Descriptive statistic

• Pie chart:
  • A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion.
  • In a pie chart, the arc length of each slice is proportional to the quantity it represents.
• Bar chart:
  • A bar chart is a chart of rectangular bars with lengths proportional to the values they represent. The bars can be plotted vertically or horizontally.
  • A simple bar chart is a chart in which the length of each bar indicates the magnitude of the corresponding data item.
  • A component bar chart is a bar chart that gives a breakdown of each total into its component.
• Frequency distribution:
  • A frequency distribution records the number of times each value occurs.
  • Grouped frequency distribution: If there is a larger set of data or if data item is different, it is often convenient to group frequencies together in bands or classes.
  • Cumulative frequency distribution: A cumulative distribution can be used to show the total number of times that a value above or below a certain amount occurs.
• Histograms:
  • A histogram is the pictorial representation of a frequency distribution.
  • Histograms look like vertical bar charts, except that the bars are joined together.
• Averages:
  • Arithmetic means:
    • the arithmetic mean is calculated from the sum of values of items divided by the number of items. The arithmetic mean of a variable x is denoted by ̄x.
  • Mode:
    • The mode is the value that appears most often in a set of data.
  • Median:
    • The median is the number separating the higher half of a data sample from the lower half.
• Dispersion and skewness of data:
  • The range:
    • The range of a set of data is the difference between the largest and smallest values
  • Percentiles:
    • A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall.
  • Quartiles:
  • Interquartile
  • Deciles:
    • A decile is any of the nine values that divide the sorted data into ten equal parts, so that each part represents 10% of the sample or population.
  • Variance:
    • The average of squared mean deviation for each value in a distribution.
      • ${\sigma }^2=\frac{{\sum }_{i=1}^n(x-\bar{x}{)}^2}{n}$
      • ${\sigma }^2=\frac{\sum f{M}^2-n{\bar{x}}^2}{n}$
        • where $f$ is the class frequency and $M$ is the class midpoint
  • Standard deviation:
    • square root of the variance
  • Skewness