gradient form | y = mx + c |
general form | Ax + By + C = 0 |
intercept form | x/a + y/b = 1 |
general form | y = ax^{2} + bx + c |
perfect square form | y = a(x+p)^{2} + q |
0^{o} | 30^{o} | 45^{o} | 60^{o} | 90^{o} | |
sin | 0 | ½ | ≈ 0.707 | ≈ 0.866 | 1 |
cos | 1 | ≈ 0.866 | ≈ 0.707 | ½ | 0 |
tan | 0 | ≈ 0.577 | 1 | ≈ 1.732 | ∞ |
Sin is + | All are + |
Tan is + | Cos is + |
ungroupd data | grouped data | |
mean | x = ( ∑ x_{i} ) ÷ N | x = ( ∑ f_{i}x_{i} ) ÷ ( ∑ f_{i} ) |
mode | observation that occurs the most |
frequency distribution table ------> modal class
histogram ---------------------------> mode |
median |
m_{odd} = [(N+1)/2]^{th} observation
m_{even} = [ (N/2)^{th} observation + (N/2 + 1)^{th} observation ] ÷ 2 |
cumulative frequency table & m = L + [ (N/2 - F)÷ f_{m} ] C
ogive & (N/2)^{th} observation |
ungroupd data | grouped data | |
range | largest observation - smallest observation | midpoint of highest class - midpoint of lowest class |
interquartile range | SMILE ! |
Q_{1} = L_{1} + [ ¼N - F_{1})
÷ f_{Q1} ] C
Q_{3} = L_{3} + [ ¾N - F_{3}) ÷ f_{Q3} ] C |
variance | σ^{2} = [ ∑(x_{i}-x)^{2} ] ÷ N = [ ( ∑x_{i}^{2} ) ÷ N ] - x^{2} | σ^{2} = [ ∑f_{i}(x_{i}-x)^{2} ] ÷ ∑ f_{i} = [ ( ∑f_{i}x_{i}^{2} ) ÷ ∑ f_{i} ] - x^{2} |
standard deviation | σ | σ |
measures of central tendency | measures of dispersion | |
each data is added by k |
new mean = original mean + k
new mode = original mode + k new median = original median + k |
range DOES NOT CHANGE
interquartile range DOES NOT CHANGE variance DOES NOT CHANGE standard deviation DOES NOT CHANGE |
each data is multipied by k |
new mean = original mean × k
new mode = original mode × k new median = original median × k |
new range = original range × k
new interquartile range = original interquartile range × k new variance = original variance × k^{2} new standard deviation = original standard deviation × k |