CHAPTER AT A GLANCE
1. Basic Term
(I) Class limits: Suppose marks obtained by all of the students are divided into class intervals 25 – 35, 35 – 45 and so interval on.
In class 25-35,25 is called lower class limit and 35 is called upper class limit.
(ii)Class size : The difference between upper and lower class limit.
(iii) Class mark: It is given by
2. Ungrouped and Grouped Data
The data obtained in original form are called raw data or ungrouped data.
To put the data in a more condensed form, we make groups of suitable size and mention the frequency of each group. Such a table is called a grouped frequency distribution table, and the data so obtained is called grouped data.
3. Mean
4. Mode
5. Median
The median is a measure of central tendency which gives the value of the middle most observation in the data.
6. Relationship Between Mean, Mode and Median
3 Median = Mode + 2 Mean
7. Cumulative Frequency Curve (Ogive)
(i) The smooth free hand curve is formed by joining the points (xi, fi;) where xi is the upper limit of a class and t;, is the corresponding c.f. The curve so obtained is called a cumulative frequency curve, or an ogive of the less than type.
(ii) The smooth free hand curve is formed by joining the points (xi, t;;) where xi is the lower limit of a class and t;, is the corresponding c.f. The curve so obtained is called a cumulative frequency curve, or an ogive of the more than type.
8. Median by Graph
(I) Draw the ogive of the less than type and ogive of the more than type on the same axis. The two ogives will intersect each other at a point. From this point, if we draw a perpendicular on the x-axis, the point at which it cuts the x-axis gives us the median.
(ii) Draw the ogive of the less than type, then locate n/2 on the y-axis
(n = number of observations). From this point on y-axis, draw a line parallel to x-axis cutting the less than ogive at a point. From this point draw a perpendicular on the x-axis, the point at which the perpendicular cuts the x-axis gives us the median
Related Articles: