The value of $\pi$ up to $50$ decimal places is given below:
$3.14159265358979323846264338327950288419716939937510$
$(i)$ Make a frequency distribution of the digits from $0$ to $9$ after the decimal point.
$(ii)$ What are the most and the least frequently occurring digits?

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(N/A) $(i)$ By observing the digits after the decimal point,the frequency distribution table is constructed as follows:
Digit Frequency
$0$ $2$
$1$ $5$
$2$ $5$
$3$ $8$
$4$ $4$
$5$ $5$
$6$ $4$
$7$ $4$
$8$ $5$
$9$ $8$
Total $50$

$(ii)$ From the table,the least frequency is $2$ (for digit $0$),and the maximum frequency is $8$ (for digits $3$ and $9$). Thus,the most frequently occurring digits are $3$ and $9$,and the least frequently occurring digit is $0$.

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$A$ company manufactures car batteries of a particular type. The lives (in years) of $40$ such batteries were recorded as follows:
$\begin{array}{llllllll}2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 \\ 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 \\ 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 \\ 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 \\ 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6\end{array}$
Construct a grouped frequency distribution table for this data,using class intervals of size $0.5$ starting from the interval $2 - 2.5$.

$A$ teacher wanted to analyze the performance of two sections of students in a mathematics test of $100$ marks. Looking at their performances,she found that a few students got under $20$ marks and a few got $70$ marks or above. So she decided to group them into intervals of varying sizes as follows: $0-20, 20-30, ..., 60-70, 70-100$. Then she formed the following table:
MarksNumber of students
$0-20$$7$
$20-30$$10$
$30-40$$10$
$40-50$$20$
$50-60$$20$
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$70-100$$8$
Total$90$

$A$ histogram for this table was prepared by a student as shown in Fig. Carefully examine this graphical representation. Do you think that it correctly represents the data?

The heights (in $cm$) of $9$ students of a class are as follows:
$155, 160, 145, 149, 150, 147, 152, 144, 148$
Find the median of this data. (in $\text{ cm}$)

Consider a small unit of a factory where there are $5$ employees: a supervisor and four labourers. The labourers draw a salary of $Rs. 5,000$ per month each,while the supervisor gets $Rs. 15,000$ per month. Calculate the mean,median,and mode of the salaries of this unit of the factory.

Thirty children were asked about the number of hours they watched $TV$ programmes in the previous week. The results were found as follows:
$\begin{array}{rrrrrrrrrr}1 & 6 & 2 & 3 & 5 & 12 & 5 & 8 & 4 & 8 \\ 10 & 3 & 4 & 12 & 2 & 8 & 15 & 1 & 17 & 6 \\ 3 & 2 & 8 & 5 & 9 & 6 & 8 & 7 & 14 & 12\end{array}$
$(i)$ Make a grouped frequency distribution table for this data,taking class width $5$ and one of the class intervals as $5-10$.
$(ii)$ How many children watched television for $15$ or more hours a week?

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