Using a graph paper, draw an ogive for the following distribution which shows a record of the weight in kilograms of 200 students.
Weight (in kg) No. of students
40 - 45 5
45 - 50 17
50 - 55 22
55 - 60 45
60 - 65 51
65 - 70 31
70 - 75 20
75 - 80 9
Use your ogive to estimate the following :
(i) the percentage of students weighing 55 kg or more
(ii) the weight above which the heaviest 30% of the students fall
(iii) the number of students who are (a) under weight and (b) Over-weight, if 55.70 kg is considered as standard weight.
Measures of Central Tendency
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Question

Using a graph paper, draw an ogive for the following distribution which shows a record of the weight in kilograms of 200 students.
Weight (in kg) No. of students
40 - 45 5
45 - 50 17
50 - 55 22
55 - 60 45
60 - 65 51
65 - 70 31
70 - 75 20
75 - 80 9
Use your ogive to estimate the following :
(i) the percentage of students weighing 55 kg or more
(ii) the weight above which the heaviest 30% of the students fall
(iii) the number of students who are (a) under weight and (b) Over-weight, if 55.70 kg is considered as standard weight.

Measures of Central Tendency

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KnowledgeBoat · Accepted Answer

Cumulative frequency distribution table : Weight (in kg) | No. of students | Cumulative frequency -------------- | ---------------- | -------------------- 40 - 45 | 5 | 5 45 - 50 | 17 | 22 (17 + 5) 50 - 55 | 22 | 44 (22 + 22) 55 - 60 | 45 | 89 (44 + 45) 60 - 65 | 51 | 140 (89 + 51) 65 - 70 | 31 | 171 (140 + 31) 70 - 75 | 20 | 191 (171 + 20) 75 - 80 | 9 | 200 (191 + 9) Here, n = 200, which is even. Steps of construction: 1. Take 2 cm along x-axis = 5 kg 2. Take 2 cm along y-axis = 20 units. 3. Since, scale on x-axis starts at 40, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 40. 4. Plot the point (40, 0) as ogive starts from x-axis representing lower limit of first class. 5. Plot the points (45, 5), (50, 22), (55, 44), (60, 89), (65, 140), (70, 171), (75, 191) and (80, 200). 6. Join the points by a free hand curve. 7. Draw a line parallel to y-axis from point J(weight) = 55, touching the graph at point Q. From point Q draw a line parallel to x-axis touching y-axis at point K. From graph, K = 44. Hence, 44 students weight 55 kg or less. Students weighing more than 55 kg = 200 - 44 = 156 Percentage of students weighing more than 55 kg = = 78% Hence, percentage of students weighing more than 55 kg = 78%. (ii) 30% of students = = 60. Total students = 200 No. of students not in heaviest 30% = 200 - 60 = 140. Draw a line parallel to x-axis from point I (no. of students) = 140, touching the graph at point R. From point R draw a line parallel to y-axis touching x-axis at point P. From graph, P = 65 Hence, above 65 kg the heaviest 30% of the students fall. (iii) Draw a line parallel to y-axis from point L (weight) = 55.70 kg, touching the graph at point M. From point M draw a line parallel to x-axis touching y-axis at point N. (a) From graph, N = 50. ∴ 50 students have weight less than 55.70 kg Hence, 50 students are underweight. (b) Since, 50 students have weight less than 55.70 kg ∴ 150 (200 - 50) students have weight more than 55.70 kg. Hence, 150 students are overweight.

Scores obtained	Number of shooters
0 - 10	5
10 - 20	9
20 - 30	16
30 - 40	22
40 - 50	26
50 - 60	18
60 - 70	11
70 - 80	6
80 - 90	4
90 - 100	3

Wages (in ₹)	Number of workers
400 - 450	2
450 - 500	6
500 - 550	12
550 - 600	18
600 - 650	24
650 - 700	13
700 - 750	5

Marks	No. of students
0 - 10	5
10 - 20	10
20 - 30	20
30 - 40	25
40 - 50	15
50 - 60	12
60 - 70	9
70 - 80	4

Scores	Number of shooters
0 - 10	9
10 - 20	13
20 - 30	20
30 - 40	26
40 - 50	30
50 - 60	22
60 - 70	15
70 - 80	10
80 - 90	8
90 - 100	7

Mathematics

Measures of Central Tendency

Related Questions

Weight (in kg)	No. of students
40 - 45	5
45 - 50	17
50 - 55	22
55 - 60	45
60 - 65	51
65 - 70	31
70 - 75	20
75 - 80	9