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Sociology and Anthropology
SOAN 3120
Michelle Dumas

WEEK 2: CHAPTER 3: EXPLORING QUANTITATIVE DATA Tuesday, September 17 , 2013 EXPLORING QUANTITATIVE DATA  Plot your data  Look for pattern and departures from that pattern  Calculate: shape, centre, and spread  Larger numbers – the larger the sample size, the more likely you’ll get a smooth curve DENSITY CURVES  Histogram  Alternative: scale (area) – height of the bar tells us number of observations in each bin - Total area = 1.0 - Proportion - Ex: 42/193 = 0.218 - Density: 0.218/10 = 0.0218  Quantitative continuous data - Bars are narrow  The more data you collect, the more likely you can use what it looks like, in terms of this distribution – it’s why we aim to get as many survey responses as possible when collecting data – better represents the population  Curve around the data – density curve because you’re looking at the density of the population that it’s taking up in that space PROPERTIES OF DENSITY CURVE  Smooth curve = density curve – represents a continuous quantitative variable, and that we can look at the proportions of observations under the curve based on the area that it occupies 1) Area = 1.0 2) Proportion – proportion of data laying between any two values – it will always be under 1 3) Horizontal axis – density curve is always above the horizontal axis MEAN, MEDIAN, & STANDARD DEVIATION  Median is the value of the variable that has the half the area below it, and half the area above it  Mean is the average of many averages – because when you have a density curve and looking at inferential statistics, you’re usually using more than one sample, so it takes several means to get to that one - Essentially a balancing point of the density curve  Mean and median coincide when it’s symmetric  In skewed, both the mean and median are pulled in the direction of the skew – the mean more so than the median  Standard deviation – the average distance to the mean NORMAL DISTRIBUTIONS  Theoretical construct – very rare to find in the real world – a perfect normal distribution where everything works out completely symmetrical - Sometimes referred to as Gaussian distribution  They play an important role in statistical inference – taking sample and generalizing for the population  Shape = symmetric, bell shaped (bell curve), mean and standard deviation - Represented: N(u, o) THE 68-95-99.7 RULE  About 2/3 (
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