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A frequency distribution table shows marks obtained by students. The first quartile (Q1) is 35. Find the first quartile class and the value of x.
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4 partsStep-by-step solution
12 stepsHere are the solutions to the questions based on the provided data:
The given frequency distribution table is:
| Marks Obtained | No. of Students (f) |
|---|---|
| 0-20 | 2 |
| 20-40 | x |
| 40-60 | 8 |
| 60-80 | 5 |
| 80-100 | 1 |
The first quartile () of the given data is 35.
First, we construct the cumulative frequency (cf) table:
| Marks Obtained | No. of Students (f) | Cumulative Frequency (cf) |
|---|---|---|
| 0-20 | 2 | 2 |
| 20-40 | x | |
| 40-60 | 8 | |
| 60-80 | 5 | |
| 80-100 | 1 |
The total number of students is .
Part a· 1 step
Find the first quartile class.
Identify the class interval where the first quartile value (35) falls.
Since , the first quartile class is 20-40.
The first quartile class is .
Part b4
Find the value of x.
Use the formula for the first quartile ()
From part (a), the first quartile class is 20-40.
(lower boundary of the quartile class)
(frequency of the quartile class)
(cumulative frequency of the class preceding the quartile class)
(class width)
(given)
(total number of students)Substitute the values into the formula
Solve for
Divide both sides by 5:
The value of is .
Part c51.43
If modal class is 40-60 then what is the value of mode?
Update the frequency table with
Marks Obtained No. of Students (f) 0-20 2 20-40 4 40-60 8 60-80 5 80-100 1 Use the formula for the mode for grouped data
The modal class is given as 40-60.
(lower boundary of the modal class)
(frequency of the modal class)
(frequency of the class preceding the modal class, 20-40)
(frequency of the class succeeding the modal class, 60-80)
(class width)Substitute the values into the formula
The value of the mode is .
Part d7:1
Find the ratio of students who are above and below the first quartile class.
Identify the first quartile class.
From part (a), the first quartile class is 20-40.
Calculate the number of students below the first quartile class.
Students below the 20-40 class are those in the 0-20 class.
Number of students below the first quartile class = 2.Calculate the number of students above the first quartile class.
Students above the 20-40 class are those in the 40-60, 60-80, and 80-100 classes.
Number of students above the first quartile class = .Find the ratio of students above to students below the first quartile class.
Ratio = (Number of students above) : (Number of students below)
Ratio = $14 : 2$Simplify the ratio.
Divide both sides by 2:
Ratio =The ratio of students who are above and below the first quartile class is .
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