| Method or Example Name | Data Subject | Calculation Type | Total Frequency (n) | Calculated Result | Formula or Condition |
|---|---|---|---|---|---|
| Example 1 | Student marks | Mean | 30 | 59.3 | $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$ |
| Direct Method (Ex 1) | Student marks | Mean | 30 | 62 | $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$ |
| Assumed Mean Method (Ex 1) | Student marks | Mean | 30 | 62 | $\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$ where $a = 47.5$ |
| Step-deviation method (Ex 1) | Student marks | Mean | 30 | 62 | $\bar{x} = a + h \cdot \bar{u}$ where $a = 47.5, h = 15$ |
| Example 2 | Female teachers in primary schools | Mean | 35 | 39.71 | Direct, Assumed Mean ( $a = 50$ ), and Step-deviation ( $h = 10$ ) methods |
| Example 3 | Cricket wickets | Mean | 45 | 152.89 | Step-deviation method where $a = 200, h = 20$ |
| Example 4 | Cricket wickets | Mode | 10 | 2 | Value with maximum frequency |
| Example 5 | Family size | Mode | 20 | 3.286 | $Mode = l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \cdot h$ |
| Example 6 | Student marks | Mode | 30 | 52 | Modal class 40–55: $l = 40, f_1 = 7, f_0 = 3, f_2 = 6, h = 15$ |
| Median of Ungrouped Data | Student marks | Median | 100 | 28.5 | Average of $50^{th}$ and $51^{st}$ observations |
| Median of Grouped Data (Table 13.15) | Student marks | Median | 53 | 66.4 | $l = 60, n = 53, cf = 22, f = 7, h = 10$ |
| Example 7 | Height of girls | Median | 51 | 149.03 | $l = 145, n = 51, cf = 11, f = 18, h = 5$ |
| Example 8 | Class intervals | Median | 100 | 525 | Finding missing frequencies $x$ and $y$ : $x = 9, y = 15$ |
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