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If the quartiles for the following distributions are Q1=23.125 and Q3 =43.5, find the missing frequencies and median of the following frequencies distribution: daily wages 0-10. 10-20 20-30. 30-40. 40-50. 50-60. and no. of workers are 5. - 20. 30. - 10?
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If the quartiles for the following distributions are Q1=23.125 and Q3 ...
Given Information:
Q1 = 23.125
Q3 = 43.5
Class intervals and the number of workers:
0-10: 5
10-20: 20
20-30: ?
30-40: 30
40-50: ?
50-60: 10
Finding the Missing Frequencies:
To find the missing frequencies, we need to use the formula for the interquartile range (IQR), which is:
IQR = Q3 - Q1
Substituting the given values, we get:
IQR = 43.5 - 23.125 = 20.375
Next, we need to find the median of the data set. We know that the median is the middle value of the data set. Since we have 65 workers in total, the median will be the average of the 33rd and 34th values when the data is arranged in ascending order.
To find the values corresponding to the 33rd and 34th positions, we need to add up the frequencies until we reach the median. We start with the first class interval:
0-10: 5
Adding the next class interval:
10-20: 20 (total: 25)
Adding the next class interval:
20-30: ? (total: ?)
Adding the next class interval:
30-40: 30 (total: ?)
Adding the next class interval:
40-50: ? (total: ?)
Adding the final class interval:
50-60: 10 (total: 65)
Since the median is between the 33rd and 34th values, we know that it falls within the 20-30 class interval. Let the frequency of this interval be x. Then, we can write:
25 + x/2 = 33.5
Subtracting 25 from both sides, we get:
x/2 = 8.5
Multiplying both sides by 2, we get:
x = 17
Therefore, the missing frequencies are:
20-30: 17
40-50: 8
Final Frequency Distribution:
0-10: 5
10-20: 20
20-30: 17
30-40: 30
40-50: 8
50-60: 10
Conclusion:
In this question, we used the interquartile range formula to find the missing frequencies and the median of a frequency distribution. We also used simple arithmetic to solve for the missing values and arrived at a final frequency distribution.
Q1 = 23.125
Q3 = 43.5
Class intervals and the number of workers:
0-10: 5
10-20: 20
20-30: ?
30-40: 30
40-50: ?
50-60: 10
Finding the Missing Frequencies:
To find the missing frequencies, we need to use the formula for the interquartile range (IQR), which is:
IQR = Q3 - Q1
Substituting the given values, we get:
IQR = 43.5 - 23.125 = 20.375
Next, we need to find the median of the data set. We know that the median is the middle value of the data set. Since we have 65 workers in total, the median will be the average of the 33rd and 34th values when the data is arranged in ascending order.
To find the values corresponding to the 33rd and 34th positions, we need to add up the frequencies until we reach the median. We start with the first class interval:
0-10: 5
Adding the next class interval:
10-20: 20 (total: 25)
Adding the next class interval:
20-30: ? (total: ?)
Adding the next class interval:
30-40: 30 (total: ?)
Adding the next class interval:
40-50: ? (total: ?)
Adding the final class interval:
50-60: 10 (total: 65)
Since the median is between the 33rd and 34th values, we know that it falls within the 20-30 class interval. Let the frequency of this interval be x. Then, we can write:
25 + x/2 = 33.5
Subtracting 25 from both sides, we get:
x/2 = 8.5
Multiplying both sides by 2, we get:
x = 17
Therefore, the missing frequencies are:
20-30: 17
40-50: 8
Final Frequency Distribution:
0-10: 5
10-20: 20
20-30: 17
30-40: 30
40-50: 8
50-60: 10
Conclusion:
In this question, we used the interquartile range formula to find the missing frequencies and the median of a frequency distribution. We also used simple arithmetic to solve for the missing values and arrived at a final frequency distribution.
Community Answer
If the quartiles for the following distributions are Q1=23.125 and Q3 ...
Kya ye minus 20 aur 10 h frequency? I am not sure what is the frequency
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If the quartiles for the following distributions are Q1=23.125 and Q3 =43.5, find the missing frequencies and median of the following frequencies distribution: daily wages 0-10. 10-20 20-30. 30-40. 40-50. 50-60. and no. of workers are 5. - 20. 30. - 10?
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If the quartiles for the following distributions are Q1=23.125 and Q3 =43.5, find the missing frequencies and median of the following frequencies distribution: daily wages 0-10. 10-20 20-30. 30-40. 40-50. 50-60. and no. of workers are 5. - 20. 30. - 10? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about If the quartiles for the following distributions are Q1=23.125 and Q3 =43.5, find the missing frequencies and median of the following frequencies distribution: daily wages 0-10. 10-20 20-30. 30-40. 40-50. 50-60. and no. of workers are 5. - 20. 30. - 10? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the quartiles for the following distributions are Q1=23.125 and Q3 =43.5, find the missing frequencies and median of the following frequencies distribution: daily wages 0-10. 10-20 20-30. 30-40. 40-50. 50-60. and no. of workers are 5. - 20. 30. - 10?.
If the quartiles for the following distributions are Q1=23.125 and Q3 =43.5, find the missing frequencies and median of the following frequencies distribution: daily wages 0-10. 10-20 20-30. 30-40. 40-50. 50-60. and no. of workers are 5. - 20. 30. - 10? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about If the quartiles for the following distributions are Q1=23.125 and Q3 =43.5, find the missing frequencies and median of the following frequencies distribution: daily wages 0-10. 10-20 20-30. 30-40. 40-50. 50-60. and no. of workers are 5. - 20. 30. - 10? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the quartiles for the following distributions are Q1=23.125 and Q3 =43.5, find the missing frequencies and median of the following frequencies distribution: daily wages 0-10. 10-20 20-30. 30-40. 40-50. 50-60. and no. of workers are 5. - 20. 30. - 10?.
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