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Measures of the Central Tendency

  1. The three measures are – mean, median and mode.
  2. All three are used for numerical data, and the median and mode can be used for ordinal data as well.
  3. Mean is used for numerical data and symmetric (normal) distributions.
  4. If the mean and median are equal, the data distribution is symmetric.
  5. If mean > median the distribution is skewed to the right (positively skewed).
  6. If mean< median then the distribution is skewed to the left (negatively skewed). Q
  1. Mean:-
    1. Mean or average of n observation is the sum of the observations divided by the number of observations.
    2. Merit: it uses all the data values and is, in statistical sense, efficient and effective.
    3. Mean also characterizes normal distribution.
    4. Demerit: it is venerable to what are known as extreme value in the data set.
    5. Data set should be following a pattern viz. arithmetic progression where data is 1, 2, 3, 4…etc or 1, 5, 9, 13….etc (Arithmetic mean) or geometric progression (geometric mean) where data is 1, 2, 4, 8, 16….or exponential progression (exponential mean) where data is 1, 4, 9, 16 …etc or harmonic progression (harmonic mean) where data is 1, ½, 1/3, ¼, 1/5..etc.
  2. Median:
    1. It is the middle value ,which divides the observed values into two equal parts.
    2. For calculation of medians the values are to be arranged into ascending or descending order.
    3. If the observations are ODD for eg. 4, 5, 6, 7, 8.
  1. Mode:-
    1. The mode is the value of the observation which occurs most frequently.
    2. MODE=(3 Median-2 Mean)
Extra Edge: 

To calculate Range of 95% confidence interval.

Mean ± 2SD
μ + 2SD
μ - 2SD
SD = Standard error

Correlation Vs Regression
To measure association

  1. For strength of association; use correlation
  2. For variation of one factor with another; use regression

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