At customer services centre time required to serve customer is tabulated below
Time required (in minutes) 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81 - 90
No. of customers 12 18 27 20 17 6
Draw less than cumulative frequency curve

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Solution

Time required No.of customer Class C.F
$31 - 40$ $12$ Less than $40.5$ $12$
$41 - 50$ $18$ less than $50.5$ $30$
$51 - 60$ $27$ less than $60.5$ $57$
$61 - 70$ $20$ less than $70.5$ $77$
$71 - 80$ $17$ less than $80.5$ $94$
$81 - 90$ $6$ less than $90.5$ $100$

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Q. At a customer-service centre, the time required to serve customers is tabulated below.

Time required (in minutes )	31-40	41-50	51-60	61-70	71-80	81-90
No. of customers	12	18	27	20	17	6

Draw a less-than cumulative frequency curve for the data.

Q. Construct a ‘more than’ cumulative frequency table and draw an ogive for the data given below:

Marks	1 - 10	11 - 20	21 - 30	31 - 40	41 - 50	51 - 60	61 - 70	71 - 80
Frequency	3	8	12	14	10	6	5	2

Q. Draw frequency polygon and frequency curve for the following data on land holding by the farmers.

Area in hectare	11 - 20	21 - 30	31 - 40	41 - 50	51 - 60	61 - 70	71 - 80
No. of farmers	58	103	208	392	112	34	12

Q. Calculate the mean of the distribution given below using the shortcut method.

marks	11-20	21-30	31-40	41-50	51-60	61-70	71-80
number of students	2	6	10	12	9	7	4

Following frequency distribution gives the weights of the students of a class.

$\begin{matrix} Weight(in kg) & 31 - 35 & 36 - 40 & 41 - 45 & 46 - 50 & 51 - 55 & 56 - 60 & 61 - 65 & 66 - 70 & 71 - 75 Number of students & 3 & 6 & 13 & 9 & 11 & 7 & 4 & 2 & 1 \end{matrix}$

Find the probability of

(i) choosing a student at random whose weight is atmost 40kg

(ii) choosing a student at random whose weight is greater than 40kg but less than 60kg

(iii) choosing a student at random whose weight is greater than 60kg [3 MARKS]

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Time required (in minutes)	31 - 40	41 - 50	51 - 60	61 - 70	71 - 80	81 - 90
No. of customers	12	18	27	20	17	6

Time required	No.of customer	Class	C.F
$31 - 40$	$12$	Less than $40.5$	$12$
$41 - 50$	$18$	less than $50.5$	$30$
$51 - 60$	$27$	less than $60.5$	$57$
$61 - 70$	$20$	less than $70.5$	$77$
$71 - 80$	$17$	less than $80.5$	$94$
$81 - 90$	$6$	less than $90.5$	$100$

At customer services centre time required to serve customer is tabulated belowTime required (in minutes)31 - 4041 - 5051 - 6061 - 7071 - 8081 - 90No. of customers12182720176Draw less than cumulative frequency curve

Time required No.of customer Class C.F 31−40 12 Less than 40.5 12 41−50 18 less than 50.5 30 51−60 27 less than 60.5 57 61−70 20 less than 70.5 77 71−80 17 less than 80.5 94 81−90 6 less than 90.5 100

At customer services centre time required to serve customer is tabulated below
Time required (in minutes) 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 81 - 90
No. of customers 12 18 27 20 17 6
Draw less than cumulative frequency curve

Time required No.of customer Class C.F
$31 - 40$ $12$ Less than $40.5$ $12$
$41 - 50$ $18$ less than $50.5$ $30$
$51 - 60$ $27$ less than $60.5$ $57$
$61 - 70$ $20$ less than $70.5$ $77$
$71 - 80$ $17$ less than $80.5$ $94$
$81 - 90$ $6$ less than $90.5$ $100$