Maharashtra Board Class 9 Maths Chapter 7 Set 7.4 Algebra Standard Part 1 Statistics Solutions

Question 1. Complete the following cumulative frequency table:

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक अपूर्ण संचयी आवृत्ति सारणी को दर्शाता है जहाँ छात्रों की ऊँचाई (सेंटीमीटर में) और छात्रों की संख्या (आवृत्ति) दी गई है। सारणी में 'से कम प्रकार की आवृत्ति' के लिए कुछ मान और गणना सूत्र दिए गए हैं जिन्हें छात्रों को पूरा करना है।
Answer:

In simple words: To complete a "less than type" cumulative frequency table, you add the current class's frequency to the cumulative frequency of the previous class. The first cumulative frequency is simply the frequency of the first class.

🎯 Exam Tip: Ensure that the total (N) from the frequency column matches the final value in the cumulative frequency column for "less than type" tables. This helps verify your calculations.

Question 2. Complete the following Cumulative Frequency Table:

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक अपूर्ण संचयी आवृत्ति सारणी को दर्शाता है जहाँ व्यक्तियों की मासिक आय (Rs. में) और व्यक्तियों की संख्या (आवृत्ति) दी गई है। सारणी में 'से अधिक या बराबर प्रकार की आवृत्ति' के लिए कुछ मान दिए गए हैं जिन्हें छात्रों को पूरा करना है।
Answer:

In simple words: For a "more than or equal to type" cumulative frequency table, you start with the total frequency for the first class, and then subtract the frequency of each subsequent class from the previous cumulative frequency.

🎯 Exam Tip: In a "more than or equal to type" cumulative frequency table, the last cumulative frequency should match the frequency of the last class, and the first cumulative frequency should be the total frequency (N). This is a good way to cross-check your work.

Question 3. The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0 - 10, 10 - 20,... and prepare frequency distribution table and cumulative frequency table more than or equal to type.
**55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10,**
**75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64,**
**42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 27, 36,**
**35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17,**
**77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45.**
**47,49**
**From the prepared table, answer the following questions :**
**(i) How many students obtained marks 40 or above 40?**
**(ii) How many students obtained marks 90 or above 90?**
**(iii) How many students obtained marks 60 or above 60?**
**(iv) What is the cumulative frequency of equal to or more than type of the class 0 - 10?**
Answer:

(i) 38 students obtained marks 40 or above 40.
(ii) 3 students obtained marks 90 or above 90.
(iii) 19 students obtained marks 60 or above 60.
(iv) Cumulative frequency of equal to or more than type of the class 0 - 10 is 62.
In simple words: First, organize the raw data into a frequency distribution table with the given class intervals and then calculate the "more than or equal to" cumulative frequencies. Once the table is complete, read the cumulative frequencies directly to answer the questions about students scoring above certain marks.

🎯 Exam Tip: Tally marks are crucial for accurately counting frequencies from raw data. Always double-check your tally count against the original dataset to avoid errors. Ensure your cumulative frequency calculations are consistent with the "more than or equal to" definition.

Question 4. Using the data In example (3) above, prepare less than type cumulative frequency table and answer the following questions.
**(i) How many students obtained less than 40 marks?**
**(ii) How many students obtained less than 10 marks?**
**(iii) How many students obtained less than 60 marks?**
**(iv) Find the cumulative frequency of the class 50 - 60.**
Answer:

(i) 24 students obtained less than 40 marks.
(ii) 3 students obtained less than 10 marks.
(iii) 43 students obtained less than 60 marks.
(iv) Cumulative frequency of the class 50 - 60 is 43.
In simple words: This solution reuses the frequency data from Question 3 to construct a "less than type" cumulative frequency table. Each cumulative frequency is found by adding the current class's frequency to the previous class's cumulative frequency, then these values are used to answer questions about marks below specific thresholds.

🎯 Exam Tip: Pay close attention to the class intervals when calculating "less than type" cumulative frequencies. The cumulative frequency for a class interval represents all data points *up to and including* the upper limit of that interval. The final cumulative frequency should always equal the total number of observations.

Maharashtra Board Class 9 Maths Chapter 7 Statistics Practice Set 7.4 Intext Questions and Activities

Question 1. The following information is regarding marks in mathematics, obtained out of 40, scored by 50 students of 9th std. in the first unit test. (Textbook pg. no. 120)

ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक आवृत्ति सारणी को दर्शाता है जिसमें छात्रों द्वारा गणित में प्राप्त अंकों के वर्ग अंतराल (0-10, 10-20, आदि) और प्रत्येक अंतराल में छात्रों की संख्या (आवृत्ति) दी गई है। इस सारणी का उपयोग नीचे दिए गए रिक्त स्थानों को भरने के लिए किया जाना है।
**From the table, fill in the blanks in the following statements.**
**(i) For class interval 10 - 20 the lower class limit is ______ and upper class limit is ______**
**(ii) How many students obtained marks less than 10? 2**
**(iii) How many students obtained marks less than 20? 2 + ______ = 14**
**(iv) How many students obtained marks less than 30? ______ + ______ = 34**
**(v) How many students obtained marks less than 40? ______ + ______ =50**
Answer:
(i) 10, 20
(ii) How many students obtained marks less than 10? 2
(iii) How many students obtained marks less than 20? 2 + 12 = 14
(iv) How many students obtained marks less than 30? 14 + 20 = 34
(v) How many students obtained marks less than 40? 34 + 16 = 50
In simple words: This question asks to complete a "less than" cumulative frequency exercise using a provided frequency distribution table, identifying class limits and cumulative student counts for specific mark ranges.

🎯 Exam Tip: Clearly understand the definition of lower and upper class limits. For "less than" cumulative frequencies, remember that each cumulative value includes all frequencies from previous classes up to the upper limit of the current class.

**Question 2. A sports club has organised a table-tennis tournaments. The following table gives the distribution of players ages. Find the cumulative frequencies equal to or more than the lower class limit and complete the table (Textbook pg. no. 121)**
Answer:
Equal to lower limit or more than lower limit type of cumulative table.

In simple words: To complete this table, you need to calculate the "more than or equal to the lower class limit" cumulative frequencies, starting with the total number of students and subtracting the frequency of each class sequentially.

🎯 Exam Tip: When constructing "more than or equal to" cumulative frequency tables, the initial cumulative frequency should be the total number of observations. Carefully subtract each class frequency from the previous cumulative frequency to ensure accuracy.