Descriptive Statistics - Data Visualization

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  1. Qualitative Data
    1. Tabulation.
    2. Graphical Visualization. </aside>

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  1. Quantitative Data
    1. Tabulation.
    2. Graphical Visualization. </aside>

Qualitative Data

  1. Tabulation

    1. Frequency Distribution:

      1. Frequency refers to the number of times a particular value or category appears in a data set.
      2. Frequency Distribution: A table showing the number of occurrences (frequency) of each value or category.

    2. Relative Frequency Distribution:

      1. Relative frequency is the fraction or proportion of the total number of observations that belong to a specific category.

      2. Formula:

        $$ \text{Relative Frequency} = \frac{f_i}{n} \quad \text{where} \, n = \sum_{i=1}^{k} f_i $$

      3. $f_i$: Frequency of the $i^{th}$ value.

      4. $n$: Total number of observations.

      5. $k$: the no. of different values for the variable

    3. Percent Frequency Distribution:

      1. The percentage of the total observations that belong to each category.

      2. Formula:

        $$ \text{Percent Frequency} = \text{Relative Frequency} \times 100 $$

    4. Example: Soft Drinks Preference Data from a Sample of 50 Students.

      Students Soft Drink Preference Students Soft Drink Preference Students Soft Drink Preference Students Soft Drink Preference
      1 Sprite 2 Coca Cola 3 Coca Cola 4 Sprite
      5 Coca Cola 6 Mountain Dew 7 Sprite 8 Coca Cola
      9 Coca Cola 10 Pepsi 11 Sprite 12 Pepsi
      13 Limca 14 Coca Cola 15 Mountain Dew 16 Coca Cola
      17 Limca 18 Coca Cola 19 Mountain Dew 20 Pepsi
      21 Mountain Dew 22 Sprite 23 Sprite 24 Coca Cola
      25 Coca Cola 26 Pepsi 27 Sprite 28 Pepsi
      29 Limca 30 Mountain Dew 31 Coca Cola 32 Pepsi
      33 Mountain Dew 34 Pepsi 35 Coca Cola 36 Limca
      37 Pepsi 38 Sprite 39 Mountain Dew 40 Pepsi
      41 Coca Cola 42 Coca Cola 43 Pepsi 44 Pepsi
      45 Mountain Dew 46 Pepsi 47 Coca Cola 48 Limca
      49 Pepsi 50 Sprite
      Soft Drink Preference Frequency Relative Frequency Percent Frequency
      Coca Cola 15 15 ÷ 50 = 0.30 0.30 × 100 = 30%
      Limca 5 5 ÷ 50 = 0.10 0.10 × 100 = 10%
      Mountain Dew 8 8 ÷ 50 = 0.16 0.16 × 100 = 16%
      Pepsi 13 13 ÷ 50 = 0.26 0.26 × 100 = 26%
      Sprite 9 9 ÷ 50 = 0.18 0.18 × 100 = 18%
      Total 50 1.00 100%

    5. Key Points:

      1. The sum of frequencies equals the total number of observations.
      2. The sum of relative frequencies always equals 1.
      3. The sum of percent frequencies always equals 100%.

  2. Graphical Visualization for Qualitative Data

    1. Bar Chart

      1. Definition: A graphical representation of qualitative data where a rectangle (bar) is drawn for each category or class.

        image.png

      2. Characteristics:

        1. Bars may be vertical or horizontal.
        2. The length or height of each bar represents the frequency, relative frequency, or percent frequency.
        3. Bars do not touch each other, emphasizing the separateness of the categories.
        4. Bars can be of the same or different colors.

    2. Pie Chart

      1. Definition: A circular chart divided into slices, where each slice represents a category or class.
      2. Characteristics:

        1. The size of each slice is proportional to the frequency or percentage of observations.

        2. Formula for Slice Size:

          $$ \text{Slice Size (°)} = \text{Relative Frequency} \times 360^\circ $$

    3. Example: Soft Drink Preferences (Pie Chart Slice Sizes)

Quantitative Data