L4 & L5 Social Science Statistics

 By the end of lesson 4, you should be able to:

  • Approximate the standard deviation of a distribution visually from a bell-shaped histogram.
  • Calculate the standard deviation from quantitative data using Excel.
  • Interpret the standard deviation for symmetric distributions.
  • Properly apply the Excel functions STDEV.S, PERCENTILE.INC, QUARTILE.INC, MIN, and MAX to quantitative data.
  • Interpret the five-number summary for quantitative data.
  • Create a box-plot from quantitative data using Excel.
  • Determine the five-number summary visually from a box plot. * Explain the relationship between probabilities, percentiles, and percentages


>Larger standard deviation= the values are more spread out

>Smaller standard deviation= the values are closer together

*If all the values are the same then the standard deviation is 0

*Formula for excel: 

  • =stdev.s (array)
  • =percentile.inc (array, k) *k is the percentile that u want to find in decimal form
  • =quartile.inc (array, quart)
  • =var.s (array) *for sample variance
  • =min (array)
REMEMBER:

*If there is a difference between excel's calculations and any other software (graphing calculator), ALWAYS USE EXCEL'S CALCULATIONS.

>If the data is symmetric we will use the mean and standard deviation (as measures of center and spread)
>If the data is skewed, we will use the median and the five-number summary (as measures of center and spread)

*Boxplots can be drawn horizontally or vertically.
*You can see the five-number summary on a boxplot by drawing a line from each value point to the axis.
BUT you cannot see the mean or standard deviation.



By the end of lesson 5, you should be able to:

  • State the properties of a normal density curve.
There are 2 requirements for a density curve:
  1. all of the data must be at or above the x-axis
  2. the area under the curve must add up to 1 (100%)
  • Calculate the z-score of an individual observation, given the mean and standard deviation.
  • Interpret a z-score.
  • Calculate probability as area under a normal density curve.
  • Calculate a percentile using the normal distribution.
REMEMBER:

*Normal distribution appear frequently in real life
*Backwards normal problem: x=z0+u (z-score times st. dev. + mean)

>Formula for excel:

  • NORM.INV


>The 68-95-99.7 RULE
  • only applies to normal distributions
  • 68% of the data will be within +/-1 st. dev of the mean
  • 95% will be within +/- 2 st. dev of the mean
  • 99.7% of data will be within +/- 3 st. dev. of the mean
*The z-score tells us how many st. dev's our value is from the mean
*Values above the mean have positive z-scores
*Values below the mean have negative z-scores
*Z-scores less than -2 or greater than 2 indicate an unusual observation because only 5% of values will be 2 or more st. dev's from the mean

>Proportion of scores 30 of higher is the same (=) Probability of random student scoring 30 or higher 


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