Class 8: Statistics – Exercise 38(A) – ICSE / ISC / CBSE Mathematics Portal for K12 Students

Question 1: Arrange the following data in ascending order:

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

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

Answer:

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

Answer:

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

Answer:

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

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

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

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

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

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

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

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

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

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

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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 $0-10, 10-20, 20-30, 30-40, 40-50$

Answer:

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

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

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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 $0-5, 5-10, 10-15, 15-20, 20-25$ .

Answer:

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

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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 $30-35, 35-40, 40-45, 45-50, 50-55$ .

Answer:

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

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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 $65-75, 75-85, 85-95, 95-105, 105-115, 115-125$ .

Answer:

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

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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 $150-155, 155-160, 160-165, 165-170, 170-175$

Answer:

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

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Question 10: Complete the table

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

Answer:

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

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Question 11: Complete the table

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

Answer:

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