HARD
11th CBSE
IMPORTANT
Earn 100

Calculate the mean deviation about the mean of the set of first n natural numbers when n is an odd number.

Important Questions on Statistics

MEDIUM
11th CBSE
IMPORTANT
Calculate the mean deviation about the mean of the set of first n natural numbers when n is an even number.
MEDIUM
11th CBSE
IMPORTANT

Find the standard deviation of the first n natural numbers.

HARD
11th CBSE
IMPORTANT
The mean and standard deviation of some data for the time taken to complete a test are calculated with the following results: Number of observations=25, mean=18.2 s, standard deviation = 3.25 s. Further, another set of 15 observations x1, x2,,x15, also in seconds, is now available and we have i=115xi=279 and i=115xi2=5524. Calculate the standard deviation (correct up to 2 decimal places) based on all 40 observations.
HARD
11th CBSE
IMPORTANT
The mean and standard deviation of a set of n1 observations are x1 and s1, respectively while the mean and standard deviation of another set of n2 observations are x2 and s2, respectively. Show that the standard deviation of the combined set of n1+n2 observations is given by
S.D=n1s12+n2s22n1+n2+n1n2x¯1-x¯22n1+n22.
MEDIUM
11th CBSE
IMPORTANT
Two sets each of 20 observations, have the same standard deviation 5. The first set has a mean 17 and the second  mean 22. Determine the standard deviation (correct up to two decimal places) of the x sets obtained by combining the given two sets. 
MEDIUM
11th CBSE
IMPORTANT

The frequency distribution:

x A 2A 3A 4A 5A 6A
f 2 1 1 1 1 1

where A is a positive integer, has a variance of 160. Determine the value of A.

MEDIUM
11th CBSE
IMPORTANT

For the frequency distribution:

x234567f491614116

Find the standard deviation (round off to two decimal places).

HARD
11th CBSE
IMPORTANT

There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test:

Marks 0 1 2 3 4 5
Frequency  x-2 x x2 x+12 2x x+1

where, x is positive integer. Determine the mean and standard deviation of the marks.