Recent questions and answers in Statistics

Calculate the mean deviation about the mean of the set of first n natural numbers where numbers where n is an even number.

answered Jul 9, 2014 by meena.p

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

answered Jul 9, 2014 by meena.p

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Find the standard deviation of the first n natural numbers.

answered Jul 9, 2014 by meena.p

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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 $x_2$ and $s_2$ respectively. Show that the standard deviation of the combined set of $(n_1+n_2)$ observations is given by $ S.D= \sqrt {\large\frac{n_1 (s_1)^2 +n_2 (s_2)^2}{n_1+n_2} +\frac{n_1n_2(\bar {x_1} -\bar {x_2} )^2}{(n_1+n_2)^2}}$

answered Jul 9, 2014 by meena.p

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The standard deviation is __________ the mean deviation taken from the arithematic mean

answered Jul 9, 2014 by meena.p

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The mean deviation of the data is ________ when measured from the median .

answered Jul 9, 2014 by meena.p

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The sum of the squares of the deviations of the values of the variable is _______ when taken about their arithmetic mean.

answered Jul 9, 2014 by meena.p

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The standard deviation of data is _ of any change in origin, but is ______ on the change of scale.

answered Jul 9, 2014 by meena.p

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If the variance of a data is 121, then the standard deviation of the data is _______

answered Jul 9, 2014 by meena.p

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If $\bar {x}$ is the mean of n values of x, then $\sum \limits_{i=1}^{n} (x_i -\bar{x} )$ is always equal to _______. If a has any value other than $\bar {x}$ , then $\sum \limits_{i-1}^{n} (x_i -\bar {x} )^2$ is _________ than $\sum (x_i -a)^2$

answered Jul 9, 2014 by meena.p

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Coefficient of variation $= \large\frac{----------}{mean} $$\times 100 $

answered Jul 9, 2014 by meena.p

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The standard deviation of some temperature data in $^{\circ} C$ is 5. If the data were converted into $^{\circ} F$ the variance would be

answered Jul 9, 2014 by meena.p

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Coefficient of variance of two distributions are 50 and 60 , and their arithmetic means are 30 and 25 respectively. Difference of their standard deviation is:

answered Jul 9, 2014 by meena.p

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The following information relates to a sample of size 60: $\sum x^2 =18000, \sum x =960$ The variance is

answered Jul 9, 2014 by meena.p

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Consider the numbers $1,2,3,4,5,6,7,8,9,10$ . If $1$ is added to each number the variance of the numbers so obtained is

answered Jul 9, 2014 by meena.p

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Standard deviations for first 10 natural number is

answered Jul 8, 2014 by meena.p

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Let $x_,x_2,x_3,x_4,x_5$ be the observations with mean m and standard deviation s. The standard deviation of the observation $kx_1,kx_2,kx_3,kx_4,kx_5$ is

answered Jul 8, 2014 by meena.p

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Let $a,b,c,d,e$ be the observations with mean m and standard deviations $S$. The standard deviation of the observations $a+k,b+k,c+k,d+k,e+k$ is

answered Jul 8, 2014 by meena.p

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The mean of 100 observation is 50 and their standard deviation 5. The sum of all the observations is

answered Jul 8, 2014 by meena.p

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Find the standard deviation of the data: $6,5,9,13,12,8,10$ is

answered Jul 8, 2014 by meena.p

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Following are the marks obtained by $9$ students in a mathematics test: $50,69,20,33,53,39,40,65,59$ The mean deviation from the median is :

answered Jul 8, 2014 by meena.p

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When tested , the lives (in hours) of $5$ bulbs were noted as follows : $1357,1090,1666,1494,1623$ The mean deviations (in hours) from their mean is

answered Jul 8, 2014 by meena.p

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Mean deviation for n observation $x_1,x_2........x_n$ from their mean $\bar{x}$ is given by

answered Jul 8, 2014 by meena.p

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The mean deviation of the data $3,10,10,4,7,10,5$ from mean is

answered Jul 8, 2014 by meena.p

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While calculating the mean and variance of $10$ readings, a student wrongly used the reading $52$ for the correct reading $25$, the obtained the mean and variance as $45$ and $16$ respectively . Find the correct mean and the variance.

answered Jul 7, 2014 by meena.p

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Mean and standard deviation of $100$ observation were found to be $40$ and $10$ respectively . If at the times of calculation two observations were wrongly takes as $30$ and $70$ in place of $3$ and $27$ respectively. Find the correct standard deviation.

answered Jul 7, 2014 by meena.p

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Following are the marks obtained , out of 100 by two students Ravi and Hashina in 10 tests: Who is more intelligent and who is more consistent?

answered Jul 7, 2014 by meena.p

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Determine mean and standard deviation of first n terms of an A.P whose first term is 'a' and common difference d.

answered Jul 7, 2014 by meena.p

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The weights of coffee in 70 jars is shown in the following table : Determine variance and standard deviation of the above distribution.

answered Jul 7, 2014 by meena.p

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Determine the mean and standard deviation for the following distribution:

answered Jul 4, 2014 by meena.p

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Calculate the mean deviation from the median of the following frequency data:

answered Jul 4, 2014 by meena.p

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Calculate the mean deviation about the mean for the following frequency distribution.

answered Jul 4, 2014 by meena.p

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Find the mean and variance of the frequency distribution given below:

answered Jul 4, 2014 by meena.p

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If for a distribution $ \sum (x-5) =3,\sum (x-5)^2 =43$ and the total number of items is $18$. Find the mean and standard deviation .

answered Jul 4, 2014 by meena.p

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Mean and standard deviation of 100 items are 50 and 4 , respectively . find the sum of all items and sum of the squares of the items.

answered Jul 4, 2014 by meena.p

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The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.

answered Jul 4, 2014 by meena.p

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There are 60 students in a class .The following is the frequency distribution of the marks obtained by the students in a test : where x is a positive integer . Determine the mean and standard deviation of the marks.

answered Jul 3, 2014 by meena.p

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The frequency distribution given below find the standard deviation

answered Jul 3, 2014 by meena.p

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The frequency distribution given below : Where A is a positive integer , has a variance of 160. Determine the value of A.

answered Jul 3, 2014 by meena.p

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Two sets each of $20$ observations , have the same standard deviation $5$. The first set has a mean $17$ and the second a mean $22$. Determine the standard deviation of the set obtained by combining the given two sets.

answered Jul 3, 2014 by meena.p

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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 =$18.2$ seconds, standard deviation $=3.25$ seconds. Further another set of $15$ observations $x_1,x_2,......x_5$ also in seconds is now available and we have $\sum\limits_{i=1} ^{15}x_i =279$ and $\sum \limits_{i=1} ^{15} x_i^2 =5524$Calculate the standard deviation based on all $40$ observations

answered Jul 3, 2014 by meena.p

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Find the mean deviation about the mean of the distribution

answered Jul 2, 2014 by meena.p

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Find the mean deviation about the mean of the distribution

answered Jul 2, 2014 by meena.p

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The mean and standard deviation of a group of 100 observations were found to be 20 and 3, respectively . Later on it was found that three observations were incorrect. Which are recorded by 21,21, and 18 . Find the mean and standard deviation, if the incorrect observations are omitted.

answered Jul 2, 2014 by meena.p

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The mean and standard deviation of marks obtained by 50 students of a class in three subjects , mathematics, physics and chemistry are given below:Which of these three subjects shows the highest variability in marks and shows the lowest?

answered Jul 2, 2014 by meena.p

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The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation If it is replaced by 12.

answered Jul 2, 2014 by meena.p

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The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation If wrong item is omitted.

answered Jul 2, 2014 by meena.p

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Given $\bar{x} $ is the mean and $\sigma^2$ is the variance of n observations $x_1,x_2,x_3......x_n$ prove that the mean and variance of the observations $ax_1,ax_2,ax_3.......ax_n$ are $a \bar{x}$ and $a^2\sigma^2$, respectively , $(a\neq 0)$

answered Jul 2, 2014 by meena.p

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The mean and standard deviation of six observations are $8$ and $4$ respectively. If each observation is multiplied by $3$, find the new mean and new standard deviation of the resulting observation.

answered Jul 2, 2014 by meena.p

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The mean and variance of $7$ observation are $8$ and $16$ respectively.If six of the observations are $2,4,10,12,14$. Find the remaining two observations.

answered Jul 1, 2014 by meena.p

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