Maths-
General
Easy
Question
The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6. Then the other two are
- 2 and 9
- 3 and 8
- 4 and 7
- 5 and 6
Hint:
A fact or figure we gather regarding a certain variable is called an observation. It can be quantified or described as a quality. The observation "25" for a mother's age during the birth of her first kid is an example of a number. Here we have given the mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6 then we have to find the rest 2.
The correct answer is: 4 and 7
The mean is calculated by dividing the total number of observations by the sum of all the observations.
The median represents the "middle" value among the observations. Your observations must be sorted in either ascending or descending order in order to calculate the median.
Mode: The importance of observation is what happens most frequently. If an observation is not repeated, a mode for the list cannot exist.
In probability and statistics, variance is the expected value of the squared variation of a random variable from its mean value. Informally, variance calculates the degree to which a random group of numbers deviates from the mean value.
Here the number of observations is 5. The mean of five observations is 4 and their variance is 5.2. Let the 2 observations be a and b.
Using the variance formula, we get:
![sum from blank to blank of left parenthesis X minus X with bar on top right parenthesis squared equals 5.2 cross times 5
sum from blank to blank of left parenthesis X minus X with bar on top right parenthesis squared equals 26
S o space n o w space i f space a space a b d space b space a r e space t h e space r e s t space t w o space n u m b e r s comma space t h e n colon
space left parenthesis space 1 space minus space 4 space right parenthesis squared space plus space left parenthesis space 2 space minus space 4 space right parenthesis squared space plus space left parenthesis space 6 space minus space 4 space right parenthesis squared space plus space left parenthesis space a space minus space 4 space right parenthesis squared space plus space left parenthesis space b space minus space 4 space right parenthesis squared space equals space 26 space S i m p l i f y i n g space i t comma space w e space g e t colon
space left parenthesis space a space minus space 4 space right parenthesis squared space plus space left parenthesis space b space minus space 4 space right parenthesis squared space equals space 9 space
N o w space m e a n space i s colon
fraction numerator 1 plus 2 plus 6 plus a plus b over denominator 5 end fraction equals 4
S i m p l i f y i n g space i t comma space w e space g e t colon
a plus b equals 11
S o space t h e space n u m b e r s space 4 space a n d space 7 space s a t i s f y space b o t h space t h e s e space c o n d i t i o n 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)
Here we used the concept of variance to solve this question. Using mean we found the final answer. Finding the expected difference of deviation from the actual number is what is meant by variance. As a result, variance is influenced by the data set's standard deviation. So the two numbers are 4 and 7.
Related Questions to study
Maths-
are three non zero real numbers such that ![open parentheses x subscript 1 end subscript superscript 2 end superscript plus x subscript 2 end subscript superscript 2 end superscript close parentheses open parentheses x subscript 2 end subscript superscript 2 end superscript plus x subscript 3 end subscript superscript 2 end superscript close parentheses less or equal than open parentheses x subscript 1 end subscript x subscript 2 end subscript plus x subscript 2 end subscript x subscript 3 end subscript close parentheses to the power of 2 end exponent blank text then the G.M. of end text x subscript 1 end subscript comma x subscript 2 end subscript comma x subscript 3 end subscript text is end text](data:image/png;base64,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)
are three non zero real numbers such that ![open parentheses x subscript 1 end subscript superscript 2 end superscript plus x subscript 2 end subscript superscript 2 end superscript close parentheses open parentheses x subscript 2 end subscript superscript 2 end superscript plus x subscript 3 end subscript superscript 2 end superscript close parentheses less or equal than open parentheses x subscript 1 end subscript x subscript 2 end subscript plus x subscript 2 end subscript x subscript 3 end subscript close parentheses to the power of 2 end exponent blank text then the G.M. of end text x subscript 1 end subscript comma x subscript 2 end subscript comma x subscript 3 end subscript text is end text](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAdwAAAAYCAYAAABQrUzjAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAARqpSybAAAB4tJREFUeNrtXV+EnUcUH1ddEVVW1VpRS0SsWKvEirUiQtRaq6JErVi1ljxUHlb0pQ+RhwhVKw+1QvWhomKpFRWxQqyIqCoroqJWiYo+VF6iImJd4esc99xmM3f+fTNnvm/ut+fHsXvv3Z175nfOmTNnvvnmE6IfX0q5JJoN6N8Fj79jLhgMBoORBDNS1gP/t0DpSPlFyqGa++LSZx37y1y4uWA0F7n5KoOxJ9CWsi3lg8h2WlK+kPIwk36Z9BmW8oeUfcyFlQsqXJNylsOsFixIWR0wX2UwGg1YVrxM2N5OZv3T6XNFyjJzYeWCKtkucIjVnnSvDaCvMhiNBFR0o0RtnZByP6O+mfQZxcqOuTBzEYs5KT9xeGWBdbTHoPgqg9FIjEv5jaitEdG9FnQwk7659NmScoS50HJBgUdSxjjEssAY2iOVrxYZ970K3Y7ipOYFrhQ8k3JdypRDrylHuzMJ9Ye2n0h5nbn9RJN8C67drBB88WEptzF4c4CPPt9IOc9caLmIxSRXTNnhPtolxlefZ5xw69JtUXRXiCCBtfA92BMx74gB0Oueo+1fE+r/NMEkmxOuAzekfEpQPW1IeS+T2aevPp/hLJS56OfCB1OWAeOilK/2alBlCrDHpUhfLTLmqA7dxrBKHArU93cpxwyfn8BEXrBfNwd3pRw3fLYk5WvN+5fxsx42RPjSYRmjU+szLWWTudBy4ZNoN4V5SeymlNlI3Sl5qGpgyrlvs2iXUF8tFNFxNItV2Q5Wdx9q2oHK72/8mx9E/w75XltnMJnZ2qpaNxWwGe1chF+dQTuYViQWAhLjHCbqDv78pCRfVcfYILevcncQx8ZXJm7/dTgV3CowrCyfrDqMVyQazKj12a8sQzEX8Ym2h78U3UJ0p+Shykog176NoF1ifNVWRS4pSXxR9C+pQjW3jcmuhcnqqiERwWWOUUtbdeimAiYEByL9CpLiUU2s/Rngf8dQp3F8PY6vpyL9OnWMDWr7KodbhgnO/3DdCjCzy+lOlaiCUg1mlPq0cCbCXPRzoUu09zwSbQ+vxJvrWal1b7JdqrJxLBfw/g3N93U0Kx/zynv/aNo66dFWHbqp6BBwCfeo31Y+g9W2zwP8T7cbHV7/HOnXqWNsUNsvNOPeUOxgAsaH6wmwy/F9AgVdUqU+HebCOXiAHhciHTG17k22SxU2pki4+zz+/qVm5eNFie+oW7cUCVdgZT2Bv0O1+3TXhLVMYgR928p7bUM/ihr9sCntqxyeFt0d//MxA+MyOtZEAhJCLtxT6tNhLpyDR0iFWzWXTbZLFTamSLg+7/tMYFIkXCrdVEBi3B/oO7s/W9xVhcLP84H+V5Swe5FRjA1q+zoO35XyveheKjisfuhaRp3GZYqrtqxd4WBGqU/ZJeW9xEVs4nUtKfvqDg57UZjvIfVtK+bc4BR28dWnbFvA08cRNk6dcJ87ElSdCddHNxXfCfs1O9+EC7Z5It5s2moF+l+qCpcyXuuIYco48uUQ7groOy7VtlEIdlzdQieErL2VoNQvY3RqfcpsmtprXPgkXrgOYrqlwbZpqozuP4ru5pWCiIeQc4NT2sWmT4iNx7Dq0mFYvL1pKrRCbkUkNdj5uxTId5GBbipg0L9DkHAF+sGO6D9mtew1XHUCAMucNyP8mjJe64hh6jjy5VC778B0Kwwc3r+hKDaHhFLObHwNU0afMtXDJjEXVVRSofrYZm1lbgvanXjvGj4z3RZU1q9s3IS25bOakdouLn1C22pZJk6zhoG3DB4ZKgTfpHYIK7meH8Iu5OtECbcK3XSAw0TWRHdn9dAuO4wJ87K17vtbmAzaDj1tS92T2IfegRYT+Ho60K8p43UN3z+dKGYo2295FiA2DpeE5pwC3WEPbQzMAwbSZohmNr4I0cdnJuRz8EWq766aC9esLeTgCxt0B1/E6F4QtpXi3GBKfULbgkEFbnVYtCxxxT7jGXYPPxNx110ncTIKRwo+1lRkoQm3Ct1sA/RZrKQgEbxEm14tkXB9fd91bRkSyjZOsh8rCagMn5TxqkuI1DFM1b4rjnxs8xoTfd8JblTHGYYsf1QFUzWzgv1PxUXZSio1bLM2lQu1DzbRAXZaPsjQrwbtjOsy/IDYnsz0QPTf78lgpIApXteE+UAcipiJbd8njqJwBJcxmppwbdWMemA/NRc5PYHFNWtL8fCCh4Lu4QUUfjWIZ1yXARzReEXoTz6yPbyAwagi4X6EFfc7iWKGon1XHJGA8pF0OSVc20wo9eP5cqqkXLO2VI/ngxvMb2XiVzFnXKfyzVT66FYdwA4nOQ8waky4sLQ7nDBmYtv3iSMSLGNGb1LCdVUPpoeuU3CRWyXlmrWlfAD9CtFMMdavYs64ToFU+hwX/as05wT9pRIGo+o8UGUM6+KIDG2s7IYzJZp6JjSCFV07ARe5VVKuWZuNCyp8K8KvicScTZ2iHepVBwp9ev8Ptr0j3l6hAd5XBYMxeH5ddQzb4ogcsGNrvSEJ1zUTgpNcTiXiIrdKyjVrc3HBYDAYjASA83JDbxvIqYKw6QL9W07IRa6VlG7W5ssFg8FgMCLwH5/xoiBrDbKwAAADK3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtc3Vic3VwPjxtaT54PC9taT48bW4+MTwvbW4+PG1uPjI8L21uPjwvbXN1YnN1cD48bW8+KzwvbW8+PG1zdWJzdXA+PG1pPng8L21pPjxtbj4yPC9tbj48bW4+MjwvbW4+PC9tc3Vic3VwPjwvbXJvdz48L21mZW5jZWQ+PG1mZW5jZWQgc2VwYXJhdG9ycz0ifCI+PG1yb3c+PG1zdWJzdXA+PG1pPng8L21pPjxtbj4yPC9tbj48bW4+MjwvbW4+PC9tc3Vic3VwPjxtbz4rPC9tbz48bXN1YnN1cD48bWk+eDwvbWk+PG1uPjM8L21uPjxtbj4yPC9tbj48L21zdWJzdXA+PC9tcm93PjwvbWZlbmNlZD48bW8+JiN4MjI2NDs8L21vPjxtc3VwPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93Pjxtc3ViPjxtaT54PC9taT48bW4+MTwvbW4+PC9tc3ViPjxtc3ViPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3ViPjxtbz4rPC9tbz48bXN1Yj48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1Yj48bXN1Yj48bWk+eDwvbWk+PG1uPjM8L21uPjwvbXN1Yj48L21yb3c+PC9tZmVuY2VkPjxtbj4yPC9tbj48L21zdXA+PG1pPiYjeEEwOzwvbWk+PG10ZXh0PnRoZW4mI3hBMDt0aGUmI3hBMDtHLk0uJiN4QTA7b2YmI3hBMDs8L210ZXh0Pjxtc3ViPjxtaT54PC9taT48bW4+MTwvbW4+PC9tc3ViPjxtbz4sPC9tbz48bXN1Yj48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1Yj48bW8+LDwvbW8+PG1zdWI+PG1pPng8L21pPjxtbj4zPC9tbj48L21zdWI+PG10ZXh0PiYjeEEwO2lzPC9tdGV4dD48L21hdGg+pSLVTgAAAABJRU5ErkJggg==)
Maths-General
Maths-
When 10 is subtracted from all the observations, the mean is reduced to 60% of its value. If 5 is added to all the observations, then the mean will be
Hence, the new mean is 30.
When 10 is subtracted from all the observations, the mean is reduced to 60% of its value. If 5 is added to all the observations, then the mean will be
Maths-General
Hence, the new mean is 30.
Maths-
If mean deviation through median is 15 and median is 450, then coefficient of mean deviation is
Hence, the coefficient of Mean Deviation is 1/30.
If mean deviation through median is 15 and median is 450, then coefficient of mean deviation is
Maths-General
Hence, the coefficient of Mean Deviation is 1/30.
Maths-
The standard deviation of the data given by Variate (x) 0 1 2 3. . . . . n Frequency (f) ![blank to the power of n end exponent C subscript 0 end subscript blank to the power of n end exponent C subscript 1 end subscript blank to the power of n end exponent C subscript 2 end subscript blank to the power of n end exponent C subscript 3 end subscript midline horizontal ellipsis times blank to the power of n end exponent C subscript n end subscript](data:image/png;base64,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)
The standard deviation of the data given by Variate (x) 0 1 2 3. . . . . n Frequency (f) ![blank to the power of n end exponent C subscript 0 end subscript blank to the power of n end exponent C subscript 1 end subscript blank to the power of n end exponent C subscript 2 end subscript blank to the power of n end exponent C subscript 3 end subscript midline horizontal ellipsis times blank to the power of n end exponent C subscript n end subscript](data:image/png;base64,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)
Maths-General
Maths-
If the standard deviation of 0,1,2,3…..9 is K, then the standard deviation of 10,11,12,13…. 19 is
If the standard deviation of 0,1,2,3…..9 is K, then the standard deviation of 10,11,12,13…. 19 is
Maths-General
Maths-
When 15 was subtracted from each of the seven observations the following number resulted : -3,0,-2,4,6,1,1. The mean of the distribution is
When 15 was subtracted from each of the seven observations the following number resulted : -3,0,-2,4,6,1,1. The mean of the distribution is
Maths-General
Maths-
The standard deviation of a variable x is
. The standard deviation of the variable
where a, b, c are constants is ...
The standard deviation of a variable x is
. The standard deviation of the variable
where a, b, c are constants is ...
Maths-General
Maths-
If
then the value of
dx is equal to
If
then the value of
dx is equal to
Maths-General
Maths-
If
then I equals
If
then I equals
Maths-General
Maths-
Maths-General
Maths-
A square ABCD is inscribed in a circle of radius 4. A point P moves inside the circle such that
min(d(P,BC),d(P,DA)) where d(P,AB) is the distance of a point P from line AB. The area of region covered by the moving point P is (sq units)
A square ABCD is inscribed in a circle of radius 4. A point P moves inside the circle such that
min(d(P,BC),d(P,DA)) where d(P,AB) is the distance of a point P from line AB. The area of region covered by the moving point P is (sq units)
Maths-General
Maths-
If
then the value of
is equal to ____
If
then the value of
is equal to ____
Maths-General
Physics-
2k-mol of an ideal diatomic gas is enclosed in a vertical cylinder fitted with a piston and spring as shown in the figure. Initially the spring is compressed by 5 cm and then the electric heater starts supplying energy to the gas at constant rate of 100 J/S and due to conduction through walls of cylinder and radiation, 20 J/S has been lost to surroundings ( Take K=1000 N/m,
atomospheric pressure,
, cross section area of piston
, mass of piston m=1 kg R=8.3kj mol k) Answer the given question based on this information.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/620748/1/1119656/Picture5.png)
The initial pressure of the gas is
2k-mol of an ideal diatomic gas is enclosed in a vertical cylinder fitted with a piston and spring as shown in the figure. Initially the spring is compressed by 5 cm and then the electric heater starts supplying energy to the gas at constant rate of 100 J/S and due to conduction through walls of cylinder and radiation, 20 J/S has been lost to surroundings ( Take K=1000 N/m,
atomospheric pressure,
, cross section area of piston
, mass of piston m=1 kg R=8.3kj mol k) Answer the given question based on this information.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/620748/1/1119656/Picture5.png)
The initial pressure of the gas is
Physics-General
Physics-
A system is taken from state ' i ' to the state 'f' along the path 'iaf', it is found that
=20 cal. Along the path 'ibf'.
cal.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/625493/1/1119651/Picture14.png)
If
for curved path 'fi', what is the '
for this path ?
A system is taken from state ' i ' to the state 'f' along the path 'iaf', it is found that
=20 cal. Along the path 'ibf'.
cal.
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/625493/1/1119651/Picture14.png)
If
for curved path 'fi', what is the '
for this path ?
Physics-General
Physics-
Find the efficiency of the thermodynamic cycle shown in figure for an ideal diatomic gas.
![](data:image/png;base64,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)
Find the efficiency of the thermodynamic cycle shown in figure for an ideal diatomic gas.
![](data:image/png;base64,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)
Physics-General