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Measures of Central Tendency (MCT)

Measures of Central Tendency (MCT). Describe how MCT describe data Explain mean, median & mode Explain sample means Explain “deviations around mean”. More Statistical Notation. An important symbol is ∑, it is the Greek letter ∑ called sigma This symbol means to sum (add)

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Measures of Central Tendency (MCT)

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  1. Measures of Central Tendency (MCT) Describe how MCT describe data Explain mean, median & mode Explain sample means Explain “deviations around mean”

  2. More Statistical Notation • An important symbol is ∑, it is the Greek letter ∑ called sigma • This symbol means to sum (add) • You will see it used in notations such as ∑ X. This is pronounced as the “sum of X” and means to find the sum of the X scores

  3. Why Is It Important to Knowabout MCT?

  4. Central Tendency • MCT answer the question: • “Are the scores generally high scores or generally low scores?” • What are they? • A MCT is a score that summarizes the location of a distribution on a variable • It is the score that indicates where the center of the distribution tends to be located

  5. The Mode • The most frequently occurring score is called the mode • The mode is typically used to describe central tendency when the scores reflect a nominal scale of measurement

  6. Unimodal Distributions When a polygon has one hump (such as on the normal curve) the distribution is called unimodal.

  7. Bimodal Distributions When a distribution has two scores that are tied for the most frequently occurring score, it is called bimodal.

  8. The Median

  9. The Median • The median (Mdn) is the score at the 50th percentile • The median is used to summarize ordinal or highly skewed interval or ratio scores

  10. Determining the Median • When data are normally distributed, the median is the same score as the mode. • When data are not normally distributed, follow the following procedure: • Arrange the scores from lowest to highest. • If there are an odd number of scores, the median is the score in the middle position. • If there are an even number of scores, the median is the average of the two scores in the middle.

  11. The Mean

  12. The Mean • The mean is the score located at the exact mathematical center of a distribution • The mean is used to summarize interval or ratio data in situations when the distribution is symmetrical and unimodal

  13. Determining the Mean • The formula for the sample mean is

  14. Sample Mean versus Population Mean • is the sample mean. It is a sample statistic. • The mean of a population is a parameter. It is symbolized by m (pronounced “mew”). is used to estimate the corresponding population mean m.

  15. Central Tendency and Normal Distributions On a perfect normal distribution all three measures of central tendency are located at the same score.

  16. Central Tendency andSkewed Distributions

  17. Deviations Aroundthe Mean

  18. Deviations • A score’s deviation is equal to the score minus the mean. • In symbols, this is • The sum of the deviations around the mean always equals 0.

  19. More About Deviations • When using the mean to predict scores, a deviation indicates our error in prediction. • A deviation score indicates a raw score’s location and frequency relative to the rest of the distribution.

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