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NCERT Class 11- Math՚s: Exemplar Chapter – 15 Statistics Part 8
Question 20:
Determine mean and standard deviation of first terms of an A. P. whose first term is and common difference is .
Answer:
Given: first terms of an A. P. whose first term is a and common difference is d
To find: mean and standard deviation
The given AP in tabular form is as shown below,
Here we have assumed a as mean.
Given the AP have n terms. And we know the sum of all the terms of AP can be written as,
Now we will calculate the actual mean,
Substituting the corresponding values, we get
Now we other two columns sums, i.e.. ,
Now we know standard deviation is given by,
Substituting the corresponding values, we get
By taking the LCM, we get
Hence the mean and standard deviation of the given AP is reapectivly.