| CHAPTER 14 – STATISTICS | |
| 1. | Mean (Average) of n observations: $$\bar{x}=\frac{\sum x_i}{n} \quad (i=1,2,\dots n)$$ |
| 2. | Mean for ungrouped data: $$\bar{x}=\frac{\sum f_i x_i}{\sum f_i}$$ |
| 3. | Median: (a) Arrange data in order (b) If n is odd → $$\frac{n+1}{2}$$th observation (c) If n is even → Average of $$\frac{n}{2}$$th and $$\left(\frac{n}{2}+1\right)$$th observation |
| 4. | Mode: The most frequently repeated observation. |
| 5. | Mean, Median and Mode are called Measures of Central Tendency. |
| CONCEPTS IN CLASS X | |
| 1. | Class Mark = (Upper Limit + Lower Limit) / 2 |
| 2. | Mean by Assumed Mean Method: $$\bar{x}=a+\frac{\sum f_i d_i}{\sum f_i}$$ where $$d_i=x_i-a$$ |
| 3. | Mean by Step Deviation Method: $$\bar{x}=a+\left(\frac{\sum f_i u_i}{\sum f_i}\right)h$$ $$u_i=\frac{x_i-a}{h}$$ |
| 4. | Mode of Grouped Data: $$\text{Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)h$$ l = lower limit of modal class f₁ = frequency of modal class f₀ = preceding class frequency f₂ = succeeding class frequency h = class size |
| 5. | Median of Grouped Data: $$\text{Median}=l+\left(\frac{\frac{N}{2}-F}{f}\right)h$$ l = lower limit of median class F = cumulative frequency of preceding class f = frequency of median class N = Σf h = class size |
| 6. | Class intervals must be continuous to find the median. |
| 7. | For “less than” type data, prepare a proper frequency table first. |
| 8. | Empirical Relation: $$3\,\text{Median}=\text{Mode}+2\,\text{Mean}$$ |
