Question

I want answer of this quick​

Answer 1

Answer: 15.55

Step-by-step explanation:

• the arthmetic means is given by A.M= ∑fx/N

• x*f

       10*4= 40

       12*5= 60

       14*8= 112

       16*10= 160

       18*7= 126

       20*4= 80

       22*2= 44        

• ∑fx=622
• N= ∑f= 40
• Now, according to the formula, ∑fx/N

       =622/40= 15.55

Answer 2

Question :-

Find the arithmetic mean of the following data :

$\begin{tabular}{|c|c|c|c|c|c|c|c|} \cline{1-8} x & 10 & 12 & 14 & 16 & 18 & 20 & 22 \\ \cline{1-8} f & 4 & 5 & 8 & 10 & 7 & 4 & 2 \\ \cline{1-8} \end{tabular}$

Answer :-

Given :-

$\: \begin{tabular}{|c|c|c|c|c|c|c|c|} \cline{1-8} x & 10 & 12 & 14 & 16 & 18 & 20 & 22 \\ \cline{1-8} f & 4 & 5 & 8 & 10 & 7 & 4 & 2 \\ \cline{1-8} \end{tabular}$

Required to find :-

• Arithmetic mean ?

Formula used :-

$\boxed{\sf{ Mean = \dfrac{ \sum fi xi }{ \sum fi } }}$

Solution :-

Given information :-

$\: \begin{tabular}{|c|c|c|c|c|c|c|c|} \cline{1-8} x & 10 & 12 & 14 & 16 & 18 & 20 & 22 \\ \cline{1-8} f & 4 & 5 & 8 & 10 & 7 & 4 & 2 \\ \cline{1-8} \end{tabular}$

we need to find the arithmetic mean

In order to find the value of the arithmetic mean we should find the value of fixi and fi .

So,

The above table can be modified and can be written as ;

Here,

While using the formula we need to substitute the total sum of fixi and fi .

This is very important to be understand .

The table is as follows ;

$\large{ \begin{tabular}{|c|c|c|} \cline{1-3} x & f & fixi \\ \cline{1-3} 10 & 4 & 40 \\ \cline{1-3} 12 & 5 & 60 \\ \cline{1-3} 14 & 8 & 112 \\ \cline{1-3} 16 & 10 & 160 \\ \cline{1-3} 18 & 7 & 126 \\ \cline{ 1-3} 20 & 4 & 80 \\ \cline{ 1-3} 22 & 2 & 44 \\ \cline{ 1-3} Total & fi = 40 & fixi = 622 \\ \cline{1 - 3} \end{tabular}}$

Using the formula ;

$\boxed{\sf{ Mean = \dfrac{ \sum fi xi }{ \sum fi } }}$

$\to \tt Mean = \dfrac{ 622}{ 40 } \\ \\ \to \tt Mean = 15.55$

Therefore ,

Arithmetic mean = 15.55

Additional Information :-

The mean of any given data can be founded in 2 ways .

• 1. Simple method

• 2. Deviation method

The above sum is solved using the simple method only .

In simple method we will use the formula of the arithmetic mean i.e. sum of the observations by Number of observations in the form of xifi & fi .

The symbol $\sum$ means " sigma " .

Here, fi refers to frequency of the statical data .

Mean , mode , median are called as " central tendency "

These are very useful in solving many problems related to statics .

Mean is the average of the given data set .

Mode is the most occurring value / observations in the given data set

Median is the middle most term of the given data set .

In deviation method , we will assume one of the observation as the mean and solve the question .

The formula is ;

$\tt{ Mean \; \bar{x} = A + \dfrac{ \sum fidi }{ \sum fi } }$

Here,

A = assumed mean

di is calculated by ;

di = xi - A