CBSE Class 9 Mathematics Frequency Distribution Assignment Set D Answers

Question 1. Look at the basic points of Statistics
Answer: Basic points of statistics include collection of data, organization of data, presentation of data, analysis, and interpretation of numerical data.
In simple words: Statistics deals with gathering, organizing, and analyzing numerical facts and figures.

Exam Tip: Remember the fundamental pillars of statistical data handling for theoretical questions.

Question 2. Construct a frequency table for the given raw data of weights: 30, 30, 30, 35, 40, 40, 40, 45, 45, 45, 50, 55, 55, 60, 60, 60, 65, 65, 70, 70, 70, 70, 70, 75, 75, 75, 75, 80, 80, 84, 85, 85, 85, 90, 95, 100, 100, 100, 110, 110.
Answer:

In simple words: Count how many times each weight appears and record it in a table.

Exam Tip: Always cross-check the sum of frequencies with the total number of observations in the raw data.

Question 3A. Construct frequency distribution tables showing Inclusive Form and Exclusive Form.
Answer:

In simple words: Inclusive classes include both upper and lower limits, while exclusive classes do not include the upper limit.

Exam Tip: Be careful with class boundaries when converting between inclusive and exclusive forms.

Question 3B. Find class-size and class-limits for given intervals.
Answer:
Class-size = 10
Class-limits: (88, 98), (98, 108), (108, 118), (118, 128), (128, 138), (138, 148), (148, 158), (158, 168).
Class-intervals: 88 - 98, 98 - 108, ..., 158 - 168.
In simple words: Class size is the difference between the upper and lower limits of any class.

Question 4. Prepare a frequency table using tally marks for the given variable values.
Answer:

In simple words: Group identical values and count their frequencies using tally marks.

Exam Tip: Group tally marks in blocks of five for easy counting.

Question 5. Construct a cumulative frequency table from the given grouped data.
Answer:

In simple words: Cumulative frequency is the running total of frequencies.

Exam Tip: The last cumulative frequency must equal the sum of all individual frequencies.

Question 6. Complete the cumulative frequency table for given ages.
Answer:

In simple words: Add each frequency successively to find the cumulative frequency.

Exam Tip: Double-check addition at each step.

Question 7. Answer the given statistical sub-questions based on distribution data.
Answer:
(a) 21
(b) 31; 35
(c) 43
(d) 35.5; 40.5
(e) 5
(f) 11; 43; 94; 143; 170; 176; 180
(g) (i) 94
(ii) \(180 - 143 = 37\)
In simple words: Read values directly from the given frequency distribution table.

Exam Tip: Be precise when reading class limits and boundaries.

Question 8. Construct the frequency and cumulative frequency table.
Answer:

In simple words: Organize data into class intervals and calculate cumulative frequencies.

Exam Tip: Ensure intervals are of uniform class size.

Question 9A. Prepare a frequency distribution table for Age and No. of persons.
Answer:

In simple words: Group ages into class intervals of width 10 and count frequencies.

Exam Tip: Check that all age values fall into exactly one class interval.

Question 9B. Prepare a frequency table for lifetime of bulbs.
Answer:

In simple words: Arrange bulb lifespans in ascending order of class intervals.

Exam Tip: Pay attention to interval boundaries like 500-600, 600-700.

Question 10. Find the missing values \(a\), \(b\), \(c\), \(d\), \(e\), \(f\) from the distribution data.
Answer:
\(a = 12\)
\(b = 13\)
\(c = 35\)
\(d = 8\)
\(e = 5\)
\(f = 50\)
In simple words: Determine missing frequencies or class parameters based on totals and cumulative values.

Exam Tip: Verify consistency across row and column totals.