Homework
- Lesson 5
Any student may may do the assignments from any area.
You may run through this work an unlimited number of times. If you make
errors, you will
be referred to the appropriate area of the book for re-study. |
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Assessment
- Lesson 5
You will have two options to take the quiz. If you fail
to achieve 100% on the quiz, you will not able to advance to the next
lesson. After failing on the second take, the instructor is notified
and remedial action can be taken.
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Assignment and Information
Reading:
Chapter 4
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Definition
Page: Contains definitions arranged alphabetically. |
Chapter 4 (lesson 5) notes and vocabulary
Notes: |
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Okay, now that we have collected all our BASC data, we need a way
of sharing that data with the public in a way that makes sense. While
frequency distributions like this one are nice, they are often too
bulky for most journal publications, and they donÍt allow for easy
comparisons between groups. Measures of central tendency come in
handy, because they allow you to sum up an entire table of data into
one score. This is an average or typical score for the group. |
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Mode - the most frequently occurring score in your data - For
our BASC data 52 occurs the most often, three times.
- The modal
score
is ñtypicalî because it happened the most often. If you were
trying to guess someoneÍs score, you have the highest probability
of being exactly right if you guess the mode as their score.
- The mode
provides no information about the rest of the distribution,
just what score
happened most
- The mode can be used with all scales of measurement
(nominal, ordinal, interval and ratio)
- The mode is often
used to report strongly bimodal data
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Median - The score in the middle, when scores are ordered numerically
- for our BASC data we have 25 scores, so the half way point is
the 13th score. Counting down from the top, the 13th score is 52
- The
median score is ñtypicalî because half the scores are lower
and half the scores are higher, which minimizes the distance
between the median
and each of the raw scores. That means that if you have to
guess a score and pay a dollar for each point you are away
from that score,
your best bet is the median, because you will spend the least
amount of money on wrong guesses that way.
- The median score can be used
in ordinal, interval and ratio scales, it can not be used
for nominal data, because you canÍt order nominal data numerically.
- The median
score is less sensitive to extreme scores, or outliers,
so it is often used when reporting heavily skewed data.
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The text gives a formula for calculating the median for data that
has tied scores around the median. This formula is often used in
statistical software because it can be significant that a score is
the first or 6th score in a set of tied scores (it helps in pointing
out slight skew for example). It is helpful to understand this formula,
but for homework purposes, our data is small enough that counting
out the median score by hand is easier, and the score will make more
sense to the common reader. If you want to try and calculate the
median with the percentile formula for practice, you should get a
median BASC score of 51.67 which reflects the fact that our median
score is the first of the 3 tied scores. |
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Sample
Mean or Mean ()
- The sum of the scores divided by the number of scores in the
sample. For our BASC
data, if you sum the scores, you should get 1285. Then divide this
number by 25, since we have 25 scores, and we get a mean of 51.40.
- The mean is most typical because it is the amount or score
that each person would get if the scores were evened out, in
other words
if we were trying to be fair in giving out the same scores
to everyone.
- The mean can only be calculated on interval or ratio
data. It does
not make sense to calculate the average phone number of
people in town.
- The mean is sensitive to extreme scores, or outliers,
so
it is not good to use with heavily skewed data.
- The sum
of the deviations around the mean should be zero, this is
a good way to
check if you calculated the mean correctly. See table
below.
- The sum of the deviations squared (sum of squares, SS)
is smaller
for
the mean than for any other score which will be important
in later calculations. See table below.
- The mean is the only
measure
of
central tendency that uses every score in the data
set, so it is usually the most representative of the data.
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Power in statistics is the ability to detect differences between
groups when there actually is a difference between groups. Because
the mean uses every score in the data set, it is the most statistically
powerful of the three measures. Unless you have a good reason to
use mode or median, like bimodal distributions or heavily skewed
data, the best measure to use is the mean. |
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Vocabulary:
Measures of Central Tendency - Numbers that represent
the average or typical score obtained from measurements of a
sample. Mean, median and mode are the three most common measures
of central
tendency.
Measures of Variability - Numbers that indicate how
much scores differ from each other and the measure of central
tendency in a set of scores. These will be covered in detail in
later
chapters,
but variance and standard deviation are two examples of measures
of variability.
Mode - The most frequently occurring score
in a distribution of scores. For our BASC data, the mode is 52,
because
there are 3
subjects who scored 52. Unimodal - a distribution with one
mode. Our BASC data is unimodal. Bimodal - a distribution with
two
modes. Multimodal - a distribution with more than two modes.
Median - A
score value in the distribution with an equal number of
scores above and below it. The median is the 50th percentile in
a
distribution. The median for our BASC scores is also 52, because
the 13th
score when they are in rank order is 52.
Sample mean ( ) - The sum of a set of scores divided by the number
of scores summed. In adding all our BASC scores I get 1285,
then I divide by
25 (the number of scores) and I get a sample mean of
51.40.
Population mean () - The
sum
of
all the
scores in a population divided by the number of scores
summed. This is the
same as a sample mean, but using every score for every
subject, rather than just a small sampling.
Sum of squares (SS) - A
numerical value
obtained by subtracting the mean of a distribution
from each score in the distribution, squaring each difference,
and
then summing the
differences. This number by itself means very little,
but it is a key component of many statistical calculations. |
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