CBSE Class 7 Mathematics Data Handling Assignment Set 07

VII - Mathematics Assignment No. 02 - Data Handling

Q1. Calculate the mean of the following data

Answer: 33
Sum of frequencies (\(\sum f\)) = 3 + 5 + 2 + 5 + 3 + 2 = 20
Sum of product of marks and frequencies (\(\sum fx\)) = (10 \(\times\) 3) + (20 \(\times\) 5) + (30 \(\times\) 2) + (40 \(\times\) 5) + (50 \(\times\) 3) + (60 \(\times\) 2)
\(\sum fx = 30 + 100 + 60 + 200 + 150 + 120 = 660\)
Mean = \(\frac{\sum fx}{\sum f} = \frac{660}{20} = 33\)
In simple words: The mean is calculated by multiplying each mark by its frequency, adding them all up, and dividing by the total number of students.

Exam Tip: Construct a small horizontal or vertical table showing columns for \(x\), \(f\), and \(fx\) to avoid calculation errors.

Q2. Following are the goals scored by two hockey teams
Team A: 3, 4, 2, 0, 2, 1, 5, 6
Team B: 3, 2, 0, 5, 2, 0, 2, 1
Which team performed better?
Answer: Team A because their average is better.
Total goals scored by Team A = 3 + 4 + 2 + 0 + 2 + 1 + 5 + 6 = 23
Number of matches for Team A = 8
Average goals for Team A = \(\frac{23}{8} = 2.875\)
Total goals scored by Team B = 3 + 2 + 0 + 5 + 2 + 0 + 2 + 1 = 15
Number of matches for Team B = 8
Average goals for Team B = \(\frac{15}{8} = 1.875\)
Since the average of Team A (2.875) is greater than the average of Team B (1.875), Team A performed better.
In simple words: To find which team performed better, compare their average (mean) goals per match.

Exam Tip: When comparing performances of two groups, calculate the arithmetic mean for each group under the same conditions.

Q3. Find the median of 5, 9, 3, 4, 10, 2, 1
Answer: 4
First, arrange the given data in ascending order: 1, 2, 3, 4, 5, 9, 10
Total number of observations (\(n\)) = 7 (which is odd)
Median = Value of the \(\left(\frac{n + 1}{2}\right)\)-th observation
Median = Value of the \(\left(\frac{7 + 1}{2}\right)\)-th observation = Value of 4th observation
4th observation = 4
In simple words: Arrange the numbers from smallest to largest and pick the exact middle number.

Exam Tip: Always remember to arrange data in ascending or descending order before finding the median.

Q4. Find the median of 60, 67, 62, 61, 63, 65, 64
Answer: 63
Arrange the data in ascending order: 60, 61, 62, 63, 64, 65, 67
Total number of observations (\(n\)) = 7 (odd)
Median = Value of the \(\left(\frac{7 + 1}{2}\right)\)-th observation = 4th observation
4th observation = 63
In simple words: Sort the numbers from least to greatest and find the middle value.

Exam Tip: Cross check if the number of terms before and after your chosen median value is equal.

Q5. Find the mode of the following data: 14, 25, 14, 28, 18, 17, 18, 14, 23
Answer: 14
Listing the frequency of each observation:
14 appears 3 times
18 appears 2 times
25 appears 1 time
28 appears 1 time
17 appears 1 time
23 appears 1 time
Since 14 has the maximum frequency (3 times), the mode is 14.
In simple words: The mode is the number that repeats most often in the given list.

Exam Tip: Use tally marks or a frequency table for longer lists of numbers to ensure no count is missed.

Q6. Find the mode of the following data: 7, 9, 12, 13, 7, 12, 15, 7, 12, 7
Answer: 7
Counting the frequency of each observation:
7 appears 4 times
9 appears 1 time
12 appears 3 times
13 appears 1 time
15 appears 1 time
Since 7 occurs with the highest frequency (4 times), the mode is 7.
In simple words: Count how many times each number appears and choose the one with the highest count.

Q7. The demand of different shirt sizes, as obtained by a survey, is given below

Find the modal shirt sizes, as observed from the survey.
Answer: 39 inches
The highest number of shirts demanded is 38, which corresponds to the shirt size of 39 inches.
Therefore, the modal shirt size is 39 inches.
In simple words: Look for the largest number in the frequency row and find its corresponding shirt size.

Exam Tip: Be careful to state the variable value (shirt size) as the answer, not the frequency count itself.

Q8. The mean of 10, 12, 18, 13 and \(x\) is 13. Find the value of \(x\)
Answer: 12
Given numbers: 10, 12, 18, 13, \(x\)
Total number of observations = 5
Given mean = 13
Mean = \(\frac{\text{Sum of observations}}{\text{Number of observations}}\)
\(13 = \frac{10 + 12 + 18 + 13 + x}{5}\)
\(13 \times 5 = 53 + x\)
\(65 = 53 + x\)
\(x = 65 - 53\)
\(x = 12\)
In simple words: Multiply the mean by the total count to get the total sum, then subtract the known numbers to find the missing value.

Exam Tip: Set up the formula as an algebraic equation and solve step by step.

Q9. Find mean, mode and median of the following data, 10, 12, 10, 13, 10, 14, 15
Answer:
Mean = 12
Mode = 10
Median = 12
Step 1: Finding the Mean
Sum of observations = 10 + 12 + 10 + 13 + 10 + 14 + 15 = 84
Number of observations = 7
Mean = \(\frac{84}{7} = 12\)
Step 2: Finding the Mode
Frequencies: 10 appears 3 times, 12 appears 1 time, 13 appears 1 time, 14 appears 1 time, 15 appears 1 time.
Mode = 10 (since it has the highest frequency)
Step 3: Finding the Median
Arranging in ascending order: 10, 10, 10, 12, 13, 14, 15
Number of observations \(n = 7\) (odd)
Median = Value of the \(\left(\frac{7 + 1}{2}\right)\)-th observation = 4th observation
4th observation = 12
In simple words: Calculate all three central tendencies separately using their respective methods.

Exam Tip: Label each part clearly as Mean, Mode, and Median to secure full marks.

Q10. Find mode, median of 3, 4, 5, 4, 6, 4, 7
Answer:
Mode = 4
Median = 4
Step 1: Finding the Mode
Frequencies: 3 appears 1 time, 4 appears 3 times, 5 appears 1 time, 6 appears 1 time, 7 appears 1 time.
Mode = 4 (highest frequency)
Step 2: Finding the Median
Arranging in ascending order: 3, 4, 4, 4, 5, 6, 7
Number of observations \(n = 7\) (odd)
Median = Value of the 4th observation = 4
In simple words: Mode is the most frequent number, and median is the middle number after sorting.