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Difficulty: EasyCumulative Frequency and Ogive

The frequency distribution table below shows the scores obtained by 5050 candidates in a competitive assessment:

Score IntervalFrequency
10−1910 - 1955
20−2920 - 291212
30−3930 - 391818
40−4940 - 491010
50−5950 - 5955

When constructing a cumulative frequency curve (ogive) for this distribution, which of the following ordered pairs (x,y)(x, y) represents the point plotted for the class interval 30−3930 - 39?

  1. A
    (29.5,35)(29.5, 35)
  2. (39.5,35)(39.5, 35)Answer
  3. C
    (34.5,35)(34.5, 35)
  4. D
    (39.5,18)(39.5, 18)

Answer

The point plotted on the ogive for the class interval 30−3930 - 39 is (39.5,35)(39.5, 35).
A cumulative frequency curve (ogive) is constructed by plotting the cumulative frequency of each class against its upper class boundary. For the interval 30−3930 - 39, the upper boundary is 39.539.5 and the cumulative frequency is 5+12+18=355 + 12 + 18 = 35, resulting in the point (39.5,35)(39.5, 35).

Step-by-Step Solution

1
Determine the upper class boundary for the class interval 30−3930 - 39
Upper class boundary = 39+402=39.5\frac{39 + 40}{2} = 39.5
Cumulative frequencies in an ogive are plotted against the upper boundaries of each class interval.
2
Calculate the cumulative frequency up to the class interval 30−3930 - 39
Cumulative frequency = 5+12+18=355 + 12 + 18 = 35
The cumulative frequency is the running sum of frequencies up to and including the given interval.
3
Combine the upper class boundary (xx-axis) and cumulative frequency (yy-axis) into an ordered pair (x,y)(x, y)
Point = (39.5,35)(39.5, 35)
In an ogive, points are plotted as (Upper Class Boundary, Cumulative Frequency).

Key Concept

Plotting Points on a Cumulative Frequency Curve (Ogive)
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Topics

Cumulative Frequency and Ogive

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