chapter 11 14

145

Teachers’ Manual On Formative Assessment Constructions

CHAPTER-11Constructions

Suggested questions for oral assessment

1. Is it possible to construct a triangle with sides 3 cm, 4 cm and 8 cm ?

2. What are the instruments to be used in performing constructions ?

3. When do you say that a line is the perpendiculat bisector of another line ?

4. What is perimeter of a figure ? What is the perimeter of a given ∆ ABC.

5. What is the sum of the angles of a ∆

6. The exterior angle of a ∆ is equal to sum of the _____________________.

Learning Objective –

• To acquire the knowledge of basic requisites to construct a triangle

• To develop the skill of constructing a triangle with given conditions

Task–1 Oral Assessment

Topic Constructioins

Nature of Task Content

Content Coverage Basic Constructioins

Learning Objective • To acquire the knowledge of basic requisitesto construct a triangle

Execution of task Teacher may ask questions based on LearningObjectives

Note : Must provide an opportunity to everystudent to respond and to improve their response.

Duration 2 Periods

Criteria for assessment Students can be evaluated on the basis of theirreadiness to respond, correct response, attitude toimprove their response etc.

146

Constructions Teachers’ Manual On Formative Assessment

Suggestive Home Assignments Constructions

1. Which of the following angles can be made with the help of a ruler and compass :

35º, 40º, 57º, 75º

2. Draw a ∆ ABC, in which AB = 4 cm, ∠ A = 60º and BC – AC =115 cm.

3. Draw a ∆ ABC in which BC = 5 cm, ∠ B = 60º and AC + AB =7.5 cm.

4. Draw an equalateral ∆ whose altitude is 6 cm.

5. Draw a triangle ABC whose perimeter is 10.4 cm and the base angles are 45º and 60º.

Task–2 Home Assignment

Topic Construction

Nature of Task Post Content

Content Coverage Basic Constructioins

Learning Objective • To develop the skill of constructing a trianglewith given conditions

Execution of Task Teacher can give a home assignment containingquestions on construction covering all types ofconditions to draw a triangle

Duration Two days to complete the home assignement

Criteria for Assessment Students can be evaluated on neatness, accuracyin work and for timely submission of work

Teachers’ Manual On Formative Assessment Heron’s Formula

147

CHAPTER-12Heron’s Formula

Task-1: Multiple Choice Questions

Topic Heron’s Formula

Learning Objective • To find the area of triangle when the sides oftriangle are given.

• To find the area of quadrilateral by dividing theminto two triangle.

Nature of Task Content Oriented

Content Coverage –

Description of Task Multiple Choice Questions based on Heron’s formula

To find the area of triangle and the area of other figureslike trapezium etc. (Where the Trapezium can be dividedinto two triangles).

Execution of Task Student can be given a 15 minutes Multiple ChoiceQuestion paper based on above leaving objective.

Assessment of Task One mark for correct answer and zero for incorrectanswer.

Follow up All questions shall be discussed in class after theassessment.

Multiple Choice Questions

1. The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is

A. 12 cm2 B. 15 cm2 C. 6 cm2 D. 9cm2

2. The area of ∆ ABC is

A. 20 cm2 B. 4 5 cm2 C. 2 5 cm2 D. 10 cm2

3. The area of a triangular sign board of sides 5 cm, 12 cm and 13 cm is

A.65

2 cm2 B. 30 cm2 C. 60 cm2 D. 12 cm2

B C

A

4 cm

3cm3

cm

148

Heron’s Formula Teachers’ Manual On Formative Assessment

CD

AB

4 cm

4cm

3 cm

5cm

5cm

CD

A B40 m

28 m

15m9

m

D

B C

A

17cm

12

cm15

cm

9cm

4. The side of a triangle are in the ratio of 25 : 14 : 12 and its perimeter is 510 m. The greatestside of the triangle is

A. 120 m B. 170 m C. 250 m D. 270 m

5. The perimeter of a right triangle is 60 cm and its hypotenuse is 26 cm. The other two sidesof the triangle are

A. 24 cm, 10 cm B. 25 cm, 9 cm C. 20 cm,14 cm D. 26 cm, 8 cm2

6. The area of quadrilateral ABCD in the adjoining figure is

A. 15.2 cm2 B. 14.8 cm2 C. 15 cm2 D. 16.4 cm2

7. The area of trapezium in the adjoining figure is

A. 286 m2 B. 306 m2 C. 316 m2 D. 296 m2

8. The area of quadrilateral ABCD in the adjoining figure is

A. 57 cm2 B. 95 cm2 C. 102 cm2 D. 114 cm2


149

Task-2: Oral Questions

Topic Heron’s Formula

Learning Objective To check the knowledge of basic concepts required forfinding the area of triangle

Nature of task Pre-Content

Description of Task Students can be asked questions orally individually.

Execution of Task Students may be asked one by one. If the child is notable to respond, another chance can be given either bychanging the question or by giving some hint.

Assessment of Task Students can be graded for number of correct responses.

Follow up If any student is not able to respond at first instance, he/she may be given another opportunity i.e. give a days ortwo time to prepare again and appear for oral assessmenttest separately.

ORAL QUESTION

1. What is a scalene triangle ?

2. What is the name given to a ∆ whose two sides are equal ? Whose all the side are equal ?

3. Area of a triangle = 1

2 base × _______________.

4. Whent the sum of the squares of the lengths of two sides of a ∆ is equal to the square ofthe length of the third side, is is called a ___________triangle.

5. State the Heron's formula for the area of a triangle ?

6. What is the semi-perimeter of a triangle ?

7. Area of a rectangle = length × ___________.

8. Perimeter of a rectangle = 2 (__________+ __________).

9. Area of a rhombus = 1

2(one diagonal) × (_____________).

10. The area of a parallelogram = (base) × (__________).

11. Area of a trapezium = 1

2(__________) × Altitude

12. Area of an equilateral triangle with sides of length x cm = 3

4× __________.

150


A

C

D

B7 cm

12 cm

6cm

15

cm

9

Home Assignments

1. Find the area of a ∆ whose sides are 35 cm, 45 cm and 50 cm

2. An isosceles triangle has perimeter 30 cm and each of its equal sides is 12 cm. Find its area

(Use 15 = 3.88)

3. The me asure of one side of a right triangular field is 4.2 m. If the difference of the lengthsof hypotenuse and the other is 14m, find the sides of the triangle and its area.

4. Find the area of the quadrilateral ABCD given in the figure alongside.

5. The perimeter of a rhombus is 40 cm. If one of its diagonal is 16 cm, find the area of therhombus.

6. Two parallel sides of a irapezium are 60 cm and 77 cm and the other sides are 25 cm and26 cm. Find the area of the trapezium.

Task-3: Home AssignmentTopic Heron’s Formula

Learning Objective • To apply the Heron’s formula to the problem oftriangle and quadrilateral.

• To develop the skill of finding areas.

Nature of task Post-Content

Description of Task Students are required to complete Home Assignment inscheduled time.

Execution of Task Students may be given home assignment sheet containing8–10 questions. Some questions may be incorporated tohelp the students to follow the steps in systematic manneror with hints. These questions will in absence benefit ofstudents while working independently and without anypeer help or teachers’ guidance (for example Q.9, 10,11 suggested in worksheet).

Assessment of Task Students will be assessed for punctuality, presentation andaccuracy. They shall be appreciated even if they comeand discuss the problems with teachers before submissionof assignment.


151

7. Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠ BAD = 90º and B, C and

D from an equilateral ∆ of side 26 cm [use 3 1.73]

8. The height of an equilateral triangle measures 9 cm. Find its area, correct to two places of

decimals [Take 3 = 1.73]

9. Area of triangle - by Heron's formula Practice Worksheet Remember.

Step 1. Semiperimeter of ∆ ABC, s = 2

a b c+ +

Step 2. area (∆ ABC) = ( )( )( )s s a s b s c− − −

1. Find the area of a triangle lengths of whose sides are 8 cm, 11 cm and 13 cm.

Sol. Step. 1. a = 8 cmb = 11 cmc = 13 cm

CB

A

c b

a

s = 2

a b c+ + =

Step. 2. s – a = ____________________

s – b = ____________________

s – c = ____________________

s(s – a)(s – b)(s – c) = ____________________

area = ( )( )( )s s a s b s c− − −

= ____________________ cm2

10. Find the area of a triangle length of whose two sides are 18 cm and 10 cm and the perimeteris 42 cm.

Sol. Hint : Length third side = Perimeter – (sum of lengths of two given sides)

Step. 1. Find the lengths of 3rd side

152


Step. 2. s = 2

a b c+ +

Step. 3. area (triangle) = ( )( )( )s s a s b s c− − − sq units.

11. The lenghts of sides of a triangular plot are in the ratio of 12 : 17 : 25 and its perimeter is540 cm. Find its area.

Sol. Hint : Let dimensions be a = 12 xb = 17 xc = 25 x

Now find s = 2

a b c+ +

then area using the Heron's formula

Note : Area of a quadrilateral, lengths of whose sides and one diagonal are given, can becalculated by dividing the quadrilateral into two triangles and using the Heron's formula.

12. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallelsides are 14 m and 13 m. Find the area of the field.


153

Sol.

A B

D C

154

Surface Areas & Volumes Teachers’ Manual On Formative Assessment

CHAPTER-13Surface Areas & Volumes

Task-1: Worksheet

Topic Surface Areas and Volumes



Learning Objective • To be able to find out the total surface areaof cube, cuboid, cylinder, cone, sphere.

• To differentiate the curved surface area fromtotal surface area.

• To identify the kind of area requiredaccording to the problem.

• To be able to find out the volume of cube,cuboid, cylinder, cone, sphere.

Execution of Task Worksheet can be distributed to each student.Class can be divided into groups each containing4 to 5 students. Let them discuss, brain storm andsolve the problems.

Duration 2 Consecutive Periods

Criteria for Assessment Teacher can observe each group to see that everychild is taking interest and is participating. Everygroup is making effort to solve the problem.Students can be assessed on attributes of thinking,social and emotional skills.

Follow up Discuss response of each group and appreciatethe students for their enthusiasm, involvement andother remarkable behaviours noticed.

155

Teachers’ Manual On Formative Assessment Surface Areas & Volumes

Suggestive Multiple Choice Questions

[Use 22

=7

π unless otherwise stated]

1. If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area is

A. 82 cm2 B. 123 cm2 C. 164 cm2 D. 216 cm2

2. The volume of the cuboid in Q.1 is

A. 17 cm3 B. 164 cm3 C. 120 cm3 D. 240 cm3

3. The surface area of a cuboid is 1372 sq. cm. If its dimensions are in the ratio of 4 : 2 : 1,then its length is

A. 7 cm B. 14 cm C. 21 cm D. 28cm

4. The base radius and height of a right circular cylinder are 7 cm and 13.5 cm. The volume ofcylinder is

A. 1579 cm3 B. 1897 cm3 C. 2079 cm3 D. 2197 cm3

Task-2: MCQ Worksheet




Learning Objective • To be able to find out the total surface areaof cube, cuboid, cylinder, cone, sphere.

• To differentiate the curved surface area fromtotal surface area.

• To identify the kind of area requiredaccording to the problem.

• To be able to find out the volume of cube,cuboid, cylinder, cone, sphere.

Execution of Task 30 Minutes time can be allotted to conduct MCQ.Teacher can take round to see that every studentis doing calculations in rough and not simplyguessing.

Duration 2 Periods

Criteria for Assessment 2 marks for correct response and no marks forincorrect response.

Follow up Discuss the answers after checking the MCQ andgive home assignment for more drill.

156


5. The base radius of a cone is 5 cm and its height is 12 cm. Its slant height is

A. 13 cm B. 19.5 cm C. 26 cm D. 52cm

6. The curred surface area of a cylinder of height 14 cm is 88 sq. cm. The diameter of thecylinder is

A. 0.5 cm B. 1.0 cm C. 1.5 cm D. 2.0 cm

7. The lateral surface area of a right circular cone of height 28 cm and base radius 21 cm is

A. 1155 cm2 B. 1055 cm2 C. 2110 cm2 D. 2310 cm2

8. The circumference of the base of a 8 m high conical tent is 264

7m2. The area of canvas

required to make the tent is

A.1360

7cm2 B.

1360

14cm2 C. 286 cm2 D. 98 cm2

9. The area of metal sheet required to make a closed hollow cone of height 24 m and base radius7 m is

A. 176 m2 B. 352 m2 C. 704 m2 D. 1408 m2

10. The diameter of a sphere whose surface area is 346.5 cm2 is

A. 5.25 cm B. 5.75 cm C. 11.5 cm D. 10.5 cm

11. The radius of a spherical baloon increases from 7 cm to 14 cm when air is pumped into it.The ratio of the surface area of original baloon to inflated one is

A. 1 : 2 B. 1 : 3 C. 1 : 4 D. 4 : 3

12. The circumference of the base of a cylinderical vessel is 132 cm and its height is 25 cm. If1000 cu.cm = 1 liter, the number of litres, of water the vessel can hold is

A. 17.325 B. 34.65 C. 34.5 D. 69.30

13. The number of litres of milk a hemispherical bowl of radius 10.5 cm can hold is

A. 2.47 B. 2.476 C. 2.376 D. 3.476

14. The number of bricks, each measuring 18 cm × 12 cm × 10 cm are required to build a 1

wall 12 m × 0.6 m × 4.5 m if 1

10 of its volume is taken by mortar, is

A. 15000 B. 13500 C. 12500 D. 13900

15. The radius of a sphere is 10 cm. If its radius is increased by 1 cm, the volume of the sphereis increased by

A. 13.3% B. 21.1% C. 30% D. 33.1%

157


Home Assignment1. The dimensions of a prayer Hall are 20 m × 15 m × 8 m. Find the cost of painting its walls

@ Rs. 10 per sq. m.

2. Find the curved surface area of a right circular cylinder whose height is 13.5 cm and radiusof its base is 7 cm. Find also its total surface area.

3. The exterior diameter of an iron pipe is 25 cm and it is one cm thick. Find the whole surfacearea of the pipe it it is 21 cm long.

4. A roller 150 cm long has a diameter of 70 cm. To level a playground it takes 750 completerevolutions. Determine the cost of levelling the playground at the rate of 75 paise per sq. metre.

5. Find the total surface area of a cone, it its slant height is 21 m and the diameter of its baseis 24 m.

6. The volume of a sphere is 4851 cm3. How much should its radius be reduced so that it volume

becomes 4312

3cm3.

7. A river, 3 m deep and 40 m wide, is flowing at the rate of 2 km/hour. How much water willfall into the sea in a minute ?

8. Find the capacity, in litres, of a conical vessel whose diameter is 14 cm and slant height is25 cm.

9. What is the total surface area of a hemisphere of base radius 7 cm?

10. A village having a population of 4000, requires 150 litres of water per head per day. It hasa tank measuring 20 m × 15 m × 6 m. For how many days, the water of the tank will besufficient for the village ?

Task-3: Home Assignment



Content Coverage Complete Chapter

Learning Objective To apply the knowledge gained in ‘Surface Areaand Volumes’ in solving the question.

Execution of Task For extra practise of content taught, homeassignment can be given after the completion ofChapter.

Duration 2 to 3 days

Criteria for Assessment Follow CW / HW assignment rubric

Follow up Class Discussion. Answers to the questions maybe discussed in class room and individual queriesmay be answered.

158


Task-4: Oral Assessment

Topic Surface Area and Volumes


Learning Objective • To be able to tell the formulae, units fordifferent types of solids.

• To calculate the same mentally for simpleproblems.

• To recognise the need of finding curvedsurface area, total surface area or volumeafter reading the word problems.

Execution of Task Teacher can prepare the slips of questions basedon above LO’s AND PUT THEM IN BASKET.Students can be called one by one and must readthe question loudly and respond to it. If he/she isnot able to respond next child can be called. Thesestudents may get the chance in the end or insomebody’s turn, followed by a small completethe table for students requiring more practice.

Duration 1 Period

Criteria for Assessment 1 marks for correct response and no marks forincorrect response.

Suggestive Oral Questions–Volume and Surface Areas

1. The volume of a cuboid of dimensions l, l and h is ____________ unit3.

2. The surface area of a cube of side x is _________________.

3. The surface area of a cuboid of dimensions l, b, h is _________________.

4. The volume of a right circular cylinder of base radius r and height h is ___________.

5. The radius of base of a cylinder is 7 cm and its volume is 770 cm2. The height of the cylinderis ________________.

6. Total surface area of cylinder is _______________ cm2.

7. The height of a right circular cone is 3.5 cm and its base radius is 5 cm. Its volume is____________________ cm3.

8. The formula for volume of a right circular cone is ___________________.

9. If the base radius of a cone is 8 cm and height is 6 cm, then its slant height is _________cm.

159


10. The formula for the total surface area of a right circular cone of base radius r height h andslant height l is __________________.

11. The volume of a sphere of radius r is ___________ and its surface area is __________.

12. The total surface area of a hemisphere of radius r is ______________.

Task-5: Formulae Testing

Name of Student : _______________________________ Task List of formulae

Class/Sec. : _____________________________________ Duration 10 minutes

Roll No. : ______________________________________ Max-Marks 10

Date : _________________________________________ Marks obtaned____________

Complete the Following Table

Shape Dimensions C.S.A. T.S.A Volume

Cube Side a units a3

Cuboid length breadthl b 2( )lb + bh + lh

Right Circular rad of base = r 2p rh p r2h

Cylinder height = h

Right Circular rad of base = r

Cone height = h p r l + r( )

slant height l

Sphere rad = r 4p r2 4p r2

Hemisphere rad = r 32

3p r

(solid)

160

Statistics Teachers’ Manual On Formative Assessment

CHAPTER-14Statistics

Task-1: Newspaper ActivityTopic Statistics

Nature of Task Warm-up / Pre-content

Content Coverage Introduction of Statistics

Learning Objective To recall the meaning of the term statistics and the needof collection of data, survey and statistical analysis.

Task Group Discussion

Execution of Task Teacher can discuss some situational examples where thesurvey and statistical analysis is required e.g. census,impact of its analysis on planning, market surveyconducted by companies to enhance their sales or toimprove the quality of products.

Teacher can distribute few magazines or newspapers tothe students and ask them to identify atleast one situationby each student where the data collection is required.

Duration 1 Period

Criteria for Assessment No grading or marking is required in this case. The taskis to gear up the students for study of statistics.

Follow up Teacher must motivate the students to identify such situations.

Task-2: Worksheet-1Topic Statistics


Content Coverage Collection of data, Presentation of data, GraphicalRepresentation of Data

Learning Objective To develop the skill of representing data graphically asbargraph histogram of uniform width, histogram of varyingwidth, frequency polygon.

Execution of Task Teacher may give a 30 minutes worksheet to assess theskills developed by the students to draw the appropriategraph of given data and the basic conceptual knowledge.

Duration 1 Period

Criteria for Assessment According to the weightage of the marks the assessmentwill be done.

Follow up Teacher must discuss the worksheet in the class specially,the incorrect responses in order to modify everyone’sunderstanding. More problems of the same kind may begiven as home assignment.

161

Teachers’ Manual On Formative Assessment Statistics

Worksheet-1

Time : 15 Minutes

1. The marks of 30 students in a Mathematics Test are given below :

62, 29, 36, 41, 52, 21, 50, 75, 78, 16, 20, 35, 46, 24, 57, 65, 82, 16, 25, 30, 42, 24,18, 32, 36, 57, 75, 16, 30, 58

(i) Arrange these marks in a grouped distibution, where one of the groups is 35-45.

(ii) How many students have scored below 55 ?

(iii ) How many have scored above 75 ?

(iv) Write the class-size of the distribution.

Bar graph of the production of rice crop in India in different years.

Read the bar graph and answer the following questions.

(i) What was the crop-production in 1980-81 ?

(ii) In which year, the crop-production was maximum ?

(iii ) Write the difference between maximum and minimum production.

2. Draw a histogram to represent the following data

C.I. 10-15 15-20 20-25 25-60 30-35

Frequency 5 6 9 8 2

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

1950-51 1960-61 1970-71 1980-81 1990-91

Pro

duct

ion

of R

ice

(in l

akh

tonn

es)

Year

162


Task-3: Worksheet-2Topic Statistics


Content Coverage Measure of Central Tendency

Learning Objective To learn about measure of central tendency i.e. mean,median, mode for raw/discrete data and to apply theknowledge in solving the problems.

Execution of Task Teacher may give a 30 minutes worksheet to assess theskills developed by the students to draw the appropriategraph of given data and the basic conceptual knowledge.

Duration 1 Period

Criteria for Assessment According to the weightage of the marks the assessmentwill be done.

Follow up After checking the sheets a formula reference sheet alongwith problems can be given to students to give them morepractice.

Worksheet-2Time : 15 Minutes

1. If mean of 8 observations is 25, find the sum of all observations.

2. Complete the table.

x f f × x

6 4 ___

12 ___ 36

___ 8 72

8 7 ___

10 ___ 20

___ 6 66

f∑ = f x∑ =

Now, find the mean of this data.

3. Find the median of following observations

7, 4, 2, 5, 1, 4, 0, 10, 3, 8.

163


Follow up: Pratice Worksheet

1. Find the true class limits of the first two classes of the distibution 1–9, 10–19, 20–29, ..........

2. The following are the marks obtained by 20 students in a class-test :40, 22, 36, 27, 30, 12, 15, 20, 25, 31, 34, 36, 39, 41, 43, 48, 46, 36, 37, 40

Arrange the above data in frequency distribution with equal classes, one of them being (0–10),10 not included.

3. The electricity bills of twenty house holds in a locality are as follows :

370, 410, 520, 270, 810, 715, 1080, 712, 802, 775, 310, 375, 412, 420, 370, 218, 240,250, 610, 570 Construct a frequency distribution table with class size 100.

4. The enrolment in classes VI to X of a school is given below :

Class : VI VII VIII IX XEnrolment : 70 65 60 45 35

Draw a bar chart to depiet the data.

5. Draw a histogram and a frequency polygon for the following dats :

Marks 10-20 20-30 30-40 40-50 50-60No. of students 8 12 15 9 6

6. Draw a histogram for the following data :

Classes 10-15 15-20 20-30 30-50 50-80Frequency 6 10 10 8 18

7. Find the mean of the following data :

153, 140, 148, 150, 154, 142, 146, 147

8. The mean of the following data is 37. Find x

28, 35, 25, 32, x, 40, 45, 50

9. If the mean of n observation 2x1, 2x

2, ........, 2x

n is 2x , show that

1

( 2 ) 0n

ii

x x=

− =∑

10. The mean of 20 observations is 25. If each observation is multiplied by 2, then find the meanof new observations.

11. The means of two groups of 15 and 20 observations are 20 and 25 respectively. Find themean of all the 35 observations.

12. If the mode of the following data is 14, find the value of x

10, 12, 14, 15, 16, 14, 15, 14, 15, x, 16, 14, 16

13. The median of the observations, arranged in increasing order is 26. Find the value of x.

10, 17, 22, x + 2, x + 4, 30, 36, 40

164


Task-4: Remedial Worksheet

I. Formulae Reference Sheet

1. For Raw Data Mean, Sumof allobservations

Totalnumber of observationsx =

2. For Ungrouped Frequency Distribution

Mean = 1

1

n

i ii

n

ii

f x

f

−

−

∑

∑

3. Median : (The value of the middle-most observations)

Two cases

If n is odd If n is even

Median = value of Median = mean of value of

1

2

thn+

observations & 1

2 2

th thn n +

observations

4. Mode : It is the most frequently occurring observation.

II. Practice Questions

Q.1. The heights (in cm) of 9 students of a class are as follows :

155 160 145 149 150 147 152 144 148Find the median of the data.

Sol. Step 1. Arrange the given observations in ascending order.

144 145 147 148 149 150 152 155 160Since n = 9 is odd

∴ Median = Value of 12

thn +

observations

= Value of 9 1

2

th+

observations

= Value of 5th observation= 149

Median height = 149 cm.

165


Q.2. In a mathematics test 15 students appeared. Their marks (out of 100) are recorded as under :

41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60

Find theomedian marks.

Sol. Step 1. Arrange the given data in descending / ascending order

Step 2. n = __________________ (odd)

Step 3. Median = Value of 1

2

thn+

observation

= _________________________________________________

= _________________________________________________

= _________________________________________________

Q.3. The following observations have been arranged in ascending order. If the median of the datais 63, find the value of x.29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Sol. Step 1. Observations are already arranged in ascending order

Step 2. Note that the number of observations is even (n = 10)

Step 3. Use formula for even case

Step 3. Median = Value of 1

&2 2

th thn n+

observation

⇒ 63 =th th5 observations + 6 observations

2

⇒ 63 = _________________________________________________

= _________________________________________________

= _________________________________________________

166


Task-5: MCQ WorksheetTopic Statistics

Nature of task Post Content

Content Coverage All Concepts Learn in Statistics

Learning Objective To evaluate the understanding of all the concepts learntin the chapter and the skill to apply them.

Execution of Task Teacher may give a 15 minutes MCQ worksheet to thestudents.

Duration 1 Period

Criteria for Assessment For each correct response 1 mark to be awarded andfor incorrect response no marks.

Follow up After checking the sheets questions can be discussed andanother opportunity in the form of oral assessment canbe given in order to improve the response. Oralassessment to be done individually.

MCQ Worksheet

1. The range of the data 14, 27, 29, 61, 45, 15, 9, 18 is

A. 61 B. 52 C. 47 D. 53

2. The class mark of the class 120-150 is

A. 120 B. 130 C. 135 D. 150

3. The class mark of a class is 10 and its class width is 6. The lower limit of the class is

A. 5 B. 7 C. 8 D. 10

4. In a frequency distribution, the class-width is 4 and the lower limit of first class is 10. If thereare six classes, the upper limit of last class is

A. 22 B. 26 C. 30 D. 34

5. The class marks of a distribution are 15, 20, 25, ......., 45. The class corresponding to 45 is

A. 12.5 – 17.5 B. 22.5 – 27.5 C. 42.5 – 47.5 D. None of these

6. The number of students in which two classes are equal.

A. VI and VIII B. VI and VII C. VII and VIII D. None

0

10

20

30

40

50

VI VIIVIIClasses

No

.o

fst

ud

ens

167


7. The mean of first five prime numbers is

A. 5.0 B. 4.5 C. 5.6 D. 6.5

8. The mean of first ten multiples of 7 is

A. 35.0 B. 36.5 C. 38.5 D. 39.2

9. The mean of x + 3, x – 2, x + 5, x + 7 and x + 72 is

A. x + 5 B. x + 2 C. x + 3 D. x + 7

10. If the mean of n observations x1, x

2, x

3, .......... , x

n is x then

1

n

il

x x−

−∑ is

A. 1 B. –1 C. zero D. can not be found

11. The mean of 10 observation is 42. If each observation in the data is decreased by 12, the newmean of the data is

A. 12 B. 15 C. 30 D. 54

12. The the mean of 10 numbers is 15 and that of another 20 number is 24 then the mean of all30 observations is

A. 20 B. 15 C. 21 D. 24

13. The median of 10, 12, 14, 16, 18, 20 is

A. 12 B. 14 C. 15 D. 16

14. If the median of 12, 13, 16, x + 2, x + 4, 28, 30, 32 is 23, when x + 2, x + 4 lie between16 and 30, then the value of x is

A. 18 B. 19 C. 20 D. 22

15. If the mode of 12, 16, 19, 16, x, 12, 16, 19, 12 is 16, then the value of x is

A. 12 B. 16 C. 19 D. 18

16. The mean of the following data is

xi 5 10 15 20 25fi 3 5 8 3 1

A. 12 B. 13 C. 13.5 D. 13.6

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Follow up : Oral Assessment Sheet

1. The mid-point of a class is called _________________.

2. Data collected by the experimenter himself is called _______________ data.

3. The difference between maximum and minimum observations in the data is called________________.

4. Cumulative frequency of a class is the sum total of all frequencies ___________ that class.

5. Are the class-limits and true class limits different? If yes, explain the difference.

6. The sum total of all observations divided by their number is called _________ of the data.

7. The mode of a group of observations is that value of the variable which has _________ frequency.

8. The ___________ is the middle most observation in the data, when they are arranged inincreasing / decreasing order.

9. x , the mean of n observation x1, x

2, ........, x , is given by __________.

10. The mean of first ten natural numbers is ______________.

11. The median of first 9 natural numbers is ___________.

12. If each observation in the data is increased by ‘a’, then their ______ is also increased by ‘a’.

13. The sum of deviations of the data (observations) from the mean is _____________.

chapter 11 14

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