we observe * Example: large standard deviations let us conclude distribution has lots of variability * Now, we will test relationships based on probability
Probability – mathematical measure of the likelihood of an even occurring * Chance of the desired even occurring written in %, proportion, or ration. * 40% chance of rain * Batting average .313 * Probability of a royal flush is