Data Handling

The height of a rectangle in a histogram shows the number of time the particular observation occurred in the data that is frequency.

Hence, the height of a rectangle in a histogram shows the Frequency of the class.

A pie chart is a circular statistical graphic which is divided into slices to illustrate numerical proportion. The circle is taken as a whole and the slices are its part.

Hence, a geometric representation showing the relationship between a whole and its parts is a Pie chart.

The total angle at the center of the circle is always 360°.

Hence, in a pie chart, the total angle at the center of the circle is 360°.

Range of data = Maximum value in data – Minimum value in data

The maximum value in data is 61

And,

The minimum value in data is 20

⇒ Range of data = 61 – 20

⇒ Range of data = 41

Hence, the range of data is 41

On throwing a stone from a roof of a building we know there is only one output that is the stone will fall down therefore it is not a random experiment.

But for tossing a coin, rolling a dice and choosing a card from a deck of 52 cards have more than one outputs therefore they are random experiments.

Hence, throwing a stone from a roof of a building is not a random experiment.

Total number of vowels = 5

⇒ Total number of favourable outcomes = 5

Total number of alphabets = 26

⇒ Total number of outcomes = 26

Hence, the probability of choosing a vowel from the alphabets is.

Total number of students = 5

⇒ Total number of outcomes = 5

Number of students that can participate = 3

⇒ Number of students that cannot participate = 5 – 3 = 2

⇒ Total number of favourable outcomes = 2

⇒ Probability = 0.4

Hence, the probability of the students who do not make it to the competition is 0.4.

Votes received by Blue = 25%

Votes received by Red = 35%

Votes received by Green = 20%

Votes received by Yellow = 14%

Votes received by Others = 6%

Hence, the color that received votes is yellow.

Total number of votes = 400

Votes received by Others = 6%

Votes received by Others = 6% of 400

Votes received by Others = 24

Hence, students that voted for ‘Others’ colour as their favourite is 24.

Votes received by Red = 35%

Votes received by Green = 20%

Votes received by Yellow = 14%

Votes received by Yellow and Green = 20% + 14%

⇒ Votes received by Yellow and Green = 34%

Hence, Number of students liking together yellow and green colour (i.e., 34%) is approximately the same as those for red colour(i.e., 35%).

Range of data = Maximum value in data – Minimum value in data

The maximum value in data is 5

And,

The minimum value in data is -8

⇒ Range of data = 5 – (-8)

⇒ Range of data = 13

Hence, the range of data is 13°C

Total number of buttons = 4 + 7 + 3 + 6

⇒ Total number of buttons = 20

⇒ Total number of outcomes = 20

Number of blue buttons = 4

⇒ Total number of favourable outcomes = 4

Hence, the probability that the button on the floor is blue is .

In the figure iv, there are 2 equal portions of Red, 2 equal portions of Green and 2 equal portions of Blue, therefore, the game will be fair as each color will have same area.

Hence, figure iv should be used to make the game fair.

First class = 0 – 10

Second class = 10 – 20

Third class = 20 – 30

Fourth class = 30 – 40

Hence, the lower limit of fourth class is 30.

Total number of times coin tossed = 120

⇒ Total number of outcomes = 120

Number of times head appears = 200

⇒ Total number of favourable outcomes = 200

Hence, the probability of getting a head in this experiment is .

We know that,

Central angle of the pie chart = 360°

Buyers interested in buying a particular brand of toothpaste = 40%

Central angle of the sector = 40% of Central angle of the pie chart

⇒ Central angle of the sector = 40% of 360°

⇒ Central angle of the sector = 144°

Hence, the central angle of the sector of the pie chart representing this information is 144°.

We know that,

Central angle of the pie chart = 360°

Central angle of the sector of pie chart = 60°

Monthly salary of a person = Rs 15000

⇒ Amount spent on food and house rent = Rs 2500

Hence, the amount he spends on food and house rent is Rs 2500.

Protein = 16%

Other constituents = 14%

⇒ Protein and other constituents = 16% + 14%

⇒ Protein and other constituents = 30%

⇒ Central angle of sector = 108°

Hence, the central angle of the sector showing the distribution of protein and other constituents is 108°

Total number of cards = 5

⇒ Total number of outcomes = 5

⇒ Number of card with number 2 = 2

⇒ Total number of favourable outcomes = 2

Hence, the probability of the students who do not make it to the competition is .

Ratio of Protein in muscles to Protein in bones = 2: 1

Hence, the ratio of distribution of proteins in the muscles to that of proteins in the bones is 2: 1.

Therefore,

⇒ Central angle of sector with skin and bones = 96°

Hence, central angle of the sector representing skin and bones together is 96°

Therefore,

⇒ Central angle of sector = 144°

Hence, central angle of the sector representing hormones enzymes and other proteins is 144°.

Total number of tosses = 12

⇒ Total number of outcomes = 12

⇒ Number of heads = 5

⇒ Total number of favorable outcomes = 5

Hence, the chance of occurrence of Head is .

Total number of balls = 3 + 5 + 4

⇒ Total number of balls = 12

⇒ Total number of outcomes = 12

Hence, the total number of outcomes is 12.

A double bar graph is a graphical display of information using two bars besides each other at various heights. The bars can be arranged vertically or horizontally. We can use a double bar graph to compare two data groups.

A graph showing two sets of data simultaneously is known as Double bar graph.

Size of a class = Upper Limit – Lower Limit

⇒ Size of a 150 – 175 = 175 – 150

⇒ Size of a 150 – 175 = 25

Hence, the size of the class 150 –175 is 25.

In a dice, there are only 6 numbers that are, 1, 2, 3, 4, 5 and 6.

Therefore, there is no possibility of 7.

Hence, the probability of getting the number 7 is 0.

Pie chart is a type of graph in which a circle is divided into sectors that each represents a proportion of the whole.

Hence, the data represented using circles is known as Pie chart.

Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.

Hence, they are used to find Frequency.

The lower value of class interval (i.e., 75 here) is called lower limit and the upper value of class interval (i.e., 85 here) is called upper limit.

Hence, the upper limit of class interval 75 –85 is 85.

Odd numbers between 1 and 5 are 1, 3 and 5

∴ Total number of odd numbers = 3

⇒ Total number of favourable outcomes = 3

⇒ All Numbers = 5

⇒ Total number of outcomes = 5

Hence, the probability that the slip bears an odd number is

Total number of marbles = 6 + 5 + 4 + 5

⇒ Total number of odd numbers = 20

⇒ Total number of outcomes = 20

⇒ Number of red marbles = 6

⇒ Total number of favourable outcomes = 6

Hence, the probability that the slip bears an odd number is.

When a coin is tossed two times the possible outcomes are

HH – Two heads

HT – First head and second tail

TH – First tail and second tail

HH – Two tails

Therefore,

The sample space is {HH, HT, TH, TT} = 4

Hence, the number of possible outcomes is 4.

When a coin is tossed two times the possible outcomes are HHH, HHT, HTH, THH, HTT, TTH, THT and TTT.

Therefore,

The sample space is {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT} = 8

Hence, the number of possible outcomes is 8.

When a dice is tossed two times,

The sample space is

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} = 36

Hence, the number of possible outcomes is 36.

Raw

Raw data is the data that has not been processed for use.

Hence, Data available in an unorganised form is called Raw data.

20

The lower value of class interval (i.e., 20 here) is called lower limit and the upper value of class interval (i.e., 30 here) is called upper limit.

Hence, the upper limit of class interval 20 – 30 is 30 .

Upper Limit

The lower value of class interval (i.e., 26 here) is called lower limit and the upper value of class interval (i.e., 33 here) is called upper limit.

Hence, in the class interval 26 – 33, 33 is known as Upper Limit.

19

Range of data = Maximum value in data – Minimum value in data

The maximum value in data is 25

And,

The minimum value in data is 6

⇒ Range of data = 25 – 6

⇒ Range of data = 19

Hence, the range of the data 6, 8, 16, 22, 8, 20, 7, 25 is 19.

A part

A pie chart is a circular statistical graphic which is divided into slices to illustrate numerical proportion. The circle is taken as a whole and the slices are its part.

It is a geometric representation showing the relationship between a whole and its parts is a Pie chart.

Hence, a pie chart is used to compare a part to a whole.

head or tail

A coin has only 2 faces head and tail, therefore, while tossing it only one of the two will appear.

Hence, in the experiment of tossing a coin one time, the outcome is either head or tail.

1, 2, 3, 4, 5 and 6

A dice has 6 faces 1, 2, 3, 4, 5 and 6 therefore, while tossing it only one of the six will appear.

Hence, when a dice is rolled, the six possible outcomes are 1, 2, 3, 4, 5 and 6.

Event

An event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

Hence, each outcome or a collection of outcomes in an experiment makes an Event.

Random

An experiment is said to be random if it has more than one possible outcome.

Hence, an experiment whose outcomes cannot be predicted exactly in advance is called a Random experiment.

Size

The size of a class interval is range of the class that is, the difference between the upper and lower limit of a class interval.

Hence, the difference between the upper and lower limit of a class interval is called the size of the class interval.

35 – 40

First interval = 10 – 15

Second interval = 15 – 20

Clearly,

Size of class interval = 5

Therefore,

Third interval = 20 – 25

Fourth interval = 25 – 30

Fifth interval = 30 – 35

Sixth interval = 35 – 40

Hence, the sixth-class interval for a grouped data whose first two class intervals are 10 – 15 and 15 – 20 is 35 – 40.

35

Number of people = 8 + 14 + 5 + 6 + 2

⇒ Number of people = 35

Hence, total number of people surveyed is 35.

8

Number of people owning books more than 60 = 6 + 2

⇒ Number of people owning books more than 60 = 8

Hence, total number of people owning books more than 60 is 8.

22

Number of people owning books less than 40 = 8 + 14

⇒ Number of people owning books less than 40 = 22

Hence, total number of people owning books less than 40 is 22.

14

Number of people owning books more than 20 but less than 40 = 14

Hence, total number of people having books more than 20 and less than 40 is 14.

Frequency

The frequency of an event is the number of times the event occurred in an experiment or study.

Hence, the number of times a particular observation occurs in a given data is called its frequency.

Class Intervals

Class Interval is the size of each class into which a range of a variable is divided.

Hence, when the number of observations is large, the observations are usually organized in groups of equal width called Class Intervals.

Two

When a coin is tossed there are only 2 outcomes head and tail.

Hence, the total number of outcomes when a coin is tossed is 2.

5

The size of a class interval = Upper Limit – Lower Limit

⇒ The size of a class interval = 85 – 80

⇒ The size of a class interval = 5

Hence, class size of the interval 80 – 85 is 5.

bars

These are the histogram bars that have width that is equal to class intervals.

Hence, in a histogram bars are drawn with width equal to a class interval without leaving any gap in between.

likely

When a dice is thrown 1, 2, 3, 4, 5 and 6 have all equal chance of appearance. That is they are equally likely.

Hence, when a dice is thrown, outcomes 1, 2, 3, 4, 5, 6 are equally likely.

X, Y

There are class intervals on the X–axis and frequencies on the Y– axis.

Hence, in a histogram, class intervals and frequencies are taken along x axis and y axis.

20 – 30

Numbers that lie in 10 – 20 are 10, 11, ……, 19

And,

Numbers that lie in 20 – 30 are 20, 21, ……, 29

Hence, in the class intervals 10 – 20 , 20 – 30, etc., respectively, 20 lies in the class 20 – 30.

True

A pie chart is a type of graph in which a circle is divided into sectors that each represents a proportion of the whole.

Hence, the statement is true.

False

The sum of all central angles of a pie chart is 360° just like any circle, therefore the central angle of a sector in a pie chart cannot be more than 360° but it can be more than 180°.

Hence, the statement is false.

True

A pie chart is a circular graph, therefore just like any other circle the sum of all its central angles is 360°.

Hence, the statement is true.

True

The sum of all central angles of a pie chart does not exceed 360°.

∵ 180° + 180° = 360° (i.e., it does not exceed 360°)

Therefore, two central angles can be of 180°.

Hence, the statement is true.

True

Yes in a pie chart, two or more central angles can be equal.

Hence, the statement is true.

True

An event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

Therefore, getting a prime number on throwing a die is an event.

Hence, the statement is true.

True

The frequency of marks 10 is 9

Therefore, 9 students got full (10) marks.

Hence, the statement is true.

False

Frequency of marks 4 = 5

Frequency of marks 5 = 10

Frequency of marks 7 = 8

⇒ Frequency of marks less than 8 = 5 + 10 + 8

⇒ Frequency of marks less than 8 = 23

Therefore, the frequency of less than 8 marks is 23.

Hence, the statement is false.

True

Frequency of marks 9 = 12

Frequency of marks 10 = 9

⇒ Frequency of marks more than 8 = 12 + 9

⇒ Frequency of marks more than 8 = 21

Therefore, the frequency of more than 8 marks is 21.

Hence, the statement is true.

False

Explanation:

Frequency of marks 9 = 12

Frequency of marks 10 = 9

∵ 12 > 9

⇒ Frequency of marks 9 > Frequency of marks 10

Therefore, 9 marks has the highest frequency.

Hence, the statement is false.

False

Explanation:

Fifth class interval = 60 – 65

Fourth class interval = 55 – 60

Third class interval = 50 – 55

Second class interval = 45 – 50

First class interval = 40 – 45

Therefore, the first class interval is 40 – 45.

Hence, the statement is false.

False

Number of literate males in age 20 – 30 = 600

Number of literate males in age 30 – 40 = 800

Number of literate males in age 40 – 50 = 500

⇒ Number of literate males in above age 20 = 600 + 800 + 500

⇒ Number of literate males in above age 20 = 1900

Hence, the statement is false.

True

Class size of a class interval = Upper Limit – Lower Limit

⇒ Class size of the class interval 60 – 68 = 68 – 60

⇒ Class size of the class interval 60 – 68 = 8

Hence, the statement is true.

True

Even numbers on a dice are 2, 4 and 6

∴ Total number of even numbers = 3

⇒ Total number of favourable outcomes = 3

⇒ All Numbers on a dice = 6

⇒ Total number of outcomes = 6

Hence, the statement is true.

False

Composite numbers on a dice are 4 and 6

∴ Total number of even numbers = 2

⇒ Total number of favourable outcomes = 2

⇒ All Numbers on a dice = 6

⇒ Total number of outcomes = 6

Hence, the statement is false.

False

No we cannot infer, from the given pie chart that the production of Manganese is least in state B since we do not know the central angle of the sectors.

Hence, the statement is false.

True

An event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned.

Hence, the statement is true.

False

Favourable outcome is 5

⇒ Total number of favourable outcomes =

⇒ All Numbers on a dice = 6

⇒ Total number of outcomes = 6

The probability of getting 5 is also .

Hence, the statement is false.

False

Prime numbers on a dice are 2, 3 and 5

⇒ Number of prime numbers on a dice = 3

⇒ Number of favourable outcomes for prime numbers = 3

Composite numbers on a dice are 4 and 4

⇒ Number of composite numbers on a dice = 2

⇒ Number of favourable outcomes for composite numbers = 2

Since the number of outcomes differs therefore probability would differ too.

Hence, the statement is false.

True

Even numbers on a dice are 2, 4 and 6

⇒ Number of even numbers on a dice = 3

⇒ Number of favourable outcomes for even numbers = 3

Odd numbers on a dice are 1, 3 and 5

⇒ Number of odd numbers on a dice = 3

⇒ Number of favourable outcomes for odd numbers = 3

Since the number of outcomes is same therefore probability would be same too.

Hence, the statement is true.

False

In Pythagoras theorem, there can be only one result, therefore it is not a random experiment.

Hence, the statement is false.

True

A histogram is a display of statistical information that uses rectangles to show the frequency of data items in successive numerical intervals of equal size.

Yes, it is a histogram.

Hence, the statement is true.

(a) Second class interval is 20 – 30

⇒ Its lower limit = 20

(b) Last class interval is 50 – 60

⇒ Its upper limit = 60

(c) The third class is 30 – 40. Its frequency is 4.

(d) The interval that has a frequency of 10 is 20 – 30.

(e) The lowest frequency is 4 which corresponds to the interval 30 – 40.

(f) Class size = Upper Limit – Lower Limit

⇒ Class size is 10.

The histogram is-

(a) 6% children spend less 1 hour in playing games

Children who spend at least 2 hours = 100% – 6%

Children who spend at least 2 hours = 94%

⇒ No. of children spending atleast 2 hours = 329

(b) 34% children spend 3 hours in playing games

10% children spend 4 hours in playing games

4% children spend 5 hours in playing games

Total no. of children spending more than 2 hours = 34% + 10% + 4%

⇒ Total no. of children spending more than 2 hours = 48%

⇒ No. of children spending more than 2 hours = 168

(c) 6% children spend less than 1 hour in playing games

16% children spend 1 hour in playing games

30% children spend 2 hours in playing games

34% children spend 3 hours in playing games

Total no. of children spending 3 or lesser hours =

6% + 16% + 30% + 34%

⇒ Total no. of children spending 3 or lesser hours = 86%

⇒ No. of children spending 3 or lesser hours = 301

(d) No. of children who spent 2 hours or more = 30% + 34% + 10% + 4%

⇒ No. of children who spent 2 hours or more = 78%

And,

No. of children who spent less than 1 hour = 6%

Clearly,

No. of children who spent 2 hours or more is greater

(a) Since, bus has the highest central angle i.e., 120°

Hence, the most common mode of transport is the bus.

(b)

(c)

⇒ Total no. of Children = 18 × 4

⇒ Total no. of Children = 72

(d) Central angle of students who do not take taxi = 120° + 90° + 60° + 60°

⇒ Central angle of students who do not take taxi = 330°

⇒ Central angle of students who take taxi = 360° – 330°

⇒ Central angle of students who take taxi = 30°

⇒ No. of Children travelling by taxi = 6

(e) Since, the central angle for students travelling by cycle and those who walk is same.

Hence, the two modes of transport are equal number of children travelling are Cycle and Walk.

False

(a) All odd numbers are 1, 3, 5

No. of odd numbers = 3

⇒ Total number of favourable outcomes = 3

⇒ All Numbers on a dice = 6

⇒ Total number of outcomes = 6

(b) Number greater than 5 is 6

No. of numbers greater than 5 = 1

⇒ Total number of favourable outcomes = 1

⇒ All Numbers on a dice = 6

⇒ Total number of outcomes = 6

(c) Multiples of 3 are 3 and 6

No. of Multiples of 3 = 2

⇒ Total number of favourable outcomes = 2

⇒ All Numbers on a dice = 6

⇒ Total number of outcomes = 6

(d) There is no number less than 1

Hence, probability of less than 1 = 0

(e) Factors of 36 are 1, 2, 3, 4 and 6

No. of Factors of 36 = 5

⇒ Total number of favourable outcomes = 5

⇒ All Numbers on a dice = 6

⇒ Total number of outcomes = 6

(f) Factors of 6 are 1, 2, 3 and 6

No. of Factors of 6 = 4

⇒ Total number of favourable outcomes = 4

⇒ All Numbers on a dice = 6

⇒ Total number of outcomes = 6

(a) Since, the sum of angles of a triangle as 180° therefore, it is certain to happen.

(b) The result is unpredictable therefore, it may or may not happen

(c) Since, the sun always sets in the evening therefore, it is certain to happen.

(d) 7 is not an outcome when a dice is thrown therefore it is impossible to happen.

(e) Sun always rises from the east, therefore it is impossible to happen.

(f) The result is unpredictable therefore, it may or may not happen

Percentage of Hindi = 16.67%

⇒ Marks obtained in Hindi = 90.018 ~ 90

⇒ Marks obtained in Hindi = 90

Percentage of English = 25%

⇒ Marks obtained in English = 135

Percentage of Social Science = 5.55%

⇒ Marks obtained in Social Science = 29.97 ~ 30

⇒ Marks obtained in Social Science = 30

Percentage of Mathematics = 33.33%

⇒ Marks obtained in Mathematics = 179.98 ~ 180

⇒ Marks obtained in Mathematics = 180

Percentage of Science = 19.44%

⇒ Marks obtained in Science = 104.98 ~ 105

⇒ Marks obtained in Science = 105

Now,

⇒ No. of yellow balls = 28

(a) Number of students who have height more than or equal to 135 cm but less than 150 cm = 14 + 18 + 10 = 42

(b) Class interval that has the least number of students = 150–155

(c) Class Size = Upper Limit – Lower Limit

⇒ Class Size = 130 – 125

⇒ Class Size = 5

(d) Students that have height less than 140 cm = 6 + 8 + 14 = 28

The histogram is-

The histogram is-

(i) The class that has the least frequency is 25 – 30.

(ii) The class that has the maximum frequency is 35 – 40.

Total no. of shoes = 130 + 120 + 90 + 40 + 20 = 400

Central angle for-

(i)

⇒ Amount spent on roads = 1 crore

(ii)

⇒ Amount spent on education = 2.5 crore

⇒ Amount spent on roads = 1 crore

Now,

⇒ Amount spent on education = 2.5 × Amount spent on roads

(iii)

Total no. of animals = 42 + 15 + 26 + 24 + 13 = 120

Central angle for-

(a) No. of face cards = 1

⇒ No. of favourable outcomes = 1

Total no. of cards = 7

⇒ No. of outcomes = 7

(b) No. of face cards = 4

⇒ No. of favourable outcomes = 4

Total no. of cards = 15

⇒ No. of outcomes = 15

No. of fours = 4

⇒ No. of favourable outcomes = 4

Total no. of cards = 15

⇒ No. of outcomes = 15

(i) Number of classes = 9

(ii) The class that has the highest frequency is 70 – 75.

Total number of persons = 35

The frequency distribution table is given below:

The histogram is given below:

(a) Age group is 10 – 40 year

Therefore, dividing it in 7 classes of equal class intervals are,

10 – 15, 15 – 20, 20 – 25, 25 – 30, 30 – 35, 35 – 40 and 40 – 45

(b) Class Width = Upper Limit – Lower Limit

⇒ Class Width = 15 – 10

⇒ Class Width = 5

(c) Literal females are least in 10 – 15

(d) Literal females are highest in 15 – 20

(a) Answer: From the above histogram, we can say that the 5.

(b) From the diagram, 16 teachers have the maximum teaching experience i.e. of 15 years.

And, 2 teachers have the least experience (< 5 years)

(c) Form the chart,

16 teachers have the experience between 10 years to 20 years.

Total no. of branches = 30 + 17 + 15 + 10 = 72

Central angle for-

Total amount = 43.2 + 16.2 + 27 + 21.6 = 108

Central angle for-

Total no. of periods = 7 + 8 + 8 + 8 + 7 + 4 + 3 = 45

Central angle for-

(i) Coldrinks are liked by maximum number of people, since it has highest percentage.

(ii) Number of people that liked tea = 45

Percentage of people that liked tea = 15%

⇒ Total number of people = 300

Total amount = 40 + 30 + 20 + 10 = 100

Central angle for-

Total no. of events = 8

(i) No. of events of getting a ball = 2

(ii) No. of events of getting a toy car = 3

(iii) No. of events of getting any toy except chocolate = 7

Total no. of events = 10

(i) No. of events of an odd no = 5

(ii) No. of events of Y card = 3

(iii) No. of events of G card = 2

(iv) No. of events of getting B card bearing number > 7 = 7

Total Quantity = 800 + 700 + 550 + 450

⇒ Total Quantity = 2500

Thus, the first symbol has 32%

Thus, the second symbol has 28%

Thus, the third symbol has 22%

Thus, the fourth symbol has 18%

Total Quantity = 192 + 228 + 180

⇒ Total Quantity = 600

Thus, yellow colour is 38%

Thus, red colour is 32%

Thus, pink colour is 30%

Monthly income = 50000

Money Spent-

1. The greatest amount of total is spent in Newspapers.

2. The greatest amount of total is spent in Radio.

3. Total = 40 + 42 + 23 + 7 + 11 + 39 + 14 + 15 + 9 = 200

% Spent in direct mail = 19.5

4. Total = 40 + 42 + 23 + 7 + 11 + 39 + 14 + 15 + 9 = 200

Newspaper + Magazine = 42 + 23 = 65

% Spent in Newspaper and Magazine = 32.5

5. The various media types on which not much amount is spent must be included in Miscellaneous

False

When two coins are tossed the outcomes are,

HH, HT, TH, TT

Therefore, number of outcomes are 4.

Hence, the statement is false.