Answer :
To solve this problem, we need to organize the given data into class intervals and calculate various frequencies. We are asked specifically to find the value of [tex]\( E \)[/tex], which is the cumulative frequency for a particular interval. Let's solve this step by step.
1. Understanding the Data:
- We have a list of marks ranging from 1 to 20.
2. Determine Intervals:
- The class width is 3.
- The lower limit of the first class is 2.
- With a class width of 3 starting from 2, our intervals would be:
- [tex]\([2, 5)\)[/tex]
- [tex]\([5, 8)\)[/tex]
- [tex]\([8, 11)\)[/tex]
- [tex]\([11, 14)\)[/tex]
- [tex]\([14, 17)\)[/tex]
- [tex]\([17, 20)\)[/tex]
3. Count Frequencies for Each Interval:
- Count how many marks fall into each of the intervals:
- [tex]\([2, 5)\)[/tex]: 1
- [tex]\([5, 8)\)[/tex]: 2
- [tex]\([8, 11)\)[/tex]: 8
- [tex]\([11, 14)\)[/tex]: 9
- [tex]\([14, 17)\)[/tex]: 4
- [tex]\([17, 20)\)[/tex]: 6
4. Calculate Cumulative Frequencies:
- The cumulative frequency is the sum of the frequencies up to the current interval:
- [tex]\([2, 5)\)[/tex]: 1
- [tex]\([5, 8)\)[/tex]: 3 (1 from previous interval + 2 from this)
- [tex]\([8, 11)\)[/tex]: 11 (3 from previous intervals + 8 from this)
- [tex]\([11, 14)\)[/tex]: 20 (11 from previous intervals + 9 from this)
- [tex]\([14, 17)\)[/tex]: 24 (20 from previous intervals + 4 from this)
- [tex]\([17, 20)\)[/tex]: 30 (24 from previous intervals + 6 from this)
5. Identify Target Interval for [tex]\( E \)[/tex]:
- We need the cumulative frequency for the interval [tex]\([5, 8)\)[/tex].
6. Result for [tex]\( E \)[/tex]:
- The cumulative frequency for the interval [tex]\([5, 8)\)[/tex] is [tex]\( 3 \)[/tex].
So, the value of [tex]\( E \)[/tex] is 3.
1. Understanding the Data:
- We have a list of marks ranging from 1 to 20.
2. Determine Intervals:
- The class width is 3.
- The lower limit of the first class is 2.
- With a class width of 3 starting from 2, our intervals would be:
- [tex]\([2, 5)\)[/tex]
- [tex]\([5, 8)\)[/tex]
- [tex]\([8, 11)\)[/tex]
- [tex]\([11, 14)\)[/tex]
- [tex]\([14, 17)\)[/tex]
- [tex]\([17, 20)\)[/tex]
3. Count Frequencies for Each Interval:
- Count how many marks fall into each of the intervals:
- [tex]\([2, 5)\)[/tex]: 1
- [tex]\([5, 8)\)[/tex]: 2
- [tex]\([8, 11)\)[/tex]: 8
- [tex]\([11, 14)\)[/tex]: 9
- [tex]\([14, 17)\)[/tex]: 4
- [tex]\([17, 20)\)[/tex]: 6
4. Calculate Cumulative Frequencies:
- The cumulative frequency is the sum of the frequencies up to the current interval:
- [tex]\([2, 5)\)[/tex]: 1
- [tex]\([5, 8)\)[/tex]: 3 (1 from previous interval + 2 from this)
- [tex]\([8, 11)\)[/tex]: 11 (3 from previous intervals + 8 from this)
- [tex]\([11, 14)\)[/tex]: 20 (11 from previous intervals + 9 from this)
- [tex]\([14, 17)\)[/tex]: 24 (20 from previous intervals + 4 from this)
- [tex]\([17, 20)\)[/tex]: 30 (24 from previous intervals + 6 from this)
5. Identify Target Interval for [tex]\( E \)[/tex]:
- We need the cumulative frequency for the interval [tex]\([5, 8)\)[/tex].
6. Result for [tex]\( E \)[/tex]:
- The cumulative frequency for the interval [tex]\([5, 8)\)[/tex] is [tex]\( 3 \)[/tex].
So, the value of [tex]\( E \)[/tex] is 3.
