Math Problem Statement
Solution
Let's break down the steps to calculate the requested quantities from the given frequency distribution table:
Given:
Marks | Number of Students |
---|---|
10-20 | 4 |
20-30 | 6 |
30-40 | 10 |
40-50 | 18 |
50-60 | 12 |
60-70 | 10 |
i. Relative Frequency
Relative frequency is calculated as the frequency of each class divided by the total frequency.
- Total number of students (total frequency) =
Relative frequency for each class is:
ii. Class Mark
The class mark (midpoint of each class interval) is calculated by averaging the lower and upper limits of each class.
Class marks for each interval:
- For 10-20:
- For 20-30:
- For 30-40:
- For 40-50:
- For 50-60:
- For 60-70:
iii. Width of Class Interval
The width of a class interval is the difference between the upper and lower limits of any class.
- Class interval width:
iv. Cumulative Frequency Distribution
Cumulative frequency is the running total of frequencies up to each class.
- For 10-20:
- For 20-30:
- For 30-40:
- For 40-50:
- For 50-60:
- For 60-70:
Summary:
Marks | Frequency | Relative Frequency | Class Mark | Cumulative Frequency |
---|---|---|---|---|
10-20 | 4 | 0.067 | 15 | 4 |
20-30 | 6 | 0.100 | 25 | 10 |
30-40 | 10 | 0.167 | 35 | 20 |
40-50 | 18 | 0.300 | 45 | 38 |
50-60 | 12 | 0.200 | 55 | 50 |
60-70 | 10 | 0.167 | 65 | 60 |
Would you like more details on any part of this solution?
Here are some related questions:
- How would you calculate the mean from this table?
- What is the median class for this distribution?
- How would you compute the variance of this data?
- Can you explain the concept of cumulative relative frequency?
- How is the mode of a frequency distribution table determined?
Tip: The cumulative frequency distribution helps identify percentiles and is useful in finding the median of grouped data.
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Math Problem Analysis
Mathematical Concepts
Statistics
Frequency Distribution
Relative Frequency
Cumulative Frequency
Formulas
Relative Frequency = (Frequency of Class / Total Frequency)
Class Mark = (Lower Limit + Upper Limit) / 2
Width of Class Interval = (Upper Limit - Lower Limit)
Theorems
-
Suitable Grade Level
Grades 9-12
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