GSEB Class 7 Maths Solutions Chapter 3 માહિતીનું નિયમન Exercise 3.1

 

Question 1. તમારા વર્ગના કોઈ પણ દસ વિદ્યાર્થીઓની ઊંચાઈનો વિસ્તાર શોધો.
Answer: Let's assume the heights of ten students in the class are as follows: 117 cm, 111 cm, 114 cm, 120 cm, 110 cm, 116 cm, 119 cm, 119 cm, 115 cm, 113 cm.
Arranging the above data in ascending order, we get:
110 cm, 111 cm, 113 cm, 114 cm, 115 cm, 116 cm, 117 cm, 119 cm, 119 cm, 120 cm.
The maximum height is 120 cm and the minimum height is 110 cm.
Range \( = \) Maximum Height \( - \) Minimum Height
\( = 120 \) cm \( - 110 \) cm \( = 10 \) cm
Therefore, the range of heights for the ten students in the class is 10 cm.
In simple words: First, list ten student heights. Then, find the tallest and shortest heights. The range is the difference between these two heights.

Exam Tip: Remember to arrange the data in ascending or descending order before identifying the highest and lowest values to calculate the range accurately.

 

Question 2. કોઈ વર્ગના એક મૂલ્યાંકનમાં મેળવેલ નીચે દર્શાવેલ ગુણને કોષ્ટકમાં દર્શાવો: 4, 6, 7, 8, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7
(i) સૌથી વધારે ગુણ કેટલા છે?
(ii) સૌથી ઓછા ગુણ કેટલા છે?
(iii) માહિતીનો વિસ્તાર શો છે?
(iv) અંકગણિતીય સરાસરી શોધો.
Answer: The given marks are: 4, 6, 7, 8, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7.
The details of the given marks are shown in the table below:

(i) The highest mark is 9.
(ii) The lowest mark is 1.
(iii) The range of the data \( = \) Highest mark \( - \) Lowest mark \( = 9 - 1 = 8 \).
(iv) Arithmetic Mean \( = \frac{\text{Total sum of marks}}{\text{Total number of students}} \)
\( = \frac{[1 \times 1] + [2 \times 2] + [3 \times 1] + [4 \times 3] + [5 \times 5] + [6 \times 4] + [7 \times 2] + [8 \times 1] + [9 \times 1]}{1 + 2 + 1 + 3 + 5 + 4 + 2 + 1 + 1} \)
\( = \frac{1+4+3+12+25+24+14+8+9}{20} \)
\( = \frac{100}{20} \)
\( = 5 \) marks
Thus, the arithmetic mean is 5 marks.
In simple words: First, count how many times each mark appears. Then, identify the highest and lowest scores. The range shows how spread out the scores are. To find the average, add all the marks together and then divide by the total number of students.

Exam Tip: When making a frequency table, ensure accurate tally marks for each score. For the mean, double-check your addition and division to avoid errors.

 

Question 3. પ્રથમ 5 પૂર્ણ સંખ્યાઓની સરાસરી શોધો.
Answer: The first five whole numbers are 0, 1, 2, 3, and 4.
Sum of the first five whole numbers \( = 0 + 1 + 2 + 3 + 4 = 10 \).
Average \( = \frac{\text{Sum of numbers}}{\text{Total count of numbers}} \)
\( = \frac{10}{5} = 2 \)
The average of the first five whole numbers is 2.
In simple words: Whole numbers start from zero. Add up the first five whole numbers, then divide by five to find their average.

Exam Tip: Remember that whole numbers start with 0. Including 0 in your list is crucial for calculations involving "first whole numbers."

 

Question 4. એક ક્રિકેટરે 8 દાવમાં નીચે મુજબ રન બનાવ્યાઃ 58, 76, 40, 35, 46, 45, 0, 100 તો તેનો સરાસરી સ્કોર (રન) શોધો.
Answer: The runs scored by a cricketer in 8 innings are: 58, 76, 40, 35, 46, 45, 0, 100.
Total runs scored \( = 58 + 76 + 40 + 35 + 46 + 45 + 0 + 100 = 400 \).
Number of innings \( = 8 \).
Average score \( = \frac{\text{Total sum of runs}}{\text{Number of innings}} \)
\( = \frac{400}{8} = 50 \) runs
The average score is 50 runs.
In simple words: Add all the runs the cricketer scored in his games. Then, divide that total by how many games he played. This gives you his average score.

Exam Tip: Always include all data points, even zero, when calculating an average. Missing any value will result in an incorrect mean.

 

Question 5. નીચે દર્શાવેલ કોષ્ટક દરેક ખેલાડીએ ચાર રમતમાં મેળવેલા અંક દર્શાવે છેઃ

(i) દરેક રમતમાં 4 વડે મેળવેલ અંકની સરાસરી શોધો.
(ii) દરેક રમતમાં C વડે મેળવેલ અંકની સરાસરી જાણવા માટે તમે કુલ સંખ્યાને 3 વડે ભાગશો કે 4 વડે? શા માટે?
(iii) B ચારેય રમતમાં રમ્યો છે. તમે તેની સરાસરી કેવી રીતે શોધશો?
(iv) કોનો દેખાવ સૌથી સારો છે?
Answer:
(i) Average points scored by player A \( = \frac{\text{Total points scored}}{\text{Total number of games}} \)
\( = \frac{14 + 16 + 10 + 10}{4} = \frac{50}{4} = 12.5 \)
The average points scored by player A is 12.5.
(ii) Player C only played three games (because he did not play Game No. 3).
Therefore, to know the average points for player C, we must divide the total points he earned by 3.
Average points scored by player C \( = \frac{\text{Total points scored}}{\text{Total number of games}} \)
\( = \frac{8 + 11 + 13}{3} = \frac{32}{3} \approx 10.67 \)
The average runs for player C is approximately 10.67 runs.
(iii) Player B played in all four games. To find his average, we will sum his scores from all four games and divide by 4.
Average points scored by player B \( = \frac{\text{Total points scored}}{\text{Total number of games}} \)
\( = \frac{0 + 8 + 6 + 4}{4} = \frac{18}{4} = 4.5 \)
The average points scored by player B is 4.5.
(iv) Among the three players, player A has the highest average score, so player A's performance is the best.
In simple words: For player A, add up all scores and divide by 4 games. For player C, add scores and divide by only 3 games because he missed one. For player B, add all scores and divide by 4 games. The player with the highest average score did the best.

Exam Tip: Always pay attention to whether a player participated in all games. If not, adjust the denominator (number of games played) when calculating their average score.

 

Question 6. વિજ્ઞાનની એક કસોટીમાં વિદ્યાર્થીઓના એક સમૂહ (100માંથી) પ્રાપ્ત કરેલ ગુણ 85, 76, 90, 85, 39, 48, 56, 95, 81 અને 75 છે.
(i) વિદ્યાર્થીઓએ મેળવેલ સૌથી વધુ અને સૌથી ઓછા ગુણ
(ii) મેળવેલા ગુણનો વિસ્તાર
(iii) સમૂહ દ્વારા મેળવાયેલા ગુણની સરાસરી શોધો.
Answer: The marks obtained by 10 students in a science test, arranged in ascending order, are:
39, 48, 56, 75, 76, 81, 85, 85, 90, 95.
(i) Here, the highest mark obtained is 95, and the lowest mark is 39.
(ii) Range of marks \( = \) Highest mark \( - \) Lowest mark
\( = 95 - 39 = 56 \) marks
(iii) Average marks obtained by this group \( = \frac{\text{Sum of all marks}}{\text{Total number of students}} \)
\( = \frac{39 + 48 + 56 + 75 + 76 + 81 + 85 + 85 + 90 + 95}{10} \)
\( = \frac{730}{10} = 73 \) marks
The average marks obtained by this group is 73 marks.
In simple words: First, list all the scores from smallest to largest. Then, find the biggest and smallest numbers. The range is the difference between them. To find the average, add all the scores and divide by the total number of students.

Exam Tip: When calculating the average, make sure to add all the marks correctly and divide by the exact number of students. Arrange marks in order to easily find the highest and lowest for range.

 

Question 7. સળંગ છ વર્ષોમાં એક શાળામાં વિધાર્થીઓની સંખ્યા નીચે પ્રમાણે હતીઃ 1555, 1670, 1750, 2013, 2540 અને 2820 આ સમયગાળા દરમિયાન શાળાના વિધાર્થીઓની સરાસરી શોધો.
Answer: The number of students in a school for six consecutive years was: 1555, 1670, 1750, 2013, 2540, and 2820.
Total number of students in the school over six consecutive years
\( = 1555 + 1670 + 1750 + 2013 + 2540 + 2820 \)
\( = 12348 \)
Average number of students \( = \frac{\text{Total number of students}}{\text{Number of years}} \)
\( = \frac{12348}{6} = 2058 \)
During this period, the average number of students in the school was 2058.
In simple words: Add up the number of students for all six years. Then, divide that total by six to find the average number of students per year.

Exam Tip: When calculating averages over multiple years, ensure you add all data points accurately and divide by the correct number of years or terms.

 

Question 8. એક શહેરમાં કોઈ ચોક્કસ અઠવાડિયામાં પડેલ વરસાદ (મિમીમાં) નીચે દર્શાવ્યા પ્રમાણે નોંધવામાં આવ્યો છેઃ

(i) ઉપરની માહિતીને આધારે વરસાદનો વિસ્તાર શોધો.
(ii) આ અઠવાડિયામાં પડેલા વરસાદની સરાસરી શોધો.
(iii) કેટલા દિવસોમાં વરસાદ સરાસરી વરસાદ કરતાં ઓછો પડ્યો છે?
Answer:
(i) Rainfall range \( = \) Maximum rainfall \( - \) Minimum rainfall
\( = 20.5 - 0.0 = 20.5 \) mm
(ii) Average rainfall \( = \frac{\text{Total rainfall}}{\text{Total number of days}} \)
\( = \frac{0.0 + 12.2 + 2.1 + 0.0 + 20.5 + 5.5 + 1.0}{7} \)
\( = \frac{41.3}{7} \approx 5.9 \) mm
Thus, the average rainfall is approximately 5.9 mm.
(iii) From the table, it is clear that during this week, rainfall was less than the average rainfall (5.9 mm) on 5 days: Monday (0.0 mm), Wednesday (2.1 mm), Thursday (0.0 mm), Saturday (5.5 mm), and Sunday (1.0 mm).
In simple words: First, find the highest and lowest rainfall amounts to get the range. Then, add all the daily rainfall amounts and divide by 7 days to get the average. Finally, check which days had less rain than this average.

Exam Tip: When calculating average rainfall, ensure all recorded values, including 0.0 mm for no rain, are included in the sum. For finding days below average, compare each day's rainfall with the calculated average carefully.

 

Question 9. 10 છોકરીઓની ઊંચાઈ સેમીમાં માપવામાં આવી અને નીચે દર્શાવ્યા પ્રમાણે પરિણામ મળેલ છે: 135, 150, 139, 128, 151, 132, 146, 149, 143, 141
(i) સૌથી વધુ ઊંચાઈ ધરાવતી છોકરીની ઊંચાઈ કેટલી છે?
(ii) સૌથી ઓછી ઊંચાઈ ધરાવતી છોકરીની ઊંચાઈ કેટલી છે?
(iii) આ માહિતીનો વિસ્તાર કેટલો છે?
(iv) છોકરીઓની સરાસરી ઊંચાઈ કેટલી છે?
(v) કેટલી છોકરીઓની ઊંચાઈ સરાસરી ઊંચાઈ કરતાં વધુ છે?
Answer: The given heights of 10 girls, arranged in ascending order, are:
128, 132, 135, 139, 141, 143, 146, 149, 150, 151.
(i) The height of the tallest girl is 151 cm.
(ii) The height of the shortest girl is 128 cm.
(iii) The range of this data \( = \) Highest height \( - \) Lowest height
\( = 151 \) cm \( - 128 \) cm \( = 23 \) cm
(iv) Average height of the girls \( = \frac{\text{Total sum of girls' heights}}{\text{Total number of girls}} \)
\( = \frac{128 + 132 + 135 + 139 + 141 + 143 + 146 + 149 + 150 + 151}{10} \)
\( = \frac{1414}{10} = 141.4 \) cm
Therefore, the average height of the girls is 141.4 cm.
(v) The girls with heights greater than the average height (141.4 cm) are those with heights: 143 cm, 146 cm, 149 cm, 150 cm, and 151 cm.
There are 5 girls whose height is greater than the average height.
In simple words: First, list all heights from smallest to largest. Find the tallest and shortest heights, and their difference is the range. Add all the heights and divide by 10 to get the average height. Finally, count how many girls are taller than this average.

Exam Tip: To avoid errors in counting, it's best to arrange the data in ascending order. This helps in easily identifying the lowest, highest, and all values above or below the average.