Question

The time taken, in seconds, to solve a problem for each of 25 persons is as follows:

16	20	26	27	28
30	33	37	38	40
42	43	46	46	47
48	49	50	53	58
59	60	64	52	20

(i) Construct a frequency distribution for these data using a class interval of 10 seconds.
(ii) In a school the weekly pocket money of 50 students is as follow's:

Weekly pocket money (₹)	No. of student
40 - 50	2
59 - 60	8
60 - 70	12
70 - 80	14
80 - 90	8
90 - 100	6

Draw a histogram and a frequency polygon on the same graph. Find mode from the graph.

Answer 1

(i) Frequency table

Time (in seconds)	Tally marks	Frequency
10 - 20	I	1
20 - 30	IIIII	5
30 - 40	I I I I	4
40 - 50	IIII I I I I	8
50 - 60	IIIII	5
60 - 70	I I	2

Histogram representing the time taken in seconds, to solve. A problem for each of 25 persons.

(ii) Frequency distribution table is

Weekly pocket money (in ₹)	Class Marks	No. of Students
40 - 50	45	2
50 - 60	55	8
60 - 70	65	12
70 - 80	75	14
80 - 90	85	8
90 - 100	95	6

Draw the histogram and frequency polygon on the graph.

Now, in the highest rectangle, draw two straight line AB and CD from the corners of the rectangle on either sides of the highest rectangle to opposite corners of the highest rectangle. They intersect P. Draw PR X-axis, then abscissa of the point prepresents ₹ 72·5.
Hence, the required mode is ₹72·5.