Samacheer Kalvi Class 8 Maths Solutions Chapter 6 Statistics InText Questions

Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 6 Statistics InText Questions

Try These (Text Book Page No. 212)

Question 1. Arrange the given data in ascending and descending order: 9, 34, 4, 13, 42, 10, 25, 7, 31, 4, 40
Answer: To arrange the data, first we list all numbers from smallest to largest. Then, for descending order, we list them from largest to smallest. Organizing data helps us see patterns and understand information quickly.
Ascending order: 4, 4, 7, 9, 10, 13, 25, 31, 34, 40, 42.
Descending order: 42, 40, 34, 31, 25, 13, 10, 9, 7, 4, 4
In simple words: First, put the numbers in order from the smallest to the biggest. Then, reverse that order to put them from the biggest to the smallest.

🎯 Exam Tip: When arranging numbers, double-check that all original numbers are included and that no numbers are repeated or skipped.

Question 2. Find the range of the given data: 53, 42, 61, 9, 39, 63, 14, 20, 6, 26, 31, 4, 57
Answer: First, we need to arrange the numbers from the smallest to the largest to easily find the smallest and largest values. The range helps us understand how spread out the data is.
Ascending order of the given data: 4, 6, 9, 14, 20, 26, 31, 39, 42, 53, 57, 61, 63
Here, the largest value \( = 63 \)
The smallest value \( = 4 \)
So, the range is calculated by subtracting the smallest value from the largest value:
Range \( = \) Largest value \( - \) Smallest value
\( = 63 - 4 \)
\( = 59 \)
In simple words: To find the range, first find the biggest number and the smallest number in the list. Then, subtract the smallest number from the biggest number.

🎯 Exam Tip: Always arrange the data in order (ascending or descending) before identifying the largest and smallest values to avoid errors in calculating the range.

Try These (Text Book Page No. 217)

Question 1. Prepare a frequency table for the data: 3, 4, 2, 4, 5, 6, 1, 3, 2, 1, 5, 3, 6, 2, 1, 3, 2, 4
Answer: To create a frequency table, we first arrange the data in ascending order. Then, we count how many times each unique number appears (frequency) and mark it with tallies. This helps organize raw data into a clear summary.
Ascending order of the given data: 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6
The distribution table:

In simple words: We put the numbers in order and then count how many times each number shows up. We use tally marks to keep track of the count, and then write the final count as the frequency.

🎯 Exam Tip: Ensure that the sum of the frequencies matches the total number of data points given in the question to verify your table is correct.

Question 2. Prepare a grouped frequency table for the data: 10, 9, 3, 29, 17, 34, 23, 20, 39, 42, 5, 12, 19, 18, 19, 27, 7, 13, 40, 38, 24, 34, 15, 40
Answer: To prepare a grouped frequency table, we first find the largest and smallest values to determine the range. Then, we choose a class size and group the data into intervals. This method is useful for organizing large datasets to make them more manageable and easier to interpret.
Largest value \( = 47 \)
Smallest value \( = 3 \)
Range \( = \) Largest value \( - \) Smallest value
\( = 47 - 3 \)
\( = 44 \)
Suppose we take a class size of 10. Then, the number of class intervals possible is:
Number of class intervals \( = \frac{\text{Range}}{\text{Class size}} \)
\( = \frac{44}{10} \)
\( = 4.4 \)
Since we cannot have a fractional number of class intervals, we typically round up to 5 intervals to make sure all data points are covered, or adjust the range slightly. The table shows 5 intervals.

In simple words: We find the biggest and smallest numbers, then group all numbers into ranges like 1-10, 10-20, and so on. Then, we count how many numbers fall into each range using tally marks to show how often they appear.

🎯 Exam Tip: When forming class intervals for a grouped frequency table, ensure they are continuous (e.g., 0-10, 10-20) and cover the entire range of your data without overlapping values.