Arithmetic mean $=44,464.5/111=400.58$.

Arithmetic mean $=33,670/100=336.7$.

Incorrect mean,
$X=50$kg.
$\displaystyle\sum f _i=98$
Incorrect X$=\displaystyle\frac{Incorrect \displaystyle\sum f _iX _i}{\displaystyle\sum f _i}$
$50=\displaystyle\frac{Incorrect \displaystyle\sum f _iX _i}{98}$
$\therefore$ Incorrect $\displaystyle\sum f _iX _i=98\times 50=4900$
Now, Correct $\displaystyle\sum f _iX _i=$Incorrect $\displaystyle\sum f _iX _i-(8\times 35)+(10\times 35)$
Note, the class-mark of class interval $(30-40)$ is $35$ and for the calculation of the mean, we consider class marks.
Correct $\displaystyle\sum f _iX _i=4900-280+350$
$=4,970$
Also, Correct $\displaystyle\sum f _i=98+2=100$
$\therefore$ Correct Mean$=\displaystyle\frac{Correct \displaystyle\sum f _iX _i}{Correct \displaystyle\sum f _i}$
$=\displaystyle\frac{4970}{100}$
$X=49.70$lbs.

Arithmetic mean $=1,015/45=22.55$.

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class. 

To calculate the mean of a continuous series, mid points of the various class intervals is taken. For example, if the class is like 10-20 then before calculating the mean mid point that is 15 is calculated for the whole series which is added and divided by the number of terms in order to ascertain the mean. 

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean for grouped data like direct method where all the data are multiplied with their respective frequencies and then added up which are then divided by the summation of the frequencies or number of figures in the data in order to ascertain the mean. The formula is sfX/ sf where sfd is the summation of frequency multiplied by X for all figures and sf is the frequency or the number of element in the given data. 

In assumed mean method, any value can be taken as assumed mean whether it is there in the data or not but it should be centrally located in the data so that to simply the big figures in the data in order to ascertain mean of the given data through easy calculations. For grouped data, the formula for assumed mean is A+ sfd/sf where A is the assumed mean, sfd is the summation of frequency multiplied with X-A for all figures and sf is the summation of frequency or the number of element in the given data. 

If 150 is divided in the ratio of 2:3:5, then 

Let the number in the given problem be x. Then, according to the problem 

Arithmetic mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing the sum by 2. In the given series the first term is 1 and  the last term is 100, so the 

Mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing the sum by 2. In the given series the first term 'a' is doubled and  the last term 'b' is also doubled , so the 

Mean = {(a+a)+ (b+b)}  /2 

          = (2a+2b) /2 

          = 2 (a+b) /2 

          = 2 [ (a+b)/2} 

Therefore, the mean is also doubled. So,if the mean was 15 then now it will be 30.  

The series of first 10 natural numbers is an arithmetic progressions with first tern as 1 and common difference 1. So the sum of the series will be S_n = n/2 { 2a+ ( n-1 ) d } where n is the number of terms in the series, a is the first term and d is the common difference.

S₁₀= 10/2 { 2(1) + ( 10-1 ) 1 }

     = 5 ( 2+9)

    = 5 ( 11 )

    = 55

0−10 | 10−20 | 20−30 | 30−40 | | --- | --- | --- | --- | --- | | Frequency(f) | 8 | 10 | 12 | 15 | | Class mark ( mid points= x) | 5 | 15 | 25 | 35 | | Fx | 40 | 150 | 300 | 525 |

Mean = summation of fx / summation of f

          = 1015/ 45

          = 22.55

The mean salary of 40 females and 60 males are 5,200 and 6,800 rupees respectively. Therefore the total salary of 40 females and 60 males will be 5,200x40 and 6,800x60 rupees respectively. So the average salary of 40 females and 60 males will be

The average marks of 70, 50 and 30 students respectively is 50, 55 and 45 marks. Therefore the total marks of 70, 50 and 30 students will be 70x50, 50x55, and 30x45 respectively. So the average marks of all the 150 students is 

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation in the data which is divided by the number of observations in the data. Since mean includes all the values of the series of observation therefore only this average value is included in the algebraic calculations. 

Arithmetic mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class. 

Measures of central tendency is a mathematical concept that measures the central most value of a given series which can represent the whole set of the series. In a given series, the central location of the observation is measured through different tools in order to ascertain the most efficient value that can represent the series.

The geometric mean is a geometric series which is in the form of arⁿ where a is the first term and r is the common ratio.

T₁= 5 and T₅ = 3125

Now, T₁/T₅ = 5/ 3125

=>ar^1//ar⁵ =1/ 625

=> 1/ r⁴ = 1/625

=> r⁴ = 625

=> r = 5

So if r=5, then a= 1

T₂ = ar²

      = 1(5) ² = 25

T₃ = ar³

      = 1(5) ³ = 125

T₄ = ar⁴

      = 1(5)⁴ = 625

Therefore, three geometric means between 5 and 3125 are 25, 125 and 625. 

In geometric mean method, the average percentage increase in the population is assumed to be constant decade to decade through which future population is worked out. Therefore, it is the most appropriate average to be used to compute the average rate of growth in population. 

Mean refers to the average amount in a given group of data. So arithmetic mean can be calculated by adding the first term and the last term of the series and then dividing the sum by 2. In the given series the first term 'a' is decreased by 2 and  the last term 'b' is also decreased by 2 , so the 

Mean = {(a-2)+ (b-2)}  /2 

          = (a+b-4) /2 

          = {(a+b)/2} - 4/2

          = {(a+b)/2} - 2 

Therefore, the mean is also decreased by 2. So,if the mean was 15 then now it will be 13. 

Mathematical average refers to all such average where a figure is taken out through mathematical methods from the a given series that represents the whole series. Harmonic mean is a mathematical tool which is used to calculate average of a certain series. Therefore, it is a part of mathematical average. 

Given,

$x _1,x _2,x _3,x _4...x _10\x _1^2+x _2^2+x _3^2+x _4^2+....x _10^2=17 (Given) \rightarrow (i)$

Sum of deviations from $50$ is $-10$

Let m be the mean and s be the standard deviation and find the z score.
$z = (x - m) /s = (0.8 s + m - m) / s = 0.8$
The percentage of student who scored above Jane is (from table of normal distribution).
1 - 0.7881 = 0.2119 = 21.19%
The number of student who scored above Jane is (from table of normal distribution).
21.19% 0f 500 = 106

Consider the following table, to calculate mean by "shift of origin method":