Ogives can be helpful in locating graphically the :

Question

Accepted Answer

The correct option is 3:
Ogives, which are graphs of cumulative frequency distribution, are the definitive graphical tool used to locate the **Median** of a data set. The median is a positional average, representing the value that divides the data into two equal halves (the 50th percentile). To find it, one takes half of the total frequency ($N/2$) on the cumulative frequency (Y) axis, projects it horizontally to the ogive curve, and then vertically down to the data values (X) axis. The most accurate graphical method involves plotting both the 'less than' and 'more than' ogives on the same graph; the X-coordinate of the exact point where these two curves intersect is the median. This method provides a clear visual estimate of the central tendency of the data.

The incorrect option is 1:
The **Mean** (or Arithmetic Mean) cannot be found graphically using an ogive. The mean is a mathematically calculated average that depends on the precise magnitude and value of every observation in the data set. It is a value that is calculated from the products of the midpoint of the classes and their frequencies, which the cumulative frequency plot of an ogive deliberately conceals. While other graphs like frequency polygons or histograms can be used indirectly in certain methods, the ogive's purpose is for positional measures like percentiles, not for this type of arithmetical calculation.

The incorrect option is 2:
The **Mode**, which represents the value that occurs with the highest frequency, is typically located graphically using a **Histogram**. A histogram visually displays the individual frequency of each class interval, allowing the mode to be identified from the tallest bar. Since an ogive is a cumulative curve—meaning it adds up the frequencies—it does not show the frequency of a single class interval, which is essential for identifying the mode. Thus, the graphical estimation of the mode requires constructing a histogram, not an ogive.

The incorrect option is 4:
The option **None of these** is incorrect because the median is precisely the measure of central tendency that the ogive is designed to locate graphically. Since the intersection of the two types of ogives is the standard, recognized, and accurate graphical method for determining the median, selecting 'None of these' would ignore the primary statistical application of the cumulative frequency curve. Ogives are specifically classified as tools for positional averages.