Sometimes we want to do more than summarize a bunch of scores. Sometimes
we want to talk about particular scores within the bunch. We may want to tell
other people about whether or not a score is above or below average. We may
want to tell other people how far away a particular score is from average. We
might also want to compare scores from different bunches of data. We will want
to know which score is better. Z-scores can help with all of this.
Z-Scores tell us whether a particular score is equal to the mean, below
the mean or above the mean of a bunch of scores. They can also tell us how far
a particular score is away from the mean. Is a particular score close to the
mean or far away?
ü Has a value of 0, it
is equal to the group mean.
ü Is positive, it is
above the group mean.
ü Is negative, it is
below the group mean.
ü Is equal to +1, it is
1 Standard Deviation above the mean.
ü Is equal to +2, it is
2 Standard Deviations above the mean.
ü Is equal to -1; it is
1 Standard Deviation below the mean.
ü Is equal to -2, it is
2 Standard Deviations below the mean.
How typical a particular score is within bunch of scores. If data are
normally distributed, approximately 95% of the data should have Z-score between
-2 and +2. Z-scores that do not fall within this range may be less typical of
the data in a bunch of scores.
Individual scores from different bunches of data. We can use Z-scores to
standardize scores from different groups of data. Then we can compare raw
scores from different bunches of data.
Source: Statistics-help-for-students.com
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