Math Problem Statement

For the following frequency distribution table, calculate the relative frequency, class mark, width of the class interval, and cumulative frequency distribution for the given data.

Solution

Let's break down the steps to calculate the requested quantities from the given frequency distribution table:

Given:

MarksNumber of Students
10-204
20-306
30-4010
40-5018
50-6012
60-7010

i. Relative Frequency

Relative frequency is calculated as the frequency of each class divided by the total frequency.

  • Total number of students (total frequency) = 4+6+10+18+12+10=604 + 6 + 10 + 18 + 12 + 10 = 60

Relative frequency for each class is:

  • 460=0.067\frac{4}{60} = 0.067
  • 660=0.100\frac{6}{60} = 0.100
  • 1060=0.167\frac{10}{60} = 0.167
  • 1860=0.300\frac{18}{60} = 0.300
  • 1260=0.200\frac{12}{60} = 0.200
  • 1060=0.167\frac{10}{60} = 0.167

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: 10+202=15\frac{10 + 20}{2} = 15
  • For 20-30: 20+302=25\frac{20 + 30}{2} = 25
  • For 30-40: 30+402=35\frac{30 + 40}{2} = 35
  • For 40-50: 40+502=45\frac{40 + 50}{2} = 45
  • For 50-60: 50+602=55\frac{50 + 60}{2} = 55
  • For 60-70: 60+702=65\frac{60 + 70}{2} = 65

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: 2010=1020 - 10 = 10

iv. Cumulative Frequency Distribution

Cumulative frequency is the running total of frequencies up to each class.

  • For 10-20: 44
  • For 20-30: 4+6=104 + 6 = 10
  • For 30-40: 10+10=2010 + 10 = 20
  • For 40-50: 20+18=3820 + 18 = 38
  • For 50-60: 38+12=5038 + 12 = 50
  • For 60-70: 50+10=6050 + 10 = 60

Summary:

MarksFrequencyRelative FrequencyClass MarkCumulative Frequency
10-2040.067154
20-3060.1002510
30-40100.1673520
40-50180.3004538
50-60120.2005550
60-70100.1676560

Would you like more details on any part of this solution?

Here are some related questions:

  1. How would you calculate the mean from this table?
  2. What is the median class for this distribution?
  3. How would you compute the variance of this data?
  4. Can you explain the concept of cumulative relative frequency?
  5. 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

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Suitable Grade Level

Grades 9-12