Question

Given data, which represents the marks of the students in a particular subject,
was represented in the form of a 'less than type ogive' and more than type ogive',
as shown.

(i) How do you identify the curves 'less than type ogive' and 'more than type
ogive' by looking at in terms of increasing order of curve or decreasing order
of curve?
(ii) If the two curves meet at the point (5, 7). Then what is the median of the
data?
Gii) If mode of the data is 7, find the mean of the data.​

Answer 1

(i) How do you identify the curves 'less than type ogive' and 'more than type

ogive' by looking at in terms of increasing order of curve or decreasing order

of curve?

Curve 1 - curve that represents the increasing x-axis value

Curve 2 - curve that represents the decreasing x-axis value

The curve 1 is less than ogive

And the curve 2 is more-than ogive.

(As, in less than ogive, the cumulative frequency (cf) increases.

(ii) If the two curves meet at the point (5, 7). Then what is the median of the

data?

The point of intersection of less than ogive and more than ogive is the median.

So, we can obtain the median by drawing a perpendicular line from the point of intersection of less than ogive and more than ogive.

The abscissa of this intersection gives the median of the data.

Hence we get,

Median of the data is 5 cm.

Gii) If mode of the data is 7, find the mean of the data.​

As we know that,

3 Median = Mode + 2 Mean

Median = 5 cm

Mode = 7 cm

3 × 5 = 7 + 2 × Mean

15 = 7 + 2 × Mean

15 - 7 = 2 × Mean

8 = 2 × Mean

Mean = 4