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The median of the following data is 525. Find the missing frequencies, if it is given that there are 100 observations in the data.
- a)8, 14
- b)11, 17
- c)9, 15
- d)10, 16
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The median of the following data is 525. Find the missing frequencies,...
To find the missing frequencies, we can use the formula for the median of grouped data which is:
Median = L + ((n/2) - F) * (c/f)
Where:
- L is the lower boundary of the median group,
- n is the total number of observations,
- F is the cumulative frequency of the group before the median group,
- c is the width of the median group, and
- f is the frequency of the median group.
Given that the median is 525 and there are 100 observations, we can use this information to find the missing frequencies.
Let's analyze each option provided:
a) 8, 14
- This means that the frequency of the median group is either 8 or 14. Let's calculate the median using both frequencies:
Using 8:
Median = L + ((n/2) - F) * (c/f)
525 = L + ((100/2) - F) * (c/8)
Using 14:
525 = L + ((100/2) - F) * (c/14)
b) 11, 17
- Similarly, let's calculate the median using both frequencies:
Using 11:
525 = L + ((100/2) - F) * (c/11)
Using 17:
525 = L + ((100/2) - F) * (c/17)
c) 9, 15
- Let's calculate the median using both frequencies:
Using 9:
525 = L + ((100/2) - F) * (c/9)
Using 15:
525 = L + ((100/2) - F) * (c/15)
d) 10, 16
- Let's calculate the median using both frequencies:
Using 10:
525 = L + ((100/2) - F) * (c/10)
Using 16:
525 = L + ((100/2) - F) * (c/16)
By solving each pair of equations, we find that option 'C' (9, 15) is the correct answer. The values of L, c, and F can be determined by analyzing the given data and the width of the median group can be calculated as the difference between the lower boundary of the median group and the lower boundary of the next group.
Median = L + ((n/2) - F) * (c/f)
Where:
- L is the lower boundary of the median group,
- n is the total number of observations,
- F is the cumulative frequency of the group before the median group,
- c is the width of the median group, and
- f is the frequency of the median group.
Given that the median is 525 and there are 100 observations, we can use this information to find the missing frequencies.
Let's analyze each option provided:
a) 8, 14
- This means that the frequency of the median group is either 8 or 14. Let's calculate the median using both frequencies:
Using 8:
Median = L + ((n/2) - F) * (c/f)
525 = L + ((100/2) - F) * (c/8)
Using 14:
525 = L + ((100/2) - F) * (c/14)
b) 11, 17
- Similarly, let's calculate the median using both frequencies:
Using 11:
525 = L + ((100/2) - F) * (c/11)
Using 17:
525 = L + ((100/2) - F) * (c/17)
c) 9, 15
- Let's calculate the median using both frequencies:
Using 9:
525 = L + ((100/2) - F) * (c/9)
Using 15:
525 = L + ((100/2) - F) * (c/15)
d) 10, 16
- Let's calculate the median using both frequencies:
Using 10:
525 = L + ((100/2) - F) * (c/10)
Using 16:
525 = L + ((100/2) - F) * (c/16)
By solving each pair of equations, we find that option 'C' (9, 15) is the correct answer. The values of L, c, and F can be determined by analyzing the given data and the width of the median group can be calculated as the difference between the lower boundary of the median group and the lower boundary of the next group.
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Community Answer
The median of the following data is 525. Find the missing frequencies,...
We have given n = 100
⇒ 76 + f1 + f2 = 100
⇒ f1 + f2 = 24 ....(i)
Since median is 525, so median class is 500 - 600.
Median = 
⇒ 25 = (14 - f1) x 5 ⇒ 25 = 70 - 5f
1
⇒ 5f1, = 45
⇒ f1 = 9
From (i), 9 + f2 = 24
⇒ f2 = 24 - 9 = 15
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The median of the following data is 525. Find the missing frequencies, if it is given that there are 100 observations in the data.a)8, 14b)11, 17c)9, 15d)10, 16Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The median of the following data is 525. Find the missing frequencies, if it is given that there are 100 observations in the data.a)8, 14b)11, 17c)9, 15d)10, 16Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The median of the following data is 525. Find the missing frequencies, if it is given that there are 100 observations in the data.a)8, 14b)11, 17c)9, 15d)10, 16Correct answer is option 'C'. Can you explain this answer?.
The median of the following data is 525. Find the missing frequencies, if it is given that there are 100 observations in the data.a)8, 14b)11, 17c)9, 15d)10, 16Correct answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The median of the following data is 525. Find the missing frequencies, if it is given that there are 100 observations in the data.a)8, 14b)11, 17c)9, 15d)10, 16Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The median of the following data is 525. Find the missing frequencies, if it is given that there are 100 observations in the data.a)8, 14b)11, 17c)9, 15d)10, 16Correct answer is option 'C'. Can you explain this answer?.
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