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Bio-Statistic KUEU 3146 & KBEB 3153 Bio-Statistic

Bio-Statistic KUEU 3146 & KBEB 3153 Bio-Statistic. Data grouping and presentations Part II: Summarizing Data. Summarizing Data. Measure of central Tendency Mean, Median and Mode Measure of Variation Range, Mean Deviation, Std Deviation Coefficient of Variation

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Bio-Statistic KUEU 3146 & KBEB 3153 Bio-Statistic

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  1. Bio-Statistic KUEU 3146 & KBEB 3153Bio-Statistic Data grouping and presentations Part II: Summarizing Data

  2. Summarizing Data • Measure of central Tendency • Mean, Median and Mode • Measure of Variation • Range, Mean Deviation, Std Deviation • Coefficient of Variation • Means and Std Deviation of a population

  3. Measure of Central Tendency • Mean. Computed by summing all the observations in the sample and dividing the sum by the number of observations. • 300,300,300,940,300,300,400,300,400, 450,800,450,1050 • The sum of the above observation is 6290 and the number of observation is 13. Therefore the mean is 6290 ÷ 13 = 483.85

  4. Measure of Central Tendency • Median. Observations arranged in array. The median is the observation that divides the distribution into equal part. • 300,300,300,940,300,300,400,300,400, 450,800,450,1050 • Arrange above observation in increasing order. • Data A: 300,300,300,300,300,300,400,400,450,450,800,940,1050 • Data B: 300,300,300,300,300,300,400,400,450,450,800,940 • The median for data A is 400, and 350 for data B.

  5. Measure of Central Tendency • Mode is the observation that occurs most frequently. • Data A: 300,300,300,300,300,300,400,400,450, 450,800,940,1050 • The mode for data A is 300.

  6. Measure of Central Tendency Three types of frequency distribution • Symmetrical Frequency Distribution • Right Skewed Distribution • Left Skewed Distribution

  7. Symmetrical Frequency Distribution Mean Median Mode

  8. Right Skewed Distribution Median Mean Mode

  9. Right Skewed Distribution Mean Mode Median

  10. Measures of Variation • Range is the difference in value between the highest (max) and lowest (min) observation. • Mean Deviation. The sum of all the absolute values of deviations (each observation minus mean of observation) divided by number of observation (n). • Standard Deviation (represented by symbol s) is a square root of variance • Variance (represented by symbol s2) is the sum of all square values of deviation divided by the number of one less than the numbers of observation i.e (n -1) • Coefficient of Variation CV= percentage of (Std Dev divided by mean).

  11. Equations for Sample Means and Standard Deviations ∑x X = n (∑x)2 ∑(x-x)2 S2= ∑x2 n n-1 S2= n-1

  12. Equations for Population Means and Standard Deviations ∑x μ = N ∑(x-x)2 σ2= N-1

  13. Equations for Group-Data Means and Standard Deviations ∑xf X = n ∑(x-x)2f S2= n-1 X is class midpoint and f is class frequency

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