Question

The distribution gives the weights of 60 students of a class. find the mean and mode weights of the students.
weight (in kg)
40-44
44-48
48-52
52-56
56-60
60-64
64-68
68-72
number of students 4
6
10
14
10
8
6
2

Answer 1

The mean weight of the students=55.2

The mode weight of the students=54

Step-by-step explanation:

Total number of students$\sum f_{i}$=60

$f_i$                      4 6 10 14 10 8 6 2

Class mark:$x_i$  42 46 50 54 58 62 66 70

By using formula $x_i=\frac{Upper\;limit+lower\;limit}{2}$

$f_{i}x_{i}$:168  276 500 756 580 496 396 140

$\sum f_{i}x_{i}=168+276+500+756+580+496+396+140$

$\sum f_{i}x_{i}=3312$

Direct method: $mean(\bar x)=\frac{\sum f_{i}x_{i}}{\sum f_{i}}$

By using this formula

Mean=$\bar{x}=\frac{3312}{60}=55.2$

For mode

Mode observation=52-56

L=52,$f_1=14,f_0=10,f_2=10,h=4$

Mode=$l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$

Modal class: That observation in which frequency is highest.

Where l=Lower limit of modal class

$f_1=$ Frequency of modal class

$f_0=$ Just previous modal class frequency

$f_2=$ Just after the modal class frequency

h=Size of the class interval

Substitute the values then we get

Mode=52+$\frac{14-10}{2(14)-10-10}\times 4$

Mode=52+2=54

Hence, mode=54

#Learns more:

https://brainly.in/question/2263587 :Answered by Jackson

Answer 2

Answer:

mean 52.5and median 54.5