MEAN OF n VARIABLES:
MEAN OF n VARIABLES Mean of n variables (X) is given by X=∑X/n Example- X1=79,X2=85,X3=92,X4=87,X5=93,X6=99 Calculate mean. Solution- X=(79+85+92+87+93+99)/6 =89.166
STANDARD DEVIATION:
STANDARD DEVIATION The amount by which n measurement values are spread about the mean is called as standard deviation. mathematically it can be written as б =√(d1 ²+d2²+d3²+-------+dn²)/n procedure to calculate standard deviation 1) calculate mean of list of numbers 2) subtract mean from each value to get list of deviation 3) square the resulting list of numbers 4) add resulting squares 5) divide result by 1 less than number items in the list 6) take square root of resulting number
Slide 4:
Example-X1=1,X2=3,X3=4,X4=6,X5=9,X6=19 calculate the standard deviation. solution- X=7 to find deviation from mean di =Xi-X d1=-6,d2=-4,d3=-3,d4=- 1,d5=2,d6=12 X=210/2 X’=6.48
MEDIAN:
MEDIAN Median of a given set of variables is given by Xmedian =X(n+1)/ 2 for even number of data values the median value is midway between centre of 2 values. Example-X1=2,X2=3,X3=1,X4=5 calculate the median solution- median=X(5+1)/2 = X(3) =1
AVERAGE DEVIATION:
AVERAGE DEVIATION The average deviation is defined as the sum of absolute values of deviation divided by number of readings. Mathematically it can be written as D=∑| di |/n
HISTOGRAPH:
HISTOGRAPH 2D frequency density diagram is called histograph . It represents the class of intervals and frequency in the form of rectangles. There will be as many adjoint rectangles as there are class of intervals.
DIFFERENCE BETWEEN HISTOGRAM AND BAR GRAPH:
DIFFERENCE BETWEEN HISTOGRAM AND BAR GRAPH HISTOGRAM BARGRAPH 1) It consists of rectangles touching each other . 1) It consists of rectangles normally seperated from each other with equal space. 2) Frequency is represented by area of each rectangle. 2) Frequency is represented by height.width has no significance. 3) It is a 2D figure. 3) It is a 3D figure.