Statistics

Consider the data on x taking the values 0, 2, 4,
8,....., 2n with frequencies nC0
,
nC1
,
nC2
,....,
nCn
respectively. If the mean of this data is \({{728} \over {{2^n}}}\), then n is equal to _________ .

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is :

If the mean and the standard deviation of the
data 3, 5, 7, a, b are 5 and 2 respectively, then
a and b are the roots of the equation :

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations
are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

If the variance of the following frequency
distribution :
Class         : 10–20 20–30 30–40

Frequency :    2          x          2
is 50, then x is equal to____

For the frequency distribution :
Variate (x) :      x1   x2   x3
....  x15
Frequency (f) : f1
   f2
  f3
...... f15
where 0 < x1
< x2
< x3
< ... < x15 = 10 and
\(\sum\limits_{i = 1}^{15} {{f_i}}\) > 0, the standard deviation cannot be ...

Let xi
(1 \(\le\) i \(\le\) 10) be ten observations of a
random variable X. If \(\sum\limits_{i = 1}^{10} {\left( {{x_i} - p} \right)} = 3\) and \(\sum\limits_{i = 1}^{10} {{{\left( {{x_i} - p} \right)}^2}} = 9\) where 0 \(\ne\) p ...

Let X = {x
\(\in\) N : 1
\(\le\) x
\(\le\) 17} and
Y = {ax + b: x
\(\in\) X and a, b \(\in\) R, a > 0}. If mean
and variance of elements of Y are 17 and 216
respectively then a + b is equal to :

If the variance of the terms in an increasing A.P., b1
, b2
, b3
,....,b11 is 90, then the common
difference of this A.P. is_______.

5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is :

A data consists of n observations : x1, x2, . . . . . . ., xn.    
If     \(\sum\limits_{i = 1}^n {{{\left( {{x_i} + 1} \right)}^2}} = 9n\)    and
\(\sum\limits_{i = 1}^n {{{\left( {{x_i} - 1} \right)}^2}} = 5n,\)
then the standard devi...

If the standard deviation of the numbers
–1, 0, 1, k is \(\sqrt 5\) where k > 0, then k is equal to

The mean and the median of the following ten
numbers in increasing order 10, 22, 26, 29, 34, x,
42, 67, 70, y are 42 and 35 respectively, then \({y \over x}\) is equal to

The mean and variance of seven observations are
8 and 16, respectively. If 5 of the observations are
2, 4, 10, 12, 14, then the product of the remaining
two observations is :

A student scores the following marks in five tests
:
45, 54, 41, 57, 43.
His score is not known for the
sixth test. If the mean score is 48 in the six tests,
then the standard deviation of the marks in six tests
is

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are
3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

If the data x1, x2,......., x10 is such that the mean of first four of these is 11, the mean of the remaining six is
16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :

The outcome of each of 30 items was observed; 10 items gave an outcome \({1 \over 2}\) – d each, 10 items gave outcome \({1 \over 2}\) each and the remaining 10 items gave outcome \({1 \over 2}\)+ d each. If the variance of this outcome dat...

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is -

If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ….., x5 and –50 is equal to

If for some x \(\in\) R, the frequency distribution of the marks obtained by 20 students in a test is :

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If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4)2
, (x2 – 4)2
,....., (x50 – 4)2
is :

The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

The mean of set of 30 observations is 75. If each observation is multiplied by a non-zero number \(\lambda\) and then each of them is decreased by 25, their mean remains the same. Then \(\lambda\) is equal to :

If the mean of the data : 7, 8, 9, 7, 8, 7, \(\lambda\), 8 is 8, then the variance of this data is :

If \(\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9\) and
\(\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45\), then the standard deviation of the 9 items
\({x_1},{x_2},.......,{x_9}\) is

The sum of 100 observations and the sum of their squares are 400 and 2475,
respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If
the incorrect observations are omitted, then the variance of the remaining obs...

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly...

If the mean deviation of the numbers 1, 1 + d, ..., 1 +100d from their mean is 255, then a value of d is :

The mean of 5 observations is 5 and their variance is 124. If three of the observations
are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted
and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

The variance of first 50 even natural numbers is

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10
to each of the students. Which of the following statistical measures will not change even after the grace
marks were given?

Let x1, x2,........., xn be n observations, and let \(\overline x\) be their arithematic mean and \({\sigma ^2}\) be their variance.
Statement 1 : Variance of 2x1, 2x2,......., 2xn is 4\({\sigma ^2}\).
Statement 2 : : Arithmetic mean of 2x...

If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding
means are given to be 2 and 4, respectively. The variance of the combined data set is

If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is
equal to

Statement - 1 : The variance of first n even natural numbers is \({{{n^2} - 1} \over 4}\)
Statement - 2 : The sum of first n natural numbers is \({{n\left( {n + 1} \right)} \over 2}\) and the sum of squares of first n natural numbers is $${...

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following
gives possible values of a and b?

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys
and girls combined is 50. The percentage of boys in the class is

Suppose a population A has 100 observations 101, 102,........, 200, and another
population B has 100 observations 151, 152,......., 250. If VA and VB represent the
variances of the two populations, respectively, then $${{{V_A}} \over {{V_B}...

Let x1, x2,...........,xn be n observations such that
\(\sum {x_i^2} = 400\) and \(\sum {{x_i}} = 80\). Then a
possible value of n among the following is

If in a frequency distribution, the mean and median are 21 and 22 respectively, then
its mode is approximately :

In a series of 2n observations, half of them equal \(a\) and remaining half equal \(–a\). If the
standard deviation of the observations is 2, then \(|a|\) equals

Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of change of origin and scale.
Which of these is/are correct?

In an experiment with 15 observations on \(x\), then following results were available:
\(\sum {{x^2}} = 2830\), \(\sum x = 170\)
One observation that was 20 was found to be wrong and was replaced by the correct value
30. Then the correcte...

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of
the set is increased by 2, then the median of the new set :

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?