Descriptive Statistics - Statistics Help

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What is Descriptive Statistics?

Descriptive statistics gives us the summary and description of the features of the data under study. In order to present the data in a meaningful manner, we make use of Descriptive Statistics.

How is it different from Inferential Statistics:

Descriptive statistics only tell us about the basic descriptive and summary of the data. Inferential Statistics, on the other hand, helps us to perform deeper analysis and draw conclusions that descriptive statistics are unable to do. Inferential statistic allows us to collect a sample and that sample is used to draw conclusions about the population.

Example of Descriptive Statistics:

Suppose we have the following Box-plot:

Descriptive Statistics - Statistics Help

The above box-plot contains the median, first quartile, third quartile, minimum, and the maximum values. It tells us about the five-number summary of the data. In other words, it gives us description of the data.

The Different Measures of Descriptive Statistics:

The Measures of Descriptive Statistics is broadly divided into two groups - Measures of Central Tendency and Measures of Dispersion or Variability.

  • Measures of Central Tendency: As the name suggest a measure of central tendency is the measure used to give an idea about the centrality or center point of the given dataset.
  • The following are the various measures of Central Tendency:

    1. Mean:Mean or the Arithmetic Mean (A.M) is the simplest and most widely used measure of central tendency. It considers all the values in the data set. So if there is any change in any of the observations in the data, the mean will also change.
    2. Let x1, x2,....., xnbe n observations. Then Mean denoted byx- is given by:

      Descriptive Statistics - Statistics Help

    3. Median: Median is the central most value of the data-set. It divides the observations into two equal halves. In order to find the median we first need to arrange the data in ascending order. Next, we need to see whether the number of observations is even or odd.
    4. Case 1: For odd number of observations:

      Descriptive Statistics - Statistics Help

      In the above figure, we see 18 is the middlemost value and hence it is the median for the odd set of numbers.

      Case 2: For even number of observations:

      Descriptive Statistics - Statistics Help

      In the above figure, we see 18 and 20 are the middlemost values of the even set of numbers. For the median, we calculate the mean of 18 and 20 that is

      Descriptive Statistics - Statistics Help

      So Median=19.

    5. Mode: The Mode is the measure that tells us about the most frequent value in the data.
    6. Example:

      Descriptive Statistics - Statistics Help

      15 is the most frequent value and hence the mode of the above data.

  • Measures of Dispersion: It tells us about the variability of the data and how much the data is dispersed.
  • The following are the various measures of dispersion:

    1. Range: It is the difference between the maximum and minimum value of the data. If 4 and 45 are the minimum and maximum value of the data. Then, Range =45-4=41
    2. Standard deviation: The standard deviation is the square root of the sum of the square of the differences between the observation and the mean divided by the total number of observations.
    3. The standard deviation denoted by o is defined as:

      Descriptive Statistics - Statistics Help

    4. Quartiles: It divides the values into quarters. The interquartile range is a measure of dispersion which is calculated as the difference between third quartile (Q3) and the first quartile (Q1)
    5. Interquartile range (IQR) = Q3-Q1

    6. Mean deviation about mean and median: The sum of the absolute deviation of the observations from mean (or median) is known as Mean Deviation about mean (or median).

Thus, Descriptive Statistics gives us a general idea and summary of the data. It helps us to represent the data in a meaningful manner.

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