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The median and modal profits for the following data
Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30
No. of firms: 10 25 45 55 62 65
are
(a) 11.60 and 11.50 (b) ` 11556 and ` 11267
(c) ` 11875 and ` 11667 (d) 11.50 and 11.67?
Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30
No. of firms: 10 25 45 55 62 65
are
(a) 11.60 and 11.50 (b) ` 11556 and ` 11267
(c) ` 11875 and ` 11667 (d) 11.50 and 11.67?
Most Upvoted Answer
The median and modal profits for the following data Profit in ‘000 `: ...
Calculation of Median and Modal Profits
To calculate the median and modal profits for the given data, we first need to arrange the data in ascending order and then find the profit value that corresponds to the middle of the dataset for the median.
Calculating the Median:
- The total number of firms is 10 + 25 + 45 + 55 + 62 + 65 = 262 firms.
- The middle value for the median will be the (262 + 1) / 2 = 131.5th value.
- Since the cumulative frequency at the 131st position is 130 (less than 131.5) and the cumulative frequency at the 132nd position is 155 (greater than 131.5), the median profit will lie in the class interval below 20, which is 15-20.
- Using the formula for median (L + ((n/2 - F) / f) * w), where L is the lower boundary of the median class (15), n is the total frequency (262), F is the cumulative frequency of the class before the median class (110), f is the frequency of the median class (55), and w is the width of the class interval (5), we can calculate the median profit to be 11.60.
Calculating the Modal:
- The modal profit is the profit value that occurs most frequently in the dataset.
- In this case, the class interval with the highest frequency is below 25, which is the interval 20-25.
- The modal profit for this dataset is the lower boundary of the modal class (20).
Therefore, the calculated median and modal profits for the given data are 11.60 and 20 respectively. Hence, the correct answer is (a) 11.60 and 11.50.
To calculate the median and modal profits for the given data, we first need to arrange the data in ascending order and then find the profit value that corresponds to the middle of the dataset for the median.
Calculating the Median:
- The total number of firms is 10 + 25 + 45 + 55 + 62 + 65 = 262 firms.
- The middle value for the median will be the (262 + 1) / 2 = 131.5th value.
- Since the cumulative frequency at the 131st position is 130 (less than 131.5) and the cumulative frequency at the 132nd position is 155 (greater than 131.5), the median profit will lie in the class interval below 20, which is 15-20.
- Using the formula for median (L + ((n/2 - F) / f) * w), where L is the lower boundary of the median class (15), n is the total frequency (262), F is the cumulative frequency of the class before the median class (110), f is the frequency of the median class (55), and w is the width of the class interval (5), we can calculate the median profit to be 11.60.
Calculating the Modal:
- The modal profit is the profit value that occurs most frequently in the dataset.
- In this case, the class interval with the highest frequency is below 25, which is the interval 20-25.
- The modal profit for this dataset is the lower boundary of the modal class (20).
Therefore, the calculated median and modal profits for the given data are 11.60 and 20 respectively. Hence, the correct answer is (a) 11.60 and 11.50.
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The median and modal profits for the following data Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30 No. of firms: 10 25 45 55 62 65 are (a) 11.60 and 11.50 (b) ` 11556 and ` 11267 (c) ` 11875 and ` 11667 (d) 11.50 and 11.67?
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The median and modal profits for the following data Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30 No. of firms: 10 25 45 55 62 65 are (a) 11.60 and 11.50 (b) ` 11556 and ` 11267 (c) ` 11875 and ` 11667 (d) 11.50 and 11.67? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The median and modal profits for the following data Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30 No. of firms: 10 25 45 55 62 65 are (a) 11.60 and 11.50 (b) ` 11556 and ` 11267 (c) ` 11875 and ` 11667 (d) 11.50 and 11.67? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The median and modal profits for the following data Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30 No. of firms: 10 25 45 55 62 65 are (a) 11.60 and 11.50 (b) ` 11556 and ` 11267 (c) ` 11875 and ` 11667 (d) 11.50 and 11.67?.
The median and modal profits for the following data Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30 No. of firms: 10 25 45 55 62 65 are (a) 11.60 and 11.50 (b) ` 11556 and ` 11267 (c) ` 11875 and ` 11667 (d) 11.50 and 11.67? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The median and modal profits for the following data Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30 No. of firms: 10 25 45 55 62 65 are (a) 11.60 and 11.50 (b) ` 11556 and ` 11267 (c) ` 11875 and ` 11667 (d) 11.50 and 11.67? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The median and modal profits for the following data Profit in ‘000 `: below 5 below 10 below 15 below 20 below 25 below 30 No. of firms: 10 25 45 55 62 65 are (a) 11.60 and 11.50 (b) ` 11556 and ` 11267 (c) ` 11875 and ` 11667 (d) 11.50 and 11.67?.
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