Examkin

Question

Difficulty: MediumData Representation and Charts

The frequency distribution table below displays the examination marks of a group of candidates:

Mark ClassFrequency (ff)
10−1910 - 1955
20−2920 - 2999
30−3930 - 391616
40−4940 - 491212
50−5950 - 5988

If an ogive (cumulative frequency curve) is constructed to represent this dataset, which of the following represents the correct coordinate pair for the point corresponding to the modal class?

  1. (39.5,30)(39.5, 30)Answer
  2. B
    (29.5,30)(29.5, 30)
  3. C
    (34.5,30)(34.5, 30)
  4. D
    (39.5,16)(39.5, 16)

Answer

The correct coordinate pair is (39.5,30)(39.5, 30).
The modal class is 30−3930 - 39 because it has the highest frequency of 1616. The upper class boundary for this interval is 39.539.5. Summing frequencies up to this class gives 5+9+16=305 + 9 + 16 = 30. Therefore, the plotted point on the ogive must be (39.5,30)(39.5, 30).

Step-by-Step Solution

1
Identify the modal class interval from the frequency table.
The class with the highest frequency (1616) is 30−3930 - 39.
The modal class is defined as the interval with the maximum frequency.
2
Determine the upper class boundary of the modal class.
Upper class boundary =39+0.5=39.5= 39 + 0.5 = 39.5.
Cumulative frequency (ogive) curves are plotted using the upper class boundaries on the horizontal axis.
3
Calculate the cumulative frequency up to and including the modal class.
Cumulative frequency =5+9+16=30= 5 + 9 + 16 = 30.
An ogive plots accumulated frequencies up to each boundary.
4
Form the coordinate pair (x,y)=(Upper Class Boundary,Cumulative Frequency)(x, y) = (\text{Upper Class Boundary}, \text{Cumulative Frequency}).
(39.5,30)(39.5, 30).
Points on an ogive take the form (Upper Boundary,Cumulative Frequency)(\text{Upper Boundary}, \text{Cumulative Frequency}).

Key Concept

Plotting Cumulative Frequency Curves (Ogives)
Rate this question

Topics

Data Representation and Charts

More questions from this topic