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Describe the Important Statistical Measures to summarise the Research Data or Survey

Summarizing survey or research data typically involves several key statistical measures. These measures help to understand the central tendency, variability, and distribution of the data. Here are some of the most important statistical measures:

How will you differentiate between descriptive statistics and inferential statistics?

Measures of Central Tendency

  1. Mean (Average): The sum of all the values divided by the number of values. It provides a central value of the data set.
  2. Median: The middle value when the data is ordered from least to greatest. It divides the data into two equal parts.
  3. Mode: The value that appears most frequently in the data set. There can be more than one mode if multiple values have the same highest frequency.

Measures of Dispersion (Variability)

  1. Range: The difference between the maximum and minimum values. It gives a sense of the spread of the data.
  2. Variance: The average of the squared differences from the mean. It measures how much the data points vary from the mean.
  3. Standard Deviation: The square root of the variance. It provides a measure of the spread of the data in the same units as the data.
  4. Interquartile Range (IQR): The difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of the data.

Measures of Shape

  1. Skewness: Measures the asymmetry of the data distribution. Positive skewness indicates a distribution with a long right tail, while negative skewness indicates a long left tail.
  2. Kurtosis: Measures the “tailedness” of the data distribution. High kurtosis indicates heavy tails and sharp peaks, while low kurtosis indicates light tails and flatter peaks.

Position Measures

  1. Percentiles: Values below which a certain percentage of the data falls. For example, the 25th percentile (Q1) is the value below which 25% of the data falls.
  2. Quartiles: Specific percentiles that divide the data into four equal parts: Q1 (25th percentile), Q2 (50th percentile, or median), and Q3 (75th percentile).

Summary Statistics

  1. Five-number summary: Includes the minimum, Q1, median (Q2), Q3, and maximum. It provides a quick overview of the data distribution.
  2. Box plot: A graphical representation of the five-number summary, which also shows outliers.

Correlation and Regression (for relationships between variables)

  1. Correlation Coefficient: Measures the strength and direction of the relationship between two variables. The value ranges from -1 to 1.
  2. Regression Analysis: Assesses the relationship between a dependent variable and one or more independent variables. It helps in predicting outcomes and understanding relationships.

These statistical measures provide a comprehensive understanding of the data, helping researchers and analysts to make informed decisions and draw meaningful conclusions.

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