Descriptive Statistics

Descriptive Statistics

In my last (21.2.2019) article, I was discussed about basic of Basics of Statistics. In this article, we are going to discuss about Descriptive Statistics.

Variety of Descriptive statistics

·         Measures of  Central Tendency- Mean, Median, Mode

·         Measures of  Dispersion- Range, Variance, Std Deviation

·         Measures of Shape- Skewness, Kurtosis

These descriptive statistics are used to help describe data, especially when we are dealing with very large data sets.

Why is it important to learn about summary statistics?

Ø  Description of large number of data points

Ø  Generate inferences from the summary statistics

Measures of Central Tendency

Distribution: A collection, or group, of scores from a sample on a single variable. Often, but not necessarily, these scores are arranged in order from smallest to largest.

Bimodal: A distribution that has two values that have the highest frequency of scores.

Multimodal: When a distribution of scores has two or more values that have the highest frequency of scores.

Mean: The arithmetic average of a distribution of scores.

(17+4+33+2+51+23+3+41+18+2+4+2)/12

Mean= 16.67

Median: The score in a distribution that marks the 50th percentile. It is the score at which 50% of the distribution falls below and 50% fall above.

If even series

Median = (4+17)/2

             = 10.5

Median split: Dividing a distribution of scores into two equal groups by using the median score as the divider. Those scores above the median are the “high” group whereas those below the median are the “low” group.

Mode: The score in the distribution that occurs most frequently.

Mode=2

Minimum: Lowest value in series

Minimum=2

Maximum: Highest value in series

Maximum= 51

Skew: When a distribution of scores has a high number of scores clustered at one end of the distribution with relatively few scores spread out toward the other end of the distribution, forming a tail.

Negative skew: In a skewed distribution, when most of the scores are clustered at the higher end of the distribution with a few scores creating a tail at the lower end of the distribution.

Positive skew: In a skewed distribution, when most of the scores are clustered at the lower end of the distribution with a few scores creating a tail at the higher end of the distribution.

Outliers: Extreme scores that are more than two standard deviations above or below the mean.

Σ          The sum of; to sum.

X         An individual score in a distribution.

ΣX       The sum of X; adding up all o – f the scores in a distribution. X The mean of a sample.

μ          The mean of a population.

n          The number of cases, or scores, in a sample.

N         The number of cases, or scores, in a population.

P50      Symbol for the median