GSEB Class 7 Maths Solutions Chapter 3 Data Handling Exercise 3.2

Question 1. The scores in mathematics test (out of 25) of 15 students is as follows: 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20 Find the mode and median of this data. Are they same?
Answer: Arranging the numbers from smallest to largest, we get: 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25. The number that shows up most often is 20. Therefore, the mode of this data is 20. Also, the number in the very middle of the list is 20. So, the median of this data is 20. Clearly, the mode and the median values are identical in this case.
In simple words: First, put all the scores in order. The score that appears most times is 20, which is the mode. The score exactly in the middle is also 20, which is the median. Both are the same in this problem.

Exam Tip: Always arrange data in ascending order before calculating the median. For mode, simply identify the most frequently occurring value.

Question 2. The runs scored in a cricket match by 11 players is as follows: 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15 Find the mean, mode and median of this data. Are the three same?
Answer: First, putting the given numbers in order from smallest to largest, we get: 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120.
(i) To find the mean of the data, we sum all the observations and divide by the total number of observations.
\( \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \)
\( = \frac{6+8+10+10+15+15+15+50+80+100+120}{11} \)
\( = \frac{429}{11} \)
\( = 39 \)
(ii) The number that appears most frequently is 15. Hence, the mode of this data is 15.
(iii) The number in the middle position is 15. Consequently, the median of this data is 15. In this particular situation, the mean, mode, and median values are not the same.
In simple words: Arrange the runs in order: 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120.
To get the mean, add all the runs (429) and divide by 11 players, which gives 39.
The mode is 15 because it shows up most often.
The median is 15 because it's the middle number.
Here, the mean (39), mode (15), and median (15) are not all identical.

Exam Tip: Remember to reorder data for median, but the mode can be found by simply counting frequencies in the original or ordered list. Mean is always sum divided by count.

Question 3. The weights (in kg) of 15 students of a class are: 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
(i) Find the mode and median of this data.
(ii) Is there more than one model?
Answer: Arranging the provided data in order from lowest to highest, we have: 32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50.
(i) For the mode: The numbers appearing most frequently are 38 and 43. Therefore, the modes of this data set are 38 and 43.
For the median: The value located in the very middle of the ordered list is 40. Hence, the median of this data is 40.
(ii) Yes, this data set contains more than a single mode.
In simple words: First, arrange the weights from smallest to largest.
(i) The numbers 38 and 43 both appear three times, which is more than any other number. So, both 38 and 43 are modes. The middle number in the ordered list is 40, which is the median.
(ii) Yes, there are two modes in this set of data.

Exam Tip: A data set can have one mode, multiple modes (bimodal, trimodal, etc.), or no mode if all values appear with the same frequency. Always check for all repeating values.

Question 4. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
Answer: Ordering the provided numbers from smallest to largest, we obtain: 12, 12, 13, 13, 14, 14, 14, 16, 19. The number that occurs most frequently is 14. So, the mode for this data set is 14. Moreover, the number situated in the middle position is 14. Consequently, the median for this data is 14.
In simple words: If you put the numbers in order (12, 12, 13, 13, 14, 14, 14, 16, 19), you will see that 14 shows up the most, making it the mode. The number exactly in the middle of this sorted list is also 14, which is the median.

Exam Tip: Double-check your ordering for median, especially if there are many numbers. For mode, count occurrences carefully to avoid missing any.

Question 5. Tell whether the statement is true or false:
(i) The mode is always one of the numbers in a data.
(ii) The mean is one of the numbers in a data.
(iii) The median is always one of the numbers in a data.
(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.
Answer:
(i) True: The mode will always be one of the actual numbers existing within a given set of data.
(ii) False: The mean does not always have to be one of the numbers in the data; it can be an average not present in the original set.
(iii) True: The median is always one of the existing numbers within a data collection.
(iv) False: Let's quickly calculate the mean: \( \frac{6+4+3+8+9+12+13+9}{8} = \frac{64}{8} = 8 \). The mean is 8, not 9.
In simple words:
(i) The mode is always a number you can find in the list.
(ii) The mean does not have to be one of the numbers in the list.
(iii) The median will always be a number taken directly from the list.
(iv) If you add all the numbers (6, 4, 3, 8, 9, 12, 13, 9) you get 64. Divide 64 by 8 (because there are 8 numbers), and the mean is 8. So, saying the mean is 9 is incorrect.

Exam Tip: Understand the definitions of mean, mode, and median thoroughly. The mode is always an existing data point, while mean and median can sometimes be values not originally in the dataset (especially for even-numbered data sets regarding median).