Answer
384.6k+ views
Hint: First assume the missing frequency of class 49-52. Then take the mid values of each class as ${x_i}$ and frequency ${f_i}$. The mean value is equivalent to the fraction between the addition of a product of mid-value with frequency and the total frequency.
Complete Step by Step Solution:
Given the mean for the given frequency distribution is 47.2.
Let the missing frequency be $x$.
The frequency distribution table for the given data is as follows:
We know that the general formula to find the mean value is,
Mean $ = \dfrac{{\sum {{x_i}{f_i}} }}{{\sum {{x_i}} }}$
Now, we will substitute the value for the sum of the product of frequency and midpoint and the value for the sum of total frequency.
$ \Rightarrow 47.2 = \dfrac{{8162 + 50.5x}}{{176 + x}}$
Cross-multiply the terms,
$ \Rightarrow 8307.2 + 47.2x = 8162 + 50.5x$
Move variable part on one side and constant part on another side,
$ \Rightarrow 50.5x - 47.2x = 8307.2 - 8162$
Subtract the like terms,
$ \Rightarrow 3.3x = 145.2$
Divide both sides by 3.3,
$\therefore x = 44$
Hence the missing frequency is 44.
Note: In such types of problems, the class will not be taken only mid-point should be taken because the interval cannot be multiplied to the frequency. If we don’t remember the formula, we can multiply each midpoint with frequency and add all of them then divide it with the sum of frequency.
In the mean formula, while computing $\sum {fx} $, don’t take the sum of $f$ and $x$ separately and then multiply them. It will be difficult. Students should carefully make the frequency distribution table; there are high chances of making mistakes while copying and computing data.
Complete Step by Step Solution:
Given the mean for the given frequency distribution is 47.2.
Let the missing frequency be $x$.
The frequency distribution table for the given data is as follows:
Class | Frequency (${f_i}$) | Mid-value (${x_i}$) | ${f_i}{x_i}$ |
40-43 | 31 | 41.5 | 1286.5 |
43-46 | 58 | 44.5 | 2581 |
46-49 | 60 | 47.5 | 2850 |
49-52 | $x$ | 50.5 | \[50.5x\] |
52-55 | 27 | 53.5 | 1444.5 |
Total | $\sum {{f_i}} = 176 + x$ | $\sum {{f_i}{x_i}} = 8162 + 50.5x$ |
We know that the general formula to find the mean value is,
Mean $ = \dfrac{{\sum {{x_i}{f_i}} }}{{\sum {{x_i}} }}$
Now, we will substitute the value for the sum of the product of frequency and midpoint and the value for the sum of total frequency.
$ \Rightarrow 47.2 = \dfrac{{8162 + 50.5x}}{{176 + x}}$
Cross-multiply the terms,
$ \Rightarrow 8307.2 + 47.2x = 8162 + 50.5x$
Move variable part on one side and constant part on another side,
$ \Rightarrow 50.5x - 47.2x = 8307.2 - 8162$
Subtract the like terms,
$ \Rightarrow 3.3x = 145.2$
Divide both sides by 3.3,
$\therefore x = 44$
Hence the missing frequency is 44.
Note: In such types of problems, the class will not be taken only mid-point should be taken because the interval cannot be multiplied to the frequency. If we don’t remember the formula, we can multiply each midpoint with frequency and add all of them then divide it with the sum of frequency.
In the mean formula, while computing $\sum {fx} $, don’t take the sum of $f$ and $x$ separately and then multiply them. It will be difficult. Students should carefully make the frequency distribution table; there are high chances of making mistakes while copying and computing data.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)