Question 1: Arrange the following data in ascending order:

(i) $8, 3, 11, 15, 1, 7, 16, 25, 9, 4$

(ii) $5.7, 9.2, 3.1, 4.6, 1.8, 10.4, 2.5, 0.9, 1.2$

(i) $1, 2, 4, 7, 8, 9, 11, 15, 16, 25$

(ii) $0.9, 1.2, 1.8, 2.5, 3.1, 4.6, 5.7, 9.2, 10.4$

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Question 2: Arrange the following data in descending order:

(i) $15, 3, 0, 11, 7, 2, 23, 14, 29, 5, 1, 7$

(ii) $2.3, 4.6, 1.2, 0.4, 3.5, 9.7, 6.1, 4.8, 0.8, 1.0$

(i) $29, 23, 17, 15, 14, 11, 7, 5, 3, 2, 1, 0$

(ii) $9.7, 6.1, 4.8, 4.6, 3.5, 2.3, 1.2, 1.0, 0.8, 0.4$

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Question 3: Construct a frequency table for each of the following data:

(i) $3, 2, 5, 4, 1, 3, 2, 2, 5, 3, 1, 2, 1, 1, 2, 2, 3, 4, 5, 3, 1, 2, 3$

(ii) $7, 8, 6, 5, 6, 7, 7, 9, 8, 10, 7, 6, 7, 8, 8, 9, 10, 5, 7, 8, 7, 6$

(iii) $152, 165, 172, 144, 135, 156, 175, 140, 132, 150, 153, 147$

(iv) $13, 25, 19, 16, 8, 30, 27, 6, 0, 34, 40, 11, 4 , 17$

(i) First step is to arrange the data in ascending order.

$1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3$

 $x$$x$ Tally $f$$f$ $1$$1$ $5$$5$ $2$$2$ ${\mid \mid }$${\mid \mid }$ $7$$7$ $3$$3$ ${\mid }$${\mid }$ $6$$6$ $4$$4$ ${\mid \mid }$${\mid \mid }$ $2$$2$ $5$$5$ ${\mid \mid \mid }$${\mid \mid \mid }$ $3$$3$

(ii) First step is to arrange the data in ascending order.

$5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8 , 9, 9, 10, 10$

 $x$$x$ Tally $f$$f$ $5$$5$ ${\mid \mid }$${\mid \mid }$ $2$$2$ $6$$6$ $4$$4$ $7$$7$ ${\mid \mid }$${\mid \mid }$ $7$$7$ $8$$8$ $5$$5$ $9$$9$ ${\mid \mid }$${\mid \mid }$ $2$$2$ $10$$10$ ${\mid \mid }$${\mid \mid }$ $2$$2$

(iii) First step is to arrange the data in ascending order.

$132, 135, 140, 144, 147, 150, 152, 153, 156, 165, 172, 175$

 Class Interval Tally $f$$f$ $130-135$$130-135$ ${\mid }$${\mid }$ $1$$1$ $135-140$$135-140$ ${\mid }$${\mid }$ $1$$1$ $140-145$$140-145$ ${\mid \mid }$${\mid \mid }$ $2$$2$ $145-150$$145-150$ ${\mid }$${\mid }$ $1$$1$ $150-155$$150-155$ ${\mid \mid \mid }$${\mid \mid \mid }$ $3$$3$ $155-160$$155-160$ ${\mid }$${\mid }$ $1$$1$ $160-165$$160-165$ $0$$0$ $165-170$$165-170$ ${\mid }$${\mid }$ $1$$1$ $170-175$$170-175$ ${\mid }$${\mid }$ $1$$1$ $175-180$$175-180$ ${\mid }$${\mid }$ $1$$1$

(iv) First step is to arrange the data in ascending order.

$0, 4, 6, 8, 11, 13, 16, 17, 19, 25, 27, 30, 34, 40$

 $x$$x$ Tally $f$$f$ $0-10$$0-10$ ${\mid \mid \mid \mid}$${\mid \mid \mid \mid}$ $4$$4$ $10-20$$10-20$ $5$$5$ $20-30$$20-30$ ${\mid \mid }$${\mid \mid }$ $2$$2$ $30-40$$30-40$ ${\mid \mid }$${\mid \mid }$ $2$$2$ $40-50$$40-50$ ${\mid }$${\mid }$ $1$$1$

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Question 4: Fill in the blanks:

(i) Lower limit of the class interval $14-22$ is $\underline{14}$.

(ii) Upper limit of the class interval $16-25$ is $\underline{25}$.

(iii) Class size of the interval $20-30$ is $\underline{10}$.

(iv) If the upper and the lower limits of a class interval be $18$ and $11$ respectively, then the class interval is $\underline{11-18}$

(v) If the lower and the upper limit of the class interval be $11.5$ and $21.5$ respectively, then the class interval is $\underline{11.5 - 21.5}$.

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Question 5: The marks out of $50$, obtained by $30$ students of a class in an examination are given below:

$40, 12, 46, 37, 17, 27, 30, 6, 2, 23, 19, 39, 25, 5, 33$

$19, 21, 12, 41, 17, 12, 19, 17, 8, 10, 1, 9, 21, 13, 48$

Arrange them in ascending order and present it in a grouped data, by taking class interval as $0-10, 10-20, 20-30, 30-40, 40-50$

In ascending order: $1, 2, 5, 6, 8, 9, 10, 12, 12 , 12 , 13, 17, 17, 17, 19, 19, 19, 21, 21, \\ 23, 25, 2730, 33, 37, 39, 40, 41, 46, 48$

 $x$$x$ $f$$f$ (number of students) $0-10$$0-10$ $6$$6$ $10-20$$10-20$ $11$$11$ $20-30$$20-30$ $5$$5$ $30-40$$30-40$ $4$$4$ $40-50$$40-50$ $4$$4$

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Question 6: The fine imposed in Rs. on $40$ students for being absent is given below:

$18, 8, 12, 6, 8, 16, 12, 5, 23, 2, 16, 23, 2, 10, 20, 12, 9, 7, 0, 5,$

$3, 6, 27, 21, 19, 15, 20, 24, 2, 16, 14, 8, 23, 24, 10, 14, 3, 8, 11, 2$

Present the data in the form of frequency distribution table by taking class interval of $0-5, 5-10, 10-15, 15-20, 20-25$.

 Fine (Rs.) Tally $f$$f$ (no of students) $0-5$$0-5$ ${\mid \mid }$${\mid \mid }$ $7$$7$ $5-10$$5-10$ $10$$10$ $10-15$$10-15$ ${\mid \mid \mid }$${\mid \mid \mid }$ $8$$8$ $15-20$$15-20$ ${\mid }$${\mid }$ $6$$6$ $20-25$$20-25$ ${\mid \mid \mid }$${\mid \mid \mid }$ $8$$8$ $25-30$$25-30$ ${\mid }$${\mid }$ $1$$1$

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Question 7: The weight in kg of 30 students are given below:

$48, 55, 30, 43, 41, 36, 48, 37, 34,,38, 46, 42, 38, 52, 37,$

$34, 40, 42, 50, 37, 35, 46, 42, 45, 43, 37, 39, 45, 48, 46$

For the group frequency table by taking class intervals $30-35, 35-40, 40-45, 45-50, 50-55$.

 Weight (kgs) Tally $f$$f$ (no of students) $30-35$$30-35$ ${\mid \mid \mid }$${\mid \mid \mid }$ $3$$3$ $35-40$$35-40$ ${\mid \mid \mid \mid}$${\mid \mid \mid \mid}$ $9$$9$ $40-45$$40-45$ ${\mid \mid }$${\mid \mid }$ $7$$7$ $45-50$$45-50$ ${\mid \mid \mid }$${\mid \mid \mid }$ $8$$8$ $50-55$$50-55$ ${\mid \mid \mid }$${\mid \mid \mid }$ $3$$3$

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Question 8: The daily income in Rs of $30$ workers is given below:

$83, 96, 91, 80, 97, 111, 90, 83, 112, 120, 103, 77, 82, 90, 70,$

$68, 89, 85, 78, 105, 94, 97, 90, 89, 102, 113, 90, 106, 70, 84$

Construct a frequency table using groups $65-75, 75-85, 85-95, 95-105, 105-115, 115-125$.

 Class Interval Tally $f$$f$ $65-75$$65-75$ ${\mid \mid \mid }$${\mid \mid \mid }$ $3$$3$ $75-85$$75-85$ ${\mid \mid }$${\mid \mid }$ $7$$7$ $85-95$$85-95$ ${\mid \mid \mid \mid}$${\mid \mid \mid \mid}$ $9$$9$ $95-10$$95-10$ $5$$5$ $105-115$$105-115$ $5$$5$ $115-125$$115-125$ ${\mid }$${\mid }$ $1$$1$

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Question 9: The heights of 45 students measured to the nearest centimeter are given below:

$155, 166, 159, 161, 158, 154, 153, 159, 157, 152, 160, 157, 158, 170,$

$152, 151, 162, 164, 171, 154, 165, 161, 150, 168, 162, 154, 160, 170, 163, 164,$

$165, 169, 165, 155, 157, 158, 160, 161, 156, 153, 150, 165, 167, 169, 172$

Prepare a frequency table taking class intervals $150-155, 155-160, 160-165, 165-170, 170-175$

 Class Interval Tally $f$$f$ $150-155$$150-155$ $10$$10$ $155-160$$155-160$ ${\mid }$${\mid }$ $11$$11$ $160-165$$160-165$ ${\mid }$${\mid }$ $11$$11$ $165-170$$165-170$ ${\mid \mid \mid \mid}$${\mid \mid \mid \mid}$ $9$$9$ $170-175$$170-175$ ${\mid \mid \mid \mid}$${\mid \mid \mid \mid}$ $4$$4$

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Question 10: Complete the table

 Class Interval Class Limit Class Size Class Mark Class Boundaries Lower Upper Lower Upper 25-30 30-35 35-40 40-45

 Class Interval Class Limit Class Size Class Mark Class Boundaries Lower Upper Lower Upper 25-30 $25$$25$ $30$$30$ $5$$5$ $27.5$$27.5$ $25$$25$ $30$$30$ 30-35 $30$$30$ $35$$35$ $5$$5$ $32.5$$32.5$ $30$$30$ $35$$35$ 35-40 $35$$35$ $40$$40$ $5$$5$ $37.5$$37.5$ $35$$35$ $40$$40$ 40-45 $40$$40$ $45$$45$ $5$$5$ $42.5$$42.5$ $40$$40$ $45$$45$

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Question 11: Complete the table

 Class Interval Class Limit Class Size Class Mark Class Boundaries Lower Upper Lower Upper 26-30 31-35 36-40 41-45

 Class Interval Class Limit Class Size Class Mark Class Boundaries Lower Upper Lower Upper 26-30 $26$$26$ $30$$30$ $5$$5$ $28$$28$ $25.5$$25.5$ $30.5$$30.5$ 31-35 $31$$31$ $35$$35$ $5$$5$ $33$$33$ $30.5$$30.5$ $35.5$$35.5$ 36-40 $36$$36$ $40$$40$ $5$$5$ $38$$38$ $35.5$$35.5$ $40.5$$40.5$ 41-45 $41$$41$ $45$$45$ $5$$5$ $43$$43$ $40.5$$40.5$ $45.5$$45.5$