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Calculate the mean deviation about the median of the following observation :
3011, 2780, 3020, 2354, 3541, 4150, 5000
38, 70, 48, 34, 42, 55, 63, 46, 54, 44
34, 66, 30, 38, 44, 50, 40, 60, 42, 51
22, 24, 30, 27, 29, 31, 25, 28, 41, 42
38, 70, 48, 34, 63, 42, 55, 44, 53, 47
Calculate the mean deviation from the mean for the following data :
4, 7, 8, 9, 10, 12, 13, 17
13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17
38, 70, 48, 40, 42, 55, 63, 46, 54, 44
36, 72, 46, 42, 60, 45, 53, 46, 51, 49
57, 64, 43, 67, 49, 59, 44, 47, 61, 59
Calculate the mean deviation of the following income groups of five and seven members from their medians:
The lengths (in cm) of 10 rods in a shop are given below :
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2
(i) Find the mean deviation from the median
(ii) Find the mean deviation from the mean also.
In question 1(iii), (iv), (v) find the number of observations lying between and , where M.D. is the mean deviation from the mean.
Calculate the mean deviation from the median of the following frequency distribution :
The number of telephone calls received at an exchange in 245 successive on2-minute intervals is shown in the following frequency distribution :
Compute the mean deviation about the median.
Calculate the mean deviation about the median of the following frequency distribution :
Find the mean deviation from the mean for the following data :
Find the mean deviation from the median for the following data :
Compute the mean deviation from the median of the following distribution :
Compute mean deviation from mean of the following distribution:
The age distribution of 100 life-insurance policy holders is as follows :
Calculate the mean deviation from the median age.
Find the mean deviation from the mean and from a median of the following distribution :
Calculate mean deviation about median age for the age distribution of 100 persons given below :
Calculate the mean deviation about mean for the following frequency distribution :
Calculate mean deviation from the median of the following data :
Find the mean, variance and standard deviation for the following data :
2, 4, 5, 6, 8, 17
6, 7, 10, 12, 13, 4, 8, 12
227, 235, 255, 269, 292, 312, 321, 333, 348
15, 22, 27, 11, 9, 21, 14, 9
The variance of 20 observations is 4. If each observation is multiplied by 2, find the variance of the resulting observations.
The variance of 15 observations is 4. If each observation is increased by 9, find the variance of the resulting observations.
The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, find the other two observations.
The mean and standard deviation of 6 observations are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.
The mean and variance of 8 observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
For a group of 200 candidates, the mean find the standard deviations of scores were found to be 40 and 15 respectively. Later on, it was discovered that the scores of 43 and 35 were misread as 34 and 53 respectively. Find the correct mean and standard deviation.
The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?
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 in each of the following cases :
(i) If wrong item is omitted
(ii) if it is replaced by 12.
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 were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations were omitted.
Show that the two formula for the standard deviation of ungrouped data
are equivalent, where .
Find the standard deviation for the following distribution :
Table below shows the frequency f with which ‘x’ alpha particles were radiated from a diskette
Calculate the mean and variance.
Find the mean, and standard deviation for the following data :
Find the standard deviation for the following data :
Calculate the mean and S.D. for the following data:
Calculate the standard deviation for the following data:
Calculate the A.M. and S.D. for the following distribution:
A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later found that one observation was wrongly copied as 50, the correct figure is 40. Find the correct mean and S.D.
Calculate the mean, median and standard deviation of the following distribution
Find the mean and variance of frequency distribution given below:
The weight of coffee in 70 jars is shown in the following table:
Determine the variance and standard deviation of the above distribution.
Mean, and standard deviation of 100 observations was found to be 40 and 10 respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.
While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.
Calculate the mean, variance and standard deviation of the following frequency distribution:
Two plants A and B of a factory show the following results about the number of workers and the wages paid to them
In which plant A or B is there greater variability in individual wages?
The means and standard deviations of heights and weights of 50 students in a class are as follows:
Which shows more variability, heights or weights?
The coefficient of variation of two distribution are 60% and 70%, and their standard deviations are 21 and 16 respectively. What is their arithmetic means?
Calculate coefficient of variation from the following data :
An analysis of the weekly wages paid to workers in two firms A and B, belonging to the same industry gives the following results:
(i) Which firm A or B pays out the larger amount as weekly wages?
(ii) Which firm A or B has greater variability in individual wages?
The following are some particulars of the distribution of weights of boys and girls in a class:
Which of the distributions is more variable?
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 the three subjects shows the highest variability in marks and which shows the lowest?
From the data given below state which group is more variable G1 or G2?
Find the coefficient of variation for the following data :
From the prices of shares X and Y given below: Find out which is more stable in value:
Life of bulbs produced by two factories A and B are given below:
The bulbs of which factory are more consistent from the point of view of the length of life?
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?
Write the variance of first n natural numbers.
If the sum of the squares of deviations for 10 observations taken from their mean is 2.5, then write the value of standard deviation.
If x1, x2, ……, xn are n values of a variable X and y1, y2, ……., yn are n values of variable Y such that yi = axi + b, i = 1,2, ……, n, then write Var(Y) in terms of Var(X).
If X and Y are two variates connected by the relation and , then write the expression for the standard deviation of Y.
In a series of 20 observations, 10 observations are each equal t k, and each of the remaining halves is equal to –k. If the standard deviation of the observation is 2, then write the value of k.
If each observation of a raw data whose standard deviation is σ is multiplied by a, then write the S.D. of the new set of observations.
If a variable X takes values 0, 1, 2, ….., n with frequencies nC0, nC1, nC2, …….nCn, then write variance X.
For a frequency distribution mean deviation from mean is computed by
For a frequency distribution standard deviation is computed by applying the formula
If v is the variance and σ is the standard deviation, then
The mean deviation from the median is
If n = 10, and , then the coefficient of variation is
The standard deviation of the data:
Is
The mean deviation of the series a, a+d, a+2d, ……, a+2n from its mean is
A batsman scores runs in 10 innings as 38, 70, 48, 34, 42, 55, 63, 46, 54 and 44. The mean deviation about mean is
The mean deviation of the numbers 3, 4, 5, 6, 7 from the mean is
The sum of the squares deviations for 10 observations for 10 observations taken from their mean 50 is 250. The coefficient of variation is
Let x1, x2, ……xn be values taken by a variable X and y1, y2, …….yn be the values taken by a variable Y such that yi = axi + b, i = 1,2, …….,, n. Then,
If the standard deviation of a variable X is σ, then the standard deviation of the variable is
If the S.D. of a set of observations is 8 and if each observation is divided by -2, the S.D. of the new set of observations will be
If two variates X and Y are connected by the relation , where a, b, c are constants such that ac < o, then
If for a sample of size 60, we have the following information and , then the variance is
Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is
The standard deviation of first 10 natural numbers is
Consider the first 10 positive integers. If we multiply each numbers by -1 and then add 1 to each number, the variance of the numbers so obtained is
Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. It is added to each number, the variance of the numbers so obtained is
The mean of 100 observations is 50, and their standard deviations is 5. The sum of all squares of all the observations is
Let x1, x2, ……xn, be n observations. Let yi = axi + b for I = 1, 2, ….., n, where a and b are constant. If the mean of is 48 and their standard deviation is 12, the mean of is 55 and standard deviation of is 15, the values of a and b are
The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is
The mean deviation for n observations x1, x2, ….., xn from their mean is given by
Let x1, x2, ….., xn be n observations and be their arithmetic mean. The standard deviation is given by
The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is
