Statistics helps a business describe what its data show. Tables arrange observations so they can be checked; graphs make patterns and comparisons easier to see. The right display depends on the kind of data and the question being asked.
Organizing observations
A frequency distribution groups observations into categories or class intervals and records how many fall in each group. The count in a group is its frequency. Check that the frequencies add up to the number of observations before interpreting the table.
A stem-and-leaf plot is useful for a modest set of numerical observations because it groups values while keeping each original value visible. For example, the values 12, 14, 18, 21, and 23 can be shown as:
Stem | Leaves 1 | 2 4 8 2 | 1 3
Here the key is 1|2 = 12. The leaves are ordered, so the display makes the spread and clusters easier to inspect without losing the observations.
Choosing a display
| Display | Useful for |
|---|---|
| Simple bar diagram | Comparing values across categories. |
| Sub-divided bar diagram | Comparing totals and their component parts across categories. |
| Multiple bar diagram | Comparing two or more related series across categories. |
| Pie chart | Showing how categories make up one whole. |
| Histogram | Showing the shape of a numerical frequency distribution using adjacent rectangles for continuous class intervals. |
| Ogive | Showing cumulative frequencies; a less-than ogive uses upper class boundaries, while a more-than ogive uses lower class boundaries. |
For a histogram, the rectangles touch because the intervals represent continuous values. An ogive helps locate a median or other position in the distribution; the estimated median is read from the horizontal scale at the intersection of less-than and more-than ogives when both are drawn on the same axes.
A pie-chart example
Suppose a business records these illustrative quarterly expenses. The central angle for each slice is its share of the total multiplied by 360 degrees.
| Expense | Amount (Rs) | Share | Angle |
|---|---|---|---|
| Salaries | 450,000 | 50% | 180° |
| Rent | 150,000 | 16.67% | 60° |
| Utilities | 60,000 | 6.67% | 24° |
| Marketing | 180,000 | 20% | 72° |
| Other expenses | 60,000 | 6.67% | 24° |
| Total | 900,000 | 100% | 360° |
For example, salaries account for
Excel can help arrange observations into a frequency table and create a suitable chart. Check the source values, labels, totals, and scale before relying on the chart: a neatly drawn graph can still mislead if its data or axes are wrong.