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Describing Scores

# Describing Scores - Chapter 3 Describing and Presenting a...

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Chapter 3: Describing and Presenting a Distribution of Scores Outline: Measures of Variability Range, Variance, Standard Deviation Percentiles & Percentile Ranks Standard Scores z-Scores, T-scores Frequency Distribution Graphing Data

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Student Objectives: 1. Define and interpret range, variance and standard deviation. 2. Calculate range, variance and be able to find standard deviation with excel. 3. Define percentile and percentile rank and state how they can be used to interpret data. 4. Define standard scores and interpret their meanings. 5. Be able to calculate z and T Scores.
Measures of Variability Spread or scatter of scores is referred Example: Group A: 80, 82, 83, 84, 86 Group B: 65, 75, 90, 90, 95 1. Range (R) Determined by subtracting the low score from the high score Formula: R = H x - L x Where: H x = high score, L x = low score Mean = Mean = Range = Range =

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2. Variance Spread of scores about How different the score is from Deviation score (d) = X X raw score mean Group 1 d d 2 Group 2 d d 2 X X - X (X X) 2 X X - X (X X) 2 7 2 4 9 4 16 6 1 1 7 2 4 5 0 0 5 0 0 4 -1 1 3 -2 4 3 -2 4 1 -4 16 ∑X 25 10 25 40 N 5 5 X 5 5 Range 4 8
Variance (s 2 ) s 2 = ∑(X -X) 2 N - 1 Variance Group 1 = 10 ÷ 4 = 2.5 Variance Group 2 = 40 ÷ 4 = 10 Variance = square of the standard deviation

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3. Standard Deviation ( std dev) Describes the Most commonly Used in other Homogeneous Data Heterogeneous Data s = standard deviation of a sample σ (Greek letter sigma) = standard deviation of a population
s = ∑(X - X) 2 N - 1 Group 1: s = 10 = 2.5 = 1.58 4 Group 2: s = 40 = 10 = 3.16 4

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