Question

class 5-15,15-25,25-35,35-45,45-55,55-65. fi 6,11,21,23,14,5 find the mean​

Answer 1

Here,

First we have to construct the frequency table (attachment).

Analysis :

We will be solving this sum by direct method. After constructing the table, we have to find the class mark of each class. Then we have to multiply the class marks with the given frequencies. After getting the product of frequency and class mark we will add them all to get their summation. Then dividing the sum of the product by the sum of frequencies we will get the mean.

Explanation :

Formula,

$\bf Mean=\dfrac{\sum f_iy_i}{\sum f_i}$

where, (according to attachment)

• fᵢyᵢ = 2830
• fᵢ = 80

Substituting the values,

$\\ \implies\sf Mean=\dfrac{2830}{80}$

$\\ \implies\sf Mean=\dfrac{283\!\!\!\not{0}}{8\!\!\!\not{0}}$

$\\ \implies\sf Mean=\dfrac{283}{8}$

$\\ \therefore\boxed{\bf Mean=35.375}$

The mean is 35.375

Explore More :

• Mean by Short-Cut Method :

$\bf Mean=a+\dfrac{\sum f_id_i}{\sum f_i}$

• Mean by Step-Deviation Method :

$\bf Mean=a+c\times\dfrac{\sum f_iu_i}{\sum f_i}$

where,

• a = Assumed Mean
• c = Class Width
• fᵢ = Frequency
• dᵢ = Class Mark - a
• uᵢ = dᵢ/c