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Descriptive Stats_SP08_BB

# Descriptive Stats_SP08_BB - Lecture Outline Measures of...

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Descriptive Statistics Lecture Outline • Measures of Central Tendency • Measures of Variability • Visualizing Data Measures of Central Tendency 1. Mean (population = μ; sample = Х (X bar ) or M – “Average” – Interval/ratio scale – Usually the best descriptive except when have a few outliers (i.e., extreme scores) Calculating the Mean 1. Add up all the scores individually 2. Divide by the total number of scores Mean = Σ (X i )/N Where: Σ = Sum X i = each individual score N = Total number of scores

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What to do about rounding? • Keep as many decimal places as possible until the end result (best to keep at least 4) • Round at the very end, 3 decimal places recommended Measures of Central Tendency 2. Median ( Mdn) – “Middle score” – Ordinal/Interval/Ratio scales – Better estimate than the mean if you have outliers – Median less affected by the extreme score Calculating the Median 1. Line up scores from lowest to highest 2. Find the middle score by taking the total number of scores (N), add 1 (+1) & divide that total by 2 Median = (N+1)/2 • If there is an even number of scores, calculate the average of the two middle scores Measures of Central Tendency 3. Mode – “Most frequent” number in your sample – Most commonly used with nominal data – Can misrepresent interval/ratio data because mode does not change if add additional data points – In a perfect symmetrical distribution, the mode = the median = the mean
Calculating the Mode 1. Line up scores from lowest to highest 2. Look for most common data point ± There can be more than 1 mode 94 100 94 90 91 0 0 94 100 94 90 91 0 0 100 94 94 91 90 0 0 100 94 94 91 90 0 0 Σ (X i )/N = 67 (469/7 = 67) WHERE Σ = sum N = number of scores X i = a score Which method best represents the data? Mean = 67.0 Median = 91.0 Mode = 94.0, 0 In this case, the median. The median & mode can be better indicators of central tendency (compared to the mean) IF you have outliers. 94 100 94 90 91 0 0 We need more information…

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Central tendency is not enough… Group A Group B Group C 2 1 0 2 3 0 2 2 10 2 3 0 2 1 0 Number of siblings Mean = 2 in all three groups Lecture Outline • Measures of Central Tendency • Measures of Variability • Visualizing Data Variability • Measures of Central Tendency (mean, median, mode): summary of a data set • Measures of Variability: describe the difference among a set of scores –Tells us if the scores are close together or spread out –Distributions with identical means can have entirely different variability measures Range •Simplest measure of variability
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Descriptive Stats_SP08_BB - Lecture Outline Measures of...

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