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
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