The below distribution gives the weight of the 40 students in the class find the median weight of the students. weight of kg 30-35 35-40 40-45 45-50 50-55 55-60 No of students 4 5 10 8 8 5
Answers
Answer:
The distribution below gives the weights of 30 students of a class. Find the median weight of the students
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
Solution:
We know that,
Median = l + [(n/2 - cf)/f] × h
Class size, h
Number of observations, n
Lower limit of median class, l
Frequency of median class, f
Cumulative frequency of class preceding median class, cf
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
n = 30 ⇒ n/2 = 15
From the table, it can be observed that cumulative frequency (cf) just greater than 15 is 19, belonging to class 55 - 60.
Therefore, median class = 55 - 60
Class size, h = 5
Lower limit of median class, l = 55
Frequency of median class, f = 6
Cumulative frequency of class preceding median class, cf = 13
Median = l +[ (n/2 - cf)/f] × h
= 55 + [(15 - 13)/6] × 5
= 55 + (2/6) × 5
= 55 + 5/3
= 55 + 1.67
= 56.67
Therefore, median weight is 56.67 kg.
Step-by-step explanation:
the table is attached
Concept:
The median is the middle value in the list of given numbers, sorted numerically from smallest to biggest, while the mode is the value of the number that appears in the list the most frequently. The mean is the average where the sum of all the numbers is divided by the total number of numbers.
Given:
The below distribution gives the weight of the 40 students in the class
Find:
find the median weight of the students. weight of kg 30-35 35-40 40-45 45-50 50-55 55-60 No of students 4 5 10 8 8 5
Solution:
We know that,
Median = l + [(n/2 - cf)/f] × h
Class size, h
Number of observations, n
Lower limit of median class, l
Frequency of median class, f
Cumulative frequency of class preceding median class, cf
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
n = 30 ⇒ n/2 = 15
From the table, it can be observed that cumulatIve frequency (cf) just greater than 15 is 19, belonging to class 55 - 60.
Therefore, median class = 55 - 60
Class size, h = 5
Lower limit of median class, l = 55
Frequency of median class, f = 6
Cumulative frequency of class preceding median class, cf = 13
Median = l +[ (n/2 - cf)/f] × h
= 55 + [(15 - 13)/6] × 5
= 55 + (2/6) × 5
= 55 + 5/3
= 55 + 1.67
= 56.67
Therefore, median weight is 56.67 kg.
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