Age 5 - 15 ,15 - 25 ,25 - 35 ,35 - 45 ,45 - 55 ,55 - 65 ,65 - 75 No.of causalities 6 ,10, 16, 15 ,24, 8, 7 Construct the Ogive for the above data. From your graph determine. (i) The lower quartile (ii) The upper quartile (iii) The median. aswer fast it's very urgent
Answers
cidents
6
10
15
13
24
8
7
(i) Construct the less than cumulative frequency curve for the above data, using 2cm=10 years, on one axis and 2cm=10 casualties on the other.
(ii) From your graph determine
(1) the median and (2) the upper quartile
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Answer
(i)We write the given data in the cumulative frequency table.
Age (yrs)
No of casualties due to accidents f
Cumulative frequency c.f
5-15
6
6
15-25
10
16
25-35
15
31
35-45
13
44
45-55
24
68
55-65
8
76
65-75
7
83
(ii)To represent the data in the table graphically, we mark the upper limits of the class intervals on
the horizontal axis (x-axis) and their corresponding cumulative frequencies on the vertical axis ( y-axis),
Plot the points (15,6),(25,16),(35,31),(45,44),(55,68),(65,76) and (75,83) on the graph.
Join the points with the freehand. We get an ogive as shown:
(ii)(1). Here n=83, which is odd.
So median =(n+1)/2)
th
term
=((83+1)/2)
=84/2
=42
Now mark a point A (42) on the Y-axis and from A draw a line parallel to X-axis meeting the curve at P. From P, draw a perpendicular on x-axis meeting it at Q.
Q is the median.
Q=43
Hence the median is 43.
(ii)(2). Upper quartile =(3(n+1)/4)
=(3×(83+1)/4)
=(3×(84)/4)
=63
Now mark a point B (63) on the Y-axis and from A draw a line parallel to X-axis meeting the curve at L. From L, draw a perpendicular on x-axis meeting it at M.
M=52
Hence the upper quartile is 52
Step-by-step explanation:
(i)We write the given data in the cumulative frequency table.
Age (yrs)
No of casualties due to accidents f
Cumulative frequency c.f
5-15
6
6
15-25
10
16
25-35
15
31
35-45
13
44
45-55
24
68
55-65
8
76
65-75
7
83
(ii)To represent the data in the table graphically, we mark the upper limits of the class intervals on
the horizontal axis (x-axis) and their corresponding cumulative frequencies on the vertical axis ( y-axis),
Plot the points (15,6),(25,16),(35,31),(45,44),(55,68),(65,76) and (75,83) on the graph.
Join the points with the freehand. We get an ogive as shown:
(ii)(1). Here n=83, which is odd.
So median =(n+1)/2)
th
term
=((83+1)/2)
=84/2
=42
Now mark a point A (42) on the Y-axis and from A draw a line parallel to X-axis meeting the curve at P. From P, draw a perpendicular on x-axis meeting it at Q.
Q is the median.
Q=43
Hence the median is 43.
(ii)(2). Upper quartile =(3(n+1)/4)
=(3×(83+1)/4)
=(3×(84)/4)
=63
Now mark a point B (63) on the Y-axis and from A draw a line parallel to X-axis meeting the curve at L. From L, draw a perpendicular on x-axis meeting it at M.
M=52
Hence the upper quartile is 52.
