The salaries of five teachers in Rupees are as follows.
11500, 12400, 15000, 14500, 14800.
Find Range and standard deviation.
Solve this problem
Answers
Step-by-step explanation:
Given :-
The salaries of five teachers in Rupees are as follows.11500, 12400, 15000, 14500, 14800.
To find :-
Find Range and standard deviation?
Solution :-
Given observations are 11500, 12400, 15000, 14500, 14800.
Lowest value = 11500
Heighest value = 15000
We know that
Range = Heighest value-Lowest value
=> R = 15000 - 11500
=> R = 3500
Now,
Given values of Xi =11500, 12400, 15000, 14500, 14800.
Sum of all observations
= 11500+ 12400+ 15000+ 14500+14800
= 68200
Number of observations = 5
We know that
Mean of the data = Sum of all observations/ Number of all observations
=> Mean = ΣXi/N
=> Mean = 68200/5
=> Mean = 13640
and x1 = 11500
=> x1² = 11500² = 132250000
x2 = 12400
=> x2² = 12400² =153760000
x3 = 15000
=> x3² = 15000² = 225000000
x4 = 14500
=> x4² = 14500² = 210250000
x5 = 14800
=> x5² = 14800²= 219040000
Sum of all the values Σxi² = 132250000+153760000 +225000000 +210250000+219040000
=> Σxi² =940300000
Now,
Standard Deviation =
S =√[(Σxi²/N)-(Σxi/N)²]
=> S = √[(940300000/5)-(13640²)]
=> S =√[(188060000-186049600)
=> S =√2010400
=> S =1417.885...
=> S = 1417.89
(Correct it to two decimal numbers )
Answer:-
The range of the data is 3500
The standard deviation of the data is 1417.89
Used formulae:-
- Range = Heighest value-Lowest value
- Standard Deviation is defined as
- S =√[(Σxi²/N)-(Σxi/N)²]
- Mean = Σxi/N
- Σxi = Sum of all observations
- N = Number of all observations
the question is awn in 3500