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The number of observations in the data set
The mean or average value for the data set
The summation – calculate X-mean for every value in the data set then sum
Degrees of freedom
The graph on the right has a bigger standard deviation. More
of the values that comprise the data set on the right are
farther away from the mean than in the data set on the left.
The standard deviation
The number of observations in the data set (data points)
The standard error formula is a modification of the standard deviation formula. To get the standard
error, take the standard deviation formula and divide it by the square root of the sample size in the
data set. This indicates that if two data sets have the same standard deviation, but a different number
of observations, they will have different standard errors.
Another way to think of these two measures is as follows:
The standard deviation measures the variability for a set of data from the mean
The standard error is a measure of how far the sample mean of the data is from the true population
mean.
In
1.043
.737
.466
The standard error is just the standard deviation divided by the square root of the sample size. Larger
numbers have larger square roots, thus the standard error decreases when sample size increases. You
can see this in b. above when the sample size increases from 10 to 50.
Mean = 516/6 = 86
75, 78, 88, 90, 92, 93 Median = 90+88/2 = 89
S = (88-86)2 + (93-86)2 + (90-86)2 + (92-86)2 + (75-86)2 + (78-86)2 / 5 = 58 = √58 = 7.62
SE = 7.62/√6 = 3.11
The median (middle value of a data set) is less affected by outliers and reflects the central
tendency of a data set. The mean also reflects a central tendency, but can be influenced by
outliers and is best suited when distributions of data are normal and do not contain outliers.
Your graph should have one bar with a mean of 86 and whisker plots that extend 6 units above
and below this mean to reflect ± 2 SEM.
The means of the two classes for Teacher 1 are definitely significantly different (no overlap
between error bars). The means of the two classes of Teacher 2 appear to be definitely not
significantly different (the error bars for Teacher 2’s classes overlap).