The document explains measures of central tendency including mean, median, and mode, detailing their definitions, calculations, and when to use them. It emphasizes the importance of understanding variability through measures such as range, mean deviation, variance, and standard deviation, which indicate how observations are spread around the mean. These statistical concepts are critical for analyzing and comparing data effectively.

1. Central Tendency
To identify the center of a distribution than from an extreme

2. Mean
•Measure arithmetic mean by summing up all the
observations and dividing the total by the number of
observations.
•The mean is the most widely used measure of central
tendency
•Many statistical tests depends on mean.
•Useful in interval and ratio level measurement.

3. Uses of Mean
• Helps to find out how the normal observations lying close to
central value while few of the too large or too small lie for away
at both the ends.
• To find which group is better by comparing the average.
• Used when no extreme value in the data set.
• To calculate other tests.

4. Median
• The Median is the point in a distribution above which and below which 50% of
cases fall.
• For ungroup even number of data, arrange the data from highest to lowest or
vise versa and median is N/2 th position and for ungroup odd data N+1/2 th
positioned score is median .
• Median is better measurement of central tendency than mean in an unevenly
distributed scores.

5. Uses of median
• To find out midpoint of given distribution
• Used when the series contains extremes scores

6. Mode
• It is most frequently occurring score value in distribution
• Modes are quick way to determine a popular score.
• But it is unstable because it can fluctuate
• Primarily used for nominal level measurement.

7. Uses of Mode
• Not affected by extreme value
• Can be used to describe qualitative and quantitative data.
• But not used for further any calculations.

8. Measures of variability
• It helps to find out how individual observation are dispersed around
the mean of a large series.
• Also known as measures of dispersion.

9. Measures of variations
• Range: distance Between lowest and highest data point.
• Mean deviation: avarage of deviation scores
• Variance: relationship between mean and the data points.
• Standard deviation: square root of the variance

10. Uses of SD
• Indicates whether the difference between the mean and the
individual is real or by chance.
• Find out whether the difference between two sample mean is real or
by chance.
• Help to find out the standard error. Difference between sample mean
and population mean.
• Helps to find out suitable sample size.
• Helps in different statistical calculations.

11. Standard deviation0