Marks obtained by 200 students in an examination are given below:
Marks Number of students
0 - 10 5
10 - 20 11
20 - 30 10
30 - 40 20
40 - 50 28
50 - 60 37
60 - 70 40
70 - 80 29
80 - 90 14
90 - 100 6
Draw an ogive for the given distribution taking 1 cm = 10 marks on one axis and 2 cm = 20 students on other axis.
Using the graph, determine :
(i) The median marks
(ii) The number of students who failed, if minimum marks required to pass is 40.
(iii) If scoring 85 and more marks is considered as grade one, find the number of students who secured grade one in the examination.

Question

Marks obtained by 200 students in an examination are given below:
Marks Number of students
0 - 10 5
10 - 20 11
20 - 30 10
30 - 40 20
40 - 50 28
50 - 60 37
60 - 70 40
70 - 80 29
80 - 90 14
90 - 100 6
Draw an ogive for the given distribution taking 1 cm = 10 marks on one axis and 2 cm = 20 students on other axis.
Using the graph, determine :
(i) The median marks
(ii) The number of students who failed, if minimum marks required to pass is 40.
(iii) If scoring 85 and more marks is considered as grade one, find the number of students who secured grade one in the examination.

KnowledgeBoat · Accepted Answer

Cumulative frequency distribution table : Marks | Number of students | Cumulative frequency ------- | ------------------ | ------------------- 0 - 10 | 5 | 5 10 - 20 | 10 | 15 (10 + 5) 20 - 30 | 14 | 29 (15 + 14) 30 - 40 | 21 | 50 (29 + 21) 40 - 50 | 25 | 75 (50 + 25) 50 - 60 | 34 | 109 (75 + 34) 60 - 70 | 36 | 145 (109 + 36) 70 - 80 | 27 | 172 (145 + 27) 80 - 90 | 16 | 188 (172 + 16) 90 - 100 | 12 | 200 (188 + 12) Here, n = 200, which is even. Steps of construction: 1. Take 1 cm along x-axis = 10 marks 2. Take 2 cm along y-axis = 20 students 3. Plot the point (0, 0) as ogive starts from x- axis representing lower limit of first class. 4. Plot the points (10, 5), (20, 15), (30, 29), (40, 50), (50, 75), (60, 109), (70, 145), (80, 172), (90, 188), (100, 200). 5. Joint the points by a free hand curve. (i) To find the median : Let A be the point on y-axis representing frequency = = 100. Through A draw a horizontal line to meet the ogive at P. Through P, draw a vertical line to meet the x-axis at M. The abscissa of the points M represents 57.5. Hence, the median is 57.5. (ii) By formula, Draw a line parallel to x-axis from point R (Number of students) = 150, touching the graph at point Q. From point Q draw a line parallel to y-axis touching x-axis at point N. From graph, N = 72 Hence, the upper quartile is 72. (iii) Total marks = 100. Let E be the point on x-axis representing marks = 65. Through E draw a vertical line to meet the ogive at B. Through B, draw a horizontal line to meet the y-axis at C. The ordinate of the point C represents 128. Hence, 128 students score less than or equal to 65, so, students scoring more than 65 = 200 - 128 = 72. Hence, the number of students who scored more than 65 marks is 72. (iv) Given, 10 students qualify for merit-scholarship. This corresponds to 190th student. Since, 200 - 10 = 190 Draw a line parallel to x-axis from point F = 190, touching the graph at point G. From point G draw a line parallel to y-axis touching x-axis at point S. From graph, S = 91 Hence, the minimum marks required to qualify is 91.

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

Mathematics

Measures of Central Tendency

Related Questions

Marks	Number of students
0 - 10	5
10 - 20	10
20 - 30	14
30 - 40	21
40 - 50	25
50 - 60	34
60 - 70	36
70 - 80	27
80 - 90	16
90 - 100	12

Weight (in gm)	Number of apples
50 - 60	8
60 - 70	10
70 - 80	12
80 - 90	16
90 - 100	18
100 - 110	14
110 - 120	12
120 - 130	10