Circular Measure, Representation Of Data, Trigonometry Flashcards
Write 360° in radians
2pi
To convert from ° to rad?
× pi/180
To covert from rad to °
× 180/pi
Number of radians is in a complete revolution is:
No of times radius divides into the circumference
What is 1rad or 1c
An arc equal in length to radius, subtended at an angle of 1 radian at the centre.
Length of an arc in radians
r theta
Area of a sector in rad
0.5× r^2 × theta
What is the basic trigonometric identity
sin2x + cos2x =1
*Ie sinx whole squared
Tan2 theta =
sin2 theta / cos2 theta
What are the 4 quadrants. State and explain
1st- A 0-90, all are positive
2st - S 90-180, only sin is postive
3rd- 180-270, only tan is positive
4th- C 270-360, only cos is positive
And vice versa for negative angles
What to do to make negative angle to positive?
Add 360
State properties of each of the 3 functions graphs
Sin- continuous curve, -1<=sin0<=1, period is 2pi(repeated)
Cos- continuous curve, -1<=cos0<=1, period is 2pi(repeated)
Tan- not continuous has breaks, range values of tan theta is unlimited, period is pi(repeated)
What is sin cos tan 0?
0
1
0
What is sin cos tan 30
1/2
√3/2
1/√3
What is sin cos tan 45
1/√2
1/√2
1
What is sin cos tan 60
√3/2
1/2
√3
What is sin cos tan 90
1
0
Infinity
Each piece of info is called
Datum
Stats is the branch of maths which deals with
Collection, organisation and analysis of data
What are qualitative and quantitative data
Qualitative data consists of description using words
Quantitative data can take numerical value
What are discrete and continuous data
Discrete are those that can take only exact values
Continuous can take values within a specific range or measured Yo a degree of accuracy
Raw data is
Just collected from an experiment
2 things that must be in a stem and leaf plot
Key
Numbers in brackets stating the leaves belonging to each stem
Why is histogram often used instead of stem and leaf?
When data is large
Histogram can divide data into classes
Why is stem and leaf better than box and whisker plot
All data items can be shown
Important conditions that differ a histogram to bar chart
H bars have no spaces between them
H area is proportional to frequency
In H frequency density is y axis
H bars represent distribution of continuous, quantitative, non discrete variables (grouped ranges), where as in bar charts discrete, categorical variables are compared
Why is mean calculated from a frequency table not accurate?
Mid values of intervals are used as x
Formula of frequency density:
Frequency/class width
In frequency table intervals, what does 27-31 actually mean?
The boundaries are 26.5<= length<=31.5
Cumulative frequency is plotted again _ as x axis
Upper class boundary eg 54->54.5
Box plot illustrates … Using…
Spread/dispersion of distribution
Highest and lowest values, median, Q1(lower), Q3(higher), median Q2
What is measure of location
Aka - - ?
Single value that woukd condense the info contained in data set
Aka central tendency or average
Median is the :
n+1/2 th observation (odd)
c+d/2 th (even, where c and d are 2 middle values)
mean (x bar) =
Sigma x f / f
If data is grouped x is miss class value
Which are measures of spread
Range, interquartike range, variance, standard deviation
Advantages and disadvantages of range?
Ad- simple and easy to calculate
Disad- only 2 values considered, affected by extremes, ignores patten of spread
Outliers are
Unusual values that differ greatly in magnitude from majority of dafa
Outliers formulae (fences)
Upper fence: Q3 +1.5(Q3-Q1)
Lower fence: Q1 -1.5(Q3-Q1)
Standard deviation is
Square root of variance
Formula of variance (normal)
(Sigma x^2/n)- (x bar^2)
Formula of variance (frequency table)
(Sigma x^2/f) - (sigma xf/f)^2
Formula of variance (coded data)
Sigma (x-a)^2/n - (sigma(x-a) /n)^2
