Home
Class 11
MATHS
The mean and standard deviation of a set...

The mean and standard deviation of a set of `n_1`, observations are `bar x_1 and s_1` ,respectively while the mean and standard deviation of another set of `n_2` observations are `bar x_2 and s_2`, respectively. Show that the standard deviation of thecombined set of `(n_1 + n_2)` observations is given by `S.D.=sqrt((n_1(s_1)^2+n_2(s_2)^2)/(n_1+n_2)+(n_1 n_2(( bar x )_1-( bar x )_2)^2)/((n_1+n_2)^2))`

Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    MODERN PUBLICATION|Exercise Revision Exercise|2 Videos

  • STATISTICS

    MODERN PUBLICATION|Exercise Check your understanding|10 Videos

  • STATISTICS

    MODERN PUBLICATION|Exercise Miscellneous Exercise|6 Videos

  • SETS

    MODERN PUBLICATION|Exercise CHAPTER TEST 1|12 Videos

  • STRAIGHT LINES

    MODERN PUBLICATION|Exercise Chapter test|12 Videos

Similar Questions

Explore conceptually related problems

If mean of squares of deviations of a set of n observations about - 2 and 2 are 18 and 10 respectively,then standard deviation of this set of observations is

If mean of squares of deviations of a set of n observations about -2 and 2 are 18 and 10 respectively then standard deviation of this set of observations is 3 (b) 2 (c) 1 (d) None of these

The mean square deviations of a set of observations x_(1),x_(2), …, x_(n) about a point c is defined to be (1)/(n) sum_(i=1)^(n)(x_(i)-c)^(2) . The mean square deviations about -1 and +1 of a set of observations are 7 and 3, repectively. Find the standard deviation of this set of observations.

The mean square deviation of a set of observation x_(1), x_(2)……x_(n) about a point m is defined as (1)/(n)Sigma_(i=1)^(n)(x_(i)-m)^(2) . If the mean square deviation about -1 and 1 of a set of observation are 7 and 3 respectively. The standard deviation of those observations is

Let s be the standard deviation of n observations. Each of the n observations is multiplied by a constant c. Then the standard deviation of the resulting number is

The standard deviation of n observation x_(1),x_(2),……x_(n) is 6. The standard deviation of another set of n observations y_(1),y_(2),………..y_(n) is 8. What is the standard deviation of n observations x_(1)-y_(2),x_(2)-y_(2),………..,x_(n)-y_(n) ?

Mean deviation for n observation x_(1),x_(2),…..x_(n) from their mean bar x is given by