Basic Statistical Terms:

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Basic Statistical Terms

• Statistics refers to the sample
• A means by which a set of data may be described
  and interpreted in a meaningful way.
• A method by which data can be analyzed and
  inferences and conclusions drawn.

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• Population All of the possible subjects within a
  group.
• Sample A part of the population
• Random Sample Every member of a specified
  population has an equal chance of being selected
• Ungrouped data Raw scores presented as they were
  recorded no attempt made to arrange them into a
  more meaningful or convenient form

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• Grouped Data Scores that have been arranged in
  some manner such as from high to low or into
  classes or categories to give more meaning to the
  data or to facilitate further calculations.
• Frequency Distributions A method of grouping
  data a table that presents the raw scores or
  intervals of scores and the frequencies with
  which the raw scores occur.

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Measures of Central Tendency

• Mean The arithmetic average
• population mean ?
• sample X

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Examples

• 12
• 11 ?X 50
• 10 X N 5 10
• 9
• 8
• ? x1 50

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What is happening here?

• 30
• 11 ?X 68
• 10 X N 5 13.6
• 9
• 8
• ?X 68

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• To be a good measure of central tendency the mean
  should be in the middle of the scores...

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Median

• The point in the distribution where 50 of the
  scores lie above and 50 lie below it.
• The midpoint or 50th percentile

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• Position of the median
• 58
• 56 N 1
• 55 2
• 53 4.5th score
• 49 8 1 9
• 49 2 2
• 46
• 41 4.5th score

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• Median lies between 53 and 49.
• Average the two scores
• 53 49
• 2 51

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• Extreme scores do not greatly affect the median
• 12 30
• 11 11
• 10 median 10 median
• 9 9
• 8 8

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Mode

• The score that occurs most frequently.
• Rough measure for description more than analysis
  purposes.
• May be more than one.

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Measures of variability

• Scatter or spread of scores from the central
  tendency.
• Tells us how heterogeneous or homogeneous a group
  is.
• Groups may have the same mean or median but
  differ considerably in variability.

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Example

• Five students score 84, 80, 78, 75, 73 on a test
  their mean is 78.
• Another group of students scored 98, 95, 78, 65,
  54, their mean is also 78.
• Obvious difference in variability of their scores.

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Range

• Simplest measure or variability (weak).
• Based on the two extreme scores.
• Generally a large range a large variability.
• Difference of the highest and lowest scores in a
  data set.
• Formula high score - low score 1

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Standard Deviation

• One of the best measures of variability.
• Reflects the magnitude of the deviations of the
  scores from the mean.

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• Mean (X) ?X
• N
• Sd (s) N?X2 - (?X)2
• N(N - 1)

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Variance

• The mean of the squared deviations from the
  mean.
• The standard deviation squared.
• Computer as part of an ANOVA procedure
• Often referred to as the mean square (MS)

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Normal Curve
99.73
95.44
68.26
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Sd -3? -2? -1? 0 1? 2? 3? z
scores -3 -2 -1 0 1 2 3 T scores 20 30 40 50 60 70
80 GRE,NTE 200 300 400 500 600 700 800 IQ
Wechsler 55 70 85 100 115 130 145 Normal curve
and comparative scores for various standardized
tests
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Frequency Distributions

• 1) Establish the range of scores from high to
  low 1
• 2) Determine the size and number of step
  intervals. (keep step intervals between 10 and
  20)
• Divide the range by 15
• 52/15 3.5 round up to 4 for intervals.

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• 3) Set up the intervals
• The highest step must include the highest
  score.
• If the size of the step interval is an even
  number, the lowest score in the step interval
  should be a multiple of the interval size.
• If the size of the step is odd , the middle
  score of the step interval should be a multiple
  of the interval size.
• 4) Tabulate the scores.

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Provides the Researcher

• Info about the range
• A rough indication of the measures of central
  tendency
• General manner in which the scores are
  distributed.