CBSE Class 7 Mathematics Data Handling Assignment Set 06

Question 1. Represent the following data in a tabular form
16, 41, 16, 41, 16, 45, 19, 45, 19, 45
19, 25, 61, 61, 28, 75, 28, 61, 28, 75,
55, 25, 28, 61, 28, 75, 35, 75, 37, 82.
Answer: To represent the given raw data in a tabular form, we use tally marks to count the frequency of each distinct observation.

In simple words: Count how many times each number appears and organize it into a frequency table using tally marks.

Exam Tip: Always verify that the sum of all frequencies equals the total number of observations in the raw data.

Question 2. Find the range of the following data:
47, 52, 40, 87, 92, 37, 16
Answer: Highest value = 92
Lowest value = 16
Range = Highest value - Lowest value
Range = \(92 - 16 = 76\)
In simple words: Range is the difference between the maximum and minimum values in a data set.

Exam Tip: Always arrange numbers mentally or in order to quickly spot the highest and lowest observations.

Question 3. Calculate the mean of the following data
150, 200, 175, 170, 250, 215, 220, 260, 270, 190.
Answer: Number of observations \((n)\) = 10
Sum of observations = 150 + 200 + 175 + 170 + 250 + 215 + 220 + 260 + 270 + 190 = 2100
Mean = \(\frac{\text{Sum of observations}}{\text{Number of observations}}\)
Mean = \(\frac{2100}{10} = 210\)
In simple words: Mean is the average, found by adding all values together and dividing by the count of values.

Exam Tip: Double-check your addition by grouping numbers in pairs to avoid calculation errors.

Question 4. The daily sale of flour of a flourmill is given below,

Calculate the average daily sale of flour of the flourmill.
Answer: Number of days = 6
Total sale = 120 + 110 + 70 + 80 + 40 + 210 = 630 kg
Average daily sale = \(\frac{\text{Total sale}}{\text{Number of days}}\)
Average daily sale = \(\frac{630}{6} = 105\) kg
In simple words: Find the mean sale by dividing the total weekly sale by the number of working days.

Exam Tip: Include proper units (kg) in your final answer.

Question 5. Find the median of the following data
78, 56, 22, 34, 45, 54, 39, 68, 54, 84.
Answer: Total number of observations \((n)\) = 10 (even)
First, arrange the data in ascending order:
22, 34, 39, 45, 54, 54, 56, 68, 78, 84
Since \(n\) is even, the median is the mean of the \(\left(\frac{n}{2}\right)^{\text{th}}\) and \(\left(\frac{n}{2} + 1\right)^{\text{th}}\) terms.
\(5^{\text{th}}\) term = 54
\(6^{\text{th}}\) term = 54
Median = \(\frac{54 + 54}{2} = \frac{108}{2} = 54\)
In simple words: Arrange numbers from smallest to largest and find the average of the two middle values.

Exam Tip: Always sort data in ascending or descending order before finding the median.

Question 6. Find the mode of the following frequency distribution

Answer: The maximum frequency is 18, which corresponds to the height 156 cm.
Mode = 156 cm
In simple words: Mode is the value that appears most often. Look for the highest number of students in the table.

Exam Tip: State both the maximum frequency and its corresponding observation clearly.

Question 7. Find the median of first 50 whole nos.
Answer: The first 50 whole numbers start from 0 and go up to 49.
Total observations \((n)\) = 50 (even)
The terms are: 0, 1, 2, ..., 49.
Since \(n\) is even, median is the average of the \(\left(\frac{50}{2}\right)^{\text{th}}\) and \(\left(\frac{50}{2} + 1\right)^{\text{th}}\) terms, i.e., the \(25^{\text{th}}\) and \(26^{\text{th}}\) terms.
\(25^{\text{th}}\) term = 24
\(26^{\text{th}}\) term = 25
Median = \(\frac{24 + 25}{2} = \frac{49}{2} = 24.5\)
In simple words: Whole numbers start at 0, so the first 50 numbers are 0 to 49. Find the average of the 25th and 26th numbers.

Exam Tip: Remember that whole numbers start from 0, so the \(n^{\text{th}}\) whole number is \(n - 1\).

Question 8. Find the median of first 15 even nos.
Answer: The first 15 even numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30.
Total observations \((n)\) = 15 (odd)
Since \(n\) is odd, the median is the \(\left(\frac{n + 1}{2}\right)^{\text{th}}\) term.
Median term = \(\frac{15 + 1}{2} = 8^{\text{th}}\) term
\(8^{\text{th}}\) term = 16
Median = 16
In simple words: For an odd count of numbers arranged in order, the median is simply the exact middle number.

Question 9. Find mean, mode, median of the following data
10, 11, 12, 13, 14, 15, 16, 12, 12.
Answer: Number of observations \((n)\) = 9
First, arrange the data in ascending order:
10, 11, 12, 12, 12, 13, 14, 15, 16
1. Mean:
Sum of observations = 10 + 11 + 12 + 12 + 12 + 13 + 14 + 15 + 16 = 115
Mean = \(\frac{115}{9} \approx 12.78\) (or 12.8)
2. Mode:
12 appears 3 times, which is more than any other number.
Mode = 12
3. Median:
Since \(n = 9\) (odd), the median is the \(\left(\frac{9 + 1}{2}\right)^{\text{th}}\) = \(5^{\text{th}}\) term.
\(5^{\text{th}}\) term = 12
Median = 12
In simple words: Calculate average for mean, most frequent value for mode, and middle value for median.

Exam Tip: Always sort the data first because you need it in order to find the median correctly.

Question 10. The mean of 10 observations is 20 and that of another 15 observations is 16. Find the mean of all 25 observations.
Answer: Sum of first 10 observations = \(10 \times 20 = 200\)
Sum of another 15 observations = \(15 \times 16 = 240\)
Total sum of all 25 observations = 200 + 240 = 440
Total number of observations = 10 + 15 = 25
Mean of all 25 observations = \(\frac{440}{25} = 17.6\)
In simple words: Find the total sum of each group by multiplying mean by count, add them together, and divide by the total count.

Exam Tip: Use the formula \(\text{Sum} = \text{Mean} \times n\) to find the total sum when the mean is given.