(i) The proportion of the sector for hours:
in sleeping = \(Number\ of\ sleeping\ hours\over Whole\ day\)
\(={8\ hours\over 24\ hours}={1\over3}\)
in school =\({6\ hours\over 24\ hours}={1\over4}\)
in home work = \({4\ hours\over 24\ hours}={1\over 6}\)
in play = \({3\ hours\over 24\ hours}={1\over 8}\)
in others = \({3\ hours\over 24\ hours}={1\over 8}\)
(ii) ∵ Total angle at the centre of a circle
= 360°
i.e., Central angle for 1 (whole) = 360°
∴ Central angle for play
(\(1\over8\)th part of Whole) = \(1\over8\) x 360° = 45°
Similarly, central angle for home work
(\(1\over6\) th part of Whole) = \(1\over6\) x 360° = 60°

\(\frac{1}{3}\)

\(\frac{1}{2}\)

(a) 16%
(b) 63000

(a) Angle made by the expenditure on bricks
= 360^o - (45^o + 100^o + 90^o + 75^o)
= 360^o - 310^o = 50^o
Thus, expenditure on bricks
= \(\frac{50}{360}\times \) 540000 = Rs 75000
(b) Expenditure on bricks = Rs 75000
Expenditure on timber = \(\frac{90}{360}\times 540000\)
= \(\frac{540000}{4}\) = Rs 135000
\(\therefore\) Difference between expenditure on bricks and expenditure on timber = 135000 - 75000 = Rs 60000
Hence, expenditure on bricks is Rs 60000 less than expenditure on timber.

(a) The lower limit of the second class interval 20 - 30 is 20.
(b) The upper limit of the last class interval.ls 60.
(c) The frequency of the third class is 14.
(d) The interval 10 - 20 has a frequency of 15.
(e) The interval which has the lowest frequency is 20 - 30.
(f) The class size is 20 - 10 = 10.

Total quantity obtained from the given four symbols = 800 + 700 + 550 + 450 = 2500
28% of 2500 = \(\frac{28}{100}\times 2500\) = 700
22% of 2500 = \(\frac{22}{100}\times 2500\) = 550
18% of 2500 = \(\frac{18}{100}\times 2500\) = 450
32% of 2500 = \(\frac{32}{100}\times 2500\) = 600

Here, the types of shoppers are Wom.an (W), Man (M), Boy (B) or Girl (G). Then, frequency distribution table for the above data is given below:

Types of shoppers	Tally marks	Frequency   (Number of shoppers)
W		28
M		15
B		5
G		12
Total		60

Now, draw two perpendicular axes OX and OY and take types of shoppers along OX and frequency i.e. number of shoppers along OY. Choose a suitable scale for OX and OY and draw bars of equal gaps in between. Thus, we get the following bar graph:

Here, comparison of two activities is given, so to represent the given information, we draw the double bar graph. So, draw two perpendicular axes OX and OY. Take schools on OX and number of children on OY. Choose a suitable scale for OX and OY to draw double bar graph.
Thus, we get the following double bar graph:

Here, to represent the given information, we draw the bar graph. So, draw two perpendicular axes OX and OY. Take months on OX and number of watches sold on OY. Choose a suitable scale for OX and OY and drawbars of equal width with equal gaps in between.
Thus, we get the following bar graph