Question

The following is the distribution of height of students of certain class in a certain city:
Find the average height of maximum number of students.
Height(in cms): 160-162 163-165 166-168 169-171 172-174
No.of students: 15 118 142 127 18

Answer 1

The average height of maximum number of students is 167.35 cm.

Given data,

Height(in cms):     No. of students

160-162                        15

163-165                        118

166-168                        142

169-171                         127

172-174                         18

Gap = 163-162 = 1

Gap/2 = 1/2 = 0.5

We need to add Gap/2 to the upper limits of class and subtract Gap/2 from the lower limits of class in order to get a continuous function.

Height(in cms):     No. of students      

159.5-162.5                        15

162.5-165.5                        118

165.5-168.5                        142

168.5-171.5                         127

171.5-174.5                           18

The class interval with highest frequency is 165.5-168.5 with a frequency of 142.

Therefore, the modal class interval is 165.5-168.5.

We have formula for calculating the  average height,

$Mode = l + \dfrac{f_0-f_1}{2f_0-f_1-f_2} * h$

h = class interval size = 168.5 - 165.5 = 3

l = lower limit of modal class = 165.5

f_0 = frequency of modal class = 142

f_1 = frequency of the class preceding the modal class = 118

f_2 =  frequency of the class preceding the modal class = 127

Mode = 165.5 + [ (142-118) / (2*142 - 118 - 127) ] * 3

= 165.5 + 72/39

= 167.35.

Answer 2

Average height  = 171.18 cm.

Given:

Height(in cms): 160-162 163-165 166-168 169-171 172-174

No.of students: 15 118 142 127 18

To find:

Average height of maximum number of students.

Steps:

Height(in cms) : 160-162 163-165 166-168 169-171  172-174      

Mid value (x)    :  161   164  167   170  173

Frequency of no.of students (f) : 15   118   142  127   18

Mid value × No.of students (fx) : 2415  19352  23714 21590 3114  

                                ∑(f) : 15 + 118 + 142 + 127 + 18 = 410

                            ∑(fx) : 2415 + 19352 + 23714 + 21590 + 3114                                               = 70185          

Finding the average height :              

Average height =$\frac{\sum f x}{\sum f}$                        

                           = $\frac{70185}{410}$                            

                           = 171.18 cm.        

Note : Table is attached below, refer it for better understanding.                  

Therefore, the average height is 171.18 cm.

To learn more...

1. The mean age of a group of 100 children was 9.35 years the mean age of 25 of them was 8.75 years and that of another 65 of them was 10.51 years what is the mean age of the remaining children​

brainly.in/question/10972224

2. The mean of 25 observation is 65 and mean of next 10 observation is 62 find the mean of all 35 observation.

brainly.in/question/2396151