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The third quartile and 65th percentile for the following data are Profits in ‘000 `: les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ?
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Finding the Third Quartile and 65th Percentile for Profit Data
Introduction:
In this question, we are given data for profits in ‘000 and we are required to find the third quartile and 65th percentile for this data.
Given Data:
les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ?
Solution:
Step 1: Find the total number of firms
To find the third quartile and 65th percentile, we need to know the total number of firms in the given data. Adding up the number of firms for each profit range, we get:
Total number of firms = 5 + 18 + 38 + 20 + 9 + 2 = 92
Step 2: Find the cumulative frequency
We need to find the cumulative frequency for each profit range. This can be done by adding up the number of firms for each profit range and all the profit ranges that come before it. The cumulative frequency for each profit range is:
Profit Range Cumulative Frequency
Less than 10 5
10 – 19 23 (5 + 18)
20 – 29 61 (5 + 18 + 38)
30 – 39 81 (5 + 18 + 38 + 20)
40 – 49 90 (5 + 18 + 38 + 20 + 9)
50 – 59 92 (5 + 18 + 38 + 20 + 9 + 2)
Step 3: Find the third quartile
The third quartile is the value that divides the upper 25% of the data from the lower 75% of the data. To find the third quartile, we can use the formula:
Q3 = L + [(n/4 - F)/f] x w
Where:
L = lower limit of the profit range that contains the third quartile
n = total number of firms
F = cumulative frequency of the profit range that contains the third quartile
f = number of firms in the profit range that contains the third quartile
w = width of the profit range
Using the formula, we can find the third quartile as follows:
Q3 = 30 + [(23/4 - 5)/38] x 10
Q3 = 30 + (4.25/38) x 10
Q3 = 30 + 1.18
Q3 = 31.18
Therefore, the third quartile for the given data is 31.18.
Step 4: Find the 65th percentile
The 65th percentile is the value that divides the upper 35% of the data from the lower 65% of the data. To find the 65th percentile, we can use the formula:
P65 = L + [(n/100 x P) - F)/f] x w
Where:
L = lower limit of the profit range that contains the 65th percentile
n = total number of firms
P = percentile (65 in this case)
F = cumulative frequency of the profit range that contains the 65th percentile
f = number of firms in the profit range that contains the 65th percentile
w = width of the profit range
Introduction:
In this question, we are given data for profits in ‘000 and we are required to find the third quartile and 65th percentile for this data.
Given Data:
les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ?
Solution:
Step 1: Find the total number of firms
To find the third quartile and 65th percentile, we need to know the total number of firms in the given data. Adding up the number of firms for each profit range, we get:
Total number of firms = 5 + 18 + 38 + 20 + 9 + 2 = 92
Step 2: Find the cumulative frequency
We need to find the cumulative frequency for each profit range. This can be done by adding up the number of firms for each profit range and all the profit ranges that come before it. The cumulative frequency for each profit range is:
Profit Range Cumulative Frequency
Less than 10 5
10 – 19 23 (5 + 18)
20 – 29 61 (5 + 18 + 38)
30 – 39 81 (5 + 18 + 38 + 20)
40 – 49 90 (5 + 18 + 38 + 20 + 9)
50 – 59 92 (5 + 18 + 38 + 20 + 9 + 2)
Step 3: Find the third quartile
The third quartile is the value that divides the upper 25% of the data from the lower 75% of the data. To find the third quartile, we can use the formula:
Q3 = L + [(n/4 - F)/f] x w
Where:
L = lower limit of the profit range that contains the third quartile
n = total number of firms
F = cumulative frequency of the profit range that contains the third quartile
f = number of firms in the profit range that contains the third quartile
w = width of the profit range
Using the formula, we can find the third quartile as follows:
Q3 = 30 + [(23/4 - 5)/38] x 10
Q3 = 30 + (4.25/38) x 10
Q3 = 30 + 1.18
Q3 = 31.18
Therefore, the third quartile for the given data is 31.18.
Step 4: Find the 65th percentile
The 65th percentile is the value that divides the upper 35% of the data from the lower 65% of the data. To find the 65th percentile, we can use the formula:
P65 = L + [(n/100 x P) - F)/f] x w
Where:
L = lower limit of the profit range that contains the 65th percentile
n = total number of firms
P = percentile (65 in this case)
F = cumulative frequency of the profit range that contains the 65th percentile
f = number of firms in the profit range that contains the 65th percentile
w = width of the profit range
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The third quartile and 65th percentile for the following data are Profits in ‘000 `: les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ?
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The third quartile and 65th percentile for the following data are Profits in ‘000 `: les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The third quartile and 65th percentile for the following data are Profits in ‘000 `: les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The third quartile and 65th percentile for the following data are Profits in ‘000 `: les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ?.
The third quartile and 65th percentile for the following data are Profits in ‘000 `: les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The third quartile and 65th percentile for the following data are Profits in ‘000 `: les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The third quartile and 65th percentile for the following data are Profits in ‘000 `: les than 10 10–19 20–29 30–39 40–49 50–59 No. of firms: 5 18 38 20 9 2 ?.
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