Class 11 maths jee Brilliant Pala class notes - statistics
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Course
JEE
Institution
JEE
Excel in statistics with Class 11 Maths JEE Brilliant Pala class notes. Master essential concepts, methods, and techniques for JEE exams. These comprehensive class notes will equip you with the knowledge and skills needed to ace your statistics exams
A measure of central tendency or an average is defined as a representative value and it stands for
the entire set of observations. The important averages are
i) Arithmetic mean ( AM or x )
ii) Geometric mean (G.M)
iii) Harmonic mean (H.M)
iv) Median
v) Mode
Arithmetic mean (A.M or x )
i) For a raw data A.M is given by
xi
x
n
ii) In a frequency distribution the A.M. is given by
fi x i
x where
N
x i Value of variable in an ungraped f.d. and it is mid point (class mark) in a continuous f.d.
N = Total frequency ie N f i
1
, Properties of A.M.
1. The algebraic sum of deviation of a set of observation from their mean is zero.i.e. x i x 0
2
2. The sum of squares of deviations from the A.M is the minimum i.e. x i x is the minimum
3. The A.M is dependent of change of scale and origin
AM x i x
A.M x i k x k change of origin
A.M k x i xk change of scale
ax b ax b
A.M. changeof scaleand origin
c c
first term last term
4. A.M of an A.P. =
2
5. Combined A.M.
k
n x
i 1
i i
x k
If x1 , x 2 .....x k are means of k samples of size n1, n2.....nk then combined A.M is given by
n
i 1
i
6. Weighted A.M
In statistics, weight means the importance given to be observations
Let x1 , x 2 ....x n be the observations with corresponding weights w1, w2,....wn, then weighted A.M is
given by
wi xi
Xw
wi
Geometric mean (G.M.)
G.M. of x1 , x 2 , x 3 ....x n n th root of product
1/n
GM x1 .x 2 .x 3 ....x n
1/n
xi
1 1 1
log G.M. log x i log x1 .x 2 ...x n log x i
n n n
2
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