Using a graph paper, draw an ogive for the following distribution which shows a record of the weight in kilograms of 200 students.
Weight Frequency
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
18 Likes

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 Frequency
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

18 Likes

KnowledgeBoat · Accepted Answer

(i) Cumulative frequency distribution table : Weight | Frequency | Cumulative frequency --- | ---- | ------ 40 - 45 | 5 | 5 45 - 50 | 17 | 22 (5 + 17) 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) Steps of construction : 1. Since, the 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. 2. Take 1 cm along x-axis = 5 kg. 3. Take 1 cm along y-axis = 20 units. 3. Plot the point (40, 0) as ogive starts from x-axis representing lower limit of first class. 4. Plot the points (45, 5), (50, 22), (55, 44), (60, 89), (65, 140), (70, 171), (75, 191) and (80, 200). 5. Join the points by a free hand curve. 6. 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 O (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 = 46. ∴ 46 students have weight less than 55.70 kg Hence, 46 students are underweight. (b) Since, 46 students have weight less than 55.70 kg ∴ 154 (200 - 46) students have weight more than 55.70 kg Hence, 154 students are overweight.

Date (July)	Number
1	5
2	12
3	20
4	27
5	46
6	30
7	31
8	18
9	11
10	5
11	0
12	1

Monthly income	No. of employees
6 - 7	20
7 - 8	45
8 - 9	65
9 - 10	95
10 - 11	60
11 - 12	30
12 - 13	5

Marks	No. of students
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

Mathematics

Measures of Central Tendency

Related Questions

The distribution given below, shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution.
Marks obtained No. of students
5 3
6 9
7 6
8 4
9 2
10 1

In a malaria epidemic, the number of cases diagnosed were as follows :
Date (July) Number
1 5
2 12
3 20
4 27
5 46
6 30
7 31
8 18
9 11
10 5
11 0
12 1
On what days do the mode, the upper and the lower quartiles occur ?

Weight	Frequency
40 - 45	5
45 - 50	17
50 - 55	22
55 - 60	45
60 - 65	51
65 - 70	31
70 - 75	20
75 - 80	9

Mathematics

Measures of Central Tendency

Related Questions

The distribution given below, shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution.Marks obtainedNo. of students5369768492101

In a malaria epidemic, the number of cases diagnosed were as follows :Date (July)Number15212320427546630731818911105110121On what days do the mode, the upper and the lower quartiles occur ?

The distribution given below, shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution.
Marks obtained No. of students
5 3
6 9
7 6
8 4
9 2
10 1

In a malaria epidemic, the number of cases diagnosed were as follows :
Date (July) Number
1 5
2 12
3 20
4 27
5 46
6 30
7 31
8 18
9 11
10 5
11 0
12 1
On what days do the mode, the upper and the lower quartiles occur ?