Data Handling

Mean/Average of given observations is obtained by adding up all the numbers and dividing the result with the number of observations.

In this problem, the observations are x, y, z and the number of observations are 3.

So mean =

The mode is the number that is repeated more often than any other. We see that 33 is repeated 3 times, which is more number of times than any other number. Hence the answer is 33.

Mean is defined as the average of the given observations.

Where a₁, a₂, a₃…a_n are data points, n being the number of data points. If a₁ and a_n are removed, the mean becomes,

Which is clearly different than the previously obtained mean.

If it so happens that either a1 or an is the most repeated in the data, then removing the data points also alters the mode.

But since median is the midpoint, removing the end points does not affect in any way. So the correct answer is Mean and Mode.

Range is given by the difference between the largest value of the data and smallest value of the data.

The largest value is 21.

The smallest value is 4.

Hence the range is 21- 4 = 17

Median is the middle number in a ascending ordered data.

Arrange the numbers in ascending order.

3, 3, 4, [4], 5, 6, 7

We see that the middle number is 4.

Hence the median is 4.

Mode is the number that is repeated more often than any other. So if a boy is going to purchase the brand which is most liked by children, mode would be the measure of central tendency.

Given that there are two aces in all the four scenarios. In set C, we see that there are only two cards while the others have more than two. We have two aces, two cards so it is certain that the cards in set C are both aces. Hence there is a 100% probability of picking two aces from option C.

P(Ace) =

=

Hence, the correct option is B.

Range is given by the difference between the largest value of the data and smallest value of the data.

Let E = Event in which a student picked at random makes it to the competition

P(E) =

%(E) = = 40%

Range is given by the difference between the largest value of the data and smallest value of the data.

The largest number is +20

The smallest number is -17

Range = +20 – (-17) = 20+17 = 37

On tossing a coin, there is an equal chance for getting a head or a tail.

Let the three numbers be a, b and c.

According to the problem, a = 19

And

Or

Which gives 19+b+c = 120

So b+c = 101

Consider b = 100, which gives c = 1 which is not possible because the lowest number allowed is 19.

Consider b = 40 which gives c = 61

Consider b = 71, which gives c = 30

Consider b = 81, which gives c = 20

Among these b = 81 is the highest number.
Therefore, the correct answer is 81.

Average =

Average in first three examinations =

Average in first four examinations =

We see that the average has decreased by 86-84.5 = 1.5.

Mode is the most repeated data.

Arranging all the sets A, B, C, D in ascending order

A. 1, 2, 3, 4, 4, 5, 6

Mean = Median = 4, Mode = 4

So Mean ≠ Median = Mode

B. 1, 2, 2, 2, 3, 3, 4

Mean = Median = 2, Mode = 2

So Mean ≠ Median = Mode

C. 2, 2, 3, 3, 3, 7, 8

Mean = Median = 3, Mode = 3

So Mean ≠ Median = Mode

D. 3, 3, 4, 4, 4, 4, 6

Mean = Median = 4, Mode = 4

So Mean = Median = Mode

So correct option is D.

Range

Range is given by the difference between the largest value of the data and smallest value of the data.

Mean/Average of given observations is obtained by adding up all the numbers and dividing the result with the number of observations.

Mode

The mode is the number that is repeated more often than any other.

Median

Median is the middle most number in an arranged data.

Central Tendency

The tendency for the values of a random variable to cluster round its mean, mode, or median is called Central Tendency.

1

Probability is =

For an event that’s certain to happen P = 1.

0

Probability is =

For an event that’s impossible to happen P = 0.

1

A die has numbers marked from 1 to 6. So any number showing up is less than 7.

Probability is =

There are 6 possible outcomes i.e, 1,2,3,4,5 or 6

There are 6 total outcomes. Hence the probability is

6

When a die is thrown, it can show either 1,2,3,4,5 or 6. Hence the possible outcomes are 6.

Bar graph

A bar graph (as shown in the figure above), is a plot of two dependent quantities usually represented with bars.

Bar graph

A bar graph (as shown in the figure above), is a plot of two dependent quantities usually represented with bars.

3

AM =

5 =

30 = 8 + 4 + x + 6 + 2 + 7

So x = 3

()th and ()th

If a₁, a₂, a₃…a_n are n data points, its median always lies between the ()th and ()th data points.

Odd

Suppose a₁, a₂, a₃…a_n are n data points. If n is odd, then the median is the th data point. If n is even then the data point doesn’t exist in the observations but is calculated manually.

52-55kg

Clearly, the number of students in the 52-55kg interval is more than any other interval. So the probability is also more.

False

A die has markings of 1 to 6 on its faces. It is impossible to get a number greater than 6. So the probability is 0.

True

When a coin is tossed, there are two possible outcomes i.e., heads or tails.

False

Median is the middle number in an observation set. If each of the extreme ends of data points are removed the median does not get affected.

False

The measures of central tendency – mean, median and mode always lie between the maximum and minimum values of the data.

True

The maximum marking on a die is 6. So if two dice are thrown the maximum possible outcome will be 6 on each die, which sums up to 12. It is impossible to get any sum greater than 12.

True

Probability is =

Number of possible outcomes = 2 (shaded regions)

Total outcomes = 4

So P =

False

Total number of outcomes = 15

Number of heads = 7

Probability is =

=

= 46.66%

True

Consider this example

3, 3, 4, 4, 4, 4, 6

Mean = Median = 4, Mode = 4

So Mean = Median = Mode

False

Any probability is never greater than 1.

True

Mean = , which is entirely dependent on given data.

True

If the number of data points is even, then median is the sum of the two middle data points.

True

Mode is the most repeated data point.

False

Mean of the observations is less than some observations not all.

False

Consider this data 1,2,5,4,7 The mean is which is a fraction.

True

Range is the difference between the largest and smallest data point.

False

A data set has no mode if all the data points appear only once. Although each of them can be considered as a mode, mathematically the data has no mode.

False

Range for the original data = 7-(-5) = 12.

The new data would be 2-2, -5-2, 4-2, 3-2, 7-2, 6-2.

i.e., 0, -7, 2, 1, 5, 4.

The new range would be 5-(-7) = 12

So the range will not change.

False

Range for the original data = 7-(-5) = 12.

The new data would be 3+8, 7+8, 1+8, -2+8, 2+8, 6+8, -3+8, -5+8

i.e., 11, 15, 9, 6, 10, 14, 5, 3.

The new range would be 15-(3) = 12

So the range will not change.

Mean = 10, Median = 10, Mode = 10,

Yes they are equal.

Mean = ,

=

Median = Middle number = 10

Mode = Most repeated number = 10

So Mean = Median = Mode

Formula used/Theory.

Sum of even natural numbers = n(n + 1)

Mean =

Sum of 10 even numbers.

10(10 + 1) = 10×11 = 110

Mean = = 11

⇒ Mode of the data is item which has maximum frequency in the data

∴ here if we have height of 50 children

Then mode is the height of which maximum children have in the data

(A) As we can see in grouped data

The car which is maximum sold is of Black colour

If we asked for the colour of car which is most liked then the car that was sold the most will be the answer

Hence;

Black colour is liked most

(B) in the above part of colour which is mostly liked

is the maximum frequency of an item

∴ Mode was used

a) Range = highest marks–lowest marks

= 42–17

= 25

b) Mean =

Sum of values = 31 + 37 + 35 + 38 + 42 + 23 + 17 + 18 + 35 + 5 + 35 + 29

= 345

Number of values = 12

Mean = = 28.75

c) Median

1^st arrange data in ascending order

17, 18, 23, 25, 29, 31, 35, 35, 35, 37, 38, 42

For even number of terms

Median = mean of and term

Median = mean of 6^th and 7^th term

= = 33

d) Mode

It is the marks which is obtained by maximum students

Mode = 35 (Comes for 3 students)

(A) Mean =

Sum of weights = 70 + 62 + 54 + 57 + 62 + 84 + 75 + 59 + 62 + 65 + 78 + 60

= 788

Number of people = 12

Mean = = 65.66

(B) Mean weight = 65.66

People above mean weight are 70, 75, 78, 84

4 peoples are above mean weight

(C) Range = Highest weight – Lowest weight

Highest weight = 84

Lowest weight = 54

= 84 – 54 = 30

(A) a vowel

As the cards are A,E,I,O,U

And all 5 are vowels

Probability =

=

= 1

Means if a card is pulled out it will surely be a vowel

∴ 100% chances are there to get a vowel

(B) The cards pulled out are A or I

Possible outcomes = 2

Total number of outcomes = 5

Probability =

=

= 0.4

∴ It is 40% chances that card will be A or E

(C) The card pulled out is U

Possible outcome = 1

Total number of outcomes = 5

Probability =

=

= 0.2

∴ it is 20% chances of card pulled out to be U

(D) The card pulled out id consonant

As all card are vowels

Possible outcome = 0

Total number of outcomes = 5

Probability =

=

= 0

∴ it is 0% chances of card pulled out to be a consonant

Data is 6, 2, 5, 4, 3, 4, 4, 2, 3

For median

Arrange the values in ascending order

⇒ 2,2,3,3,4,4,4,5,6

Median of odd number of terms is term

Where n is number of terms

Median = = 5^th term

5^th term = 4

For Mode

The value that’s repeats maximum in data

Mode = 4

Mean = = 4

Mean =

Sum of terms = 5 + 7 + 7 + 8 + x + 5 + 4 + 3 + 1 + 2

= 42 + x

Number of terms = 10

Mean = 4.5 =

42 + x = 4.5×10 = 45

x = 45 – 42 = 3

For median

Arrange terms in ascending order

1, 2, 3, 3, 4, 5, 5, 7, 7, 8

Median = mean of and terms

Median = Mean of 5 and 6^th term

Median = mean of 4 and 5

Median = = 4.5

The probability is 1

As it is universal truth

As in pie chart

Area of red color is area of circle

Area of Blue color is area of circle

Area of Yellow color is area of circle

Probability of red and blue color is

Probability of Yellow color is

Chances of red or blue colour is 25% each

Chances of Yellow color is 50%

∴ Yellow color has more chances to show up with arrow

Number of boys = 4

Number of girls = 3

Total number of student = 4 + 3 = 7

Probability =

Probability of boy =

= = 0.57

Number of D letters in Word MEDIAN = 1

Total number of letters in Word MEDIAN = 6

Probability =

Probability =

= = 0.16

(A) Impossible to happen

As dice have only 6 numbers(1,2,3,4,5,6)

There is no number less than 1 on dice

(B) May or may not happen

A coin has only head or tails as its outcome

(C) May or May not happen

If a team plays either they will win or lose

(D) Certain to happen

It is universal truth as Christmas is on 25^th December

(E) Impossible to happen

As moon revolved around earth is universal truth which cannot be denied

(F) Certain to happen

If ball thrown up in air it will definitely come back to ground due to gravitation force of earth

(A) Mean =

Sum of values = 5 + 3 + 4 + 1 + 2 + 6 + 4 + 2 + 2 + 3 + 1 + 5 + 6 + 1 + 2

= 47

Number of values = 15

Mean = = 3.13

(B) Median

1^st arrange data in ascending order

1,1,1,2,2,2,2,3,3,4,4,5,5,6,6

For odd number of terms

Median = term

Median = 8^th term

= 3

(C) Mode

It is the marks which is obtained by maximum students

Mode = 2 (Comes for 4 times)

First 6 multiples of 4 means

4,8,12,16,20,24

Mean =

Sum = 4 + 8 + 12 + 16 + 20 + 24

= 84

Number of terms = 6

Mean = = 14

1^st 9 even natural numbers are

2,4,6,8,10,12,14,16,18

As they are arranged in ascending order

Median of odd number terms term

Median = 5^th term

= 10

Mean of 3 numbers is 10

Sum of 3 numbers = Mean×3

Sum of 3 numbers = 30

Mean of other 4 numbers is 12

Sum of other 4 numbers = Mean×4

Sum of other 4 numbers = 48

Sum of all 7 numbers = 30 + 48 = 78

Mean of all 7 numbers =

= = 11.14

Mode = the value which is repeated maximum times

Given data: 10, 8, 4, 7, 8, 11, 15, 8, 4, 2, 3, 6, 8

Mode = 8

(A) As in given data

Maximum height among 15 boys

Is 154cm

∴ the tallest boy is 154cm long

(B) As in given data

Minimum height among 15 boys

Is 128cm

∴ the shortest boy is 128 cm long

(C) Range = Highest height – lowest height

= 154cm – 128cm

= 26cm

(D) For median 1^st arrange data in ascending order

128,129,136,138,140,140,142,142,143,144,144,146,

150,152,154

Median for odd number of terms is

Median = 8^th term

Median = 142

(A) Mode = the term which is repeated maximum in data

The given data is

16, 15, 16, 16, 8, 15, 17

As the mode is 16 ∵ (it is repeated 6 times in data)

∴ Adding 16 to data mode will remain the same

(B) as 15 is 2 times in the data

we need to add 15 in data 2 times

So that 15 become most repeated term(4 times)

(C) As 17 is only 1 times in data

We need to add 3 more !7 in the data to make mode of the data to be 17

Mode = it is the most repeated term in the given sat of data

Range = Highest – lowest

(A) For Group A

Mode = 7 and 10 years ∵ (Both repeated twice)

Range = Highest – lowest

= 10-7 = 3 years

For Group B

Mode = 12 years ∵ (repeated 3 times)

Range = Highest – lowest

= 12 – 7 = 5 years

(B) If both groups are joined

The data will be

7,7,7,8,9,9,10,10,11,12,12,12

Mode = 12 and 7 years ∵ (Both repeated thrice)

Range = Highest – Lowest

= 12 – 7

= 5 years

(A) This graph depicts the production of motor bikes in different months by company XYZ automobile Ltd

(B) Motor bikes produce in 1^st 3 months

Is Motor bikes produce in January, February, March

= 600 + 800 + 700

= 2100

(C) Production in may = 900

Production in January = 600

∴ Increase in production = 900-600 = 300

(D) In June the production is minimum

The production was 500

(E) Mean =

Sum of production = 600 + 800 + 700 + 1100 + 900 + 500

= 4600

Number of months = 6

Mean = = 766.66

(A) 4 students have failed

As they got marks from 30-39

(B) Students of 50-59 marks are 7

Students of 60-69 marks are 11

∴ students got 50-69 marks are 7 + 11

= 18

(C) 4 student scores 90 and above

As there 4 students having 90-99 marks

(D) Students of 80-89 marks are 6

Students of 90-99 marks are 4

∴ students got 80 marks and above marks are 6 + 4

= 10

(E) Strength of class = number of students

= 42

(A) The graph represent the production of rice in each year by our country

(B) In 2006 there is minimum production of rice

As there are only 40 million tones in 2006

(C) After 2006 there is maximum rise in production

In 2006 is lowest productivity whereas 2007 has highest production

(D) Mean =

Sum of production = 50 + 40 + 70 + 50 + 60

= 270 million tons

Mean = = 54Million tones

(E) Production in 2006 = 40 million tones

Production in 2008 = 50 million tones

Difference in production = (50-40) = 10 million tones

(A) This graph depicts the marks obtain by student in all subjects out of 100

(B) In Maths the student is very good

As We can see he scores maximum marks 89 out of 100 as compare to all others subject

(C) Mean =

Sum of marks = 64 + 75 + 82 + 71 + 49

= 341

Average marks of students =

= 68.2

(D) If 75 and above marks are called distinction then

Student got distinction in only 2 subjects

Hindi and Maths

In Hindi he scores 75

And in maths he scores 82

(E) Percentage =

Sum of marks got by student = 341

Maximum marks of 5 subject = 5× 100

= 500

∵ Subject marks are out f 100

Percentage =

= 68.2 %

(A) In Hindi = 800

In Punjabi = 400

In Urdu = 200

In Marathi = 300

In Tamil = 100

Total number of newspaper read out in these 5 language

Is 800 + 400 + 200 + 300 + 100

= 1800

(B) Hindi newspaper = 800

English newspaper = 500

Difference = 800-500

= 300

300 more Hindi newspaper read out than English newspaper

(C) The Tamil newspaper is read out to be least

Because there are only 100 newspaper in town

(D) Total number of circulation of newspaper

800 + 500 + 400 + 200 + 300 + 100

2300

2300 newspaper are circulated in town

(A) In class VIII The sports which is mostly liked is cricket

∵ the bar of class VIII is maximum among all

(B) In class VII

Students like hockey = 7

Students like Tennis = 10

Total number of students in hockey and tennis

Is 17

(C) Class VII students

Are sum of students in each sports

7 + 16 + 18 + 10 + 14

= 65

∴ there are 65 students in class VIII

(D) It is only in cricket

∵ The bar of class VIII is longer as compared to class VII

(E) Students of class VIII are less than class VII in 4 sports

Hockey, Football, Tennis, Badminton

(F) students who like Badminton in Class VII = 14

students who like Tennis in Class VIII = 7

14:7

2:1

(A) this graph represent Sales of brand A and B in different months in lakhs

(B) In march Brand A sale gets decreased

As sales in March = 30 lakhs

Sales in February = 34 lakhs

(C) In June

Sales of Brand A = 57

Sales of brand B = 54

Difference in sales of both brand = 57-54

= 3 Lakhs

(D) Average =

Total sales of Brand B = 36 + 38 + 43 + 35 + 45 + 54

= 251

Number of months = 6

Average =

= 41.83 lakhs

(E) In month of April and June sale of brand B is less than sales of brand A

∵ In both months bar of Brand A is larger than bar of Brand B

(F) in January

Sales of brand A = 31 lakhs

Sales of brand B = 36 lakhs

Ratio = 31:36

(A) This graph depicts the minimum temperature in different months of 2 years 2008 and 2009

(B) In month of November

Minimum temperature in 2008 = 18°C

Minimum temperature in 2009 = 15°C

Ratio = 18:15

= 6:5

(C) In 2 months the minimum temperature in year 2008 greater than that of year 2009

Those months are February and November

∵ Bar of 2008 is greater than bar of 2009 in both months

(D) Average minimum temperature of 2008 is

Sum of min temp of 2008 = 12 + 4 + 11 + 18

= 45

Average =

= 11.25°C

(E) In February the variation of temperature is maximum

As

Temp in 2008 = 12

Temp in 2009 = 8

Variation = 12-8

= 4°C

(A) This graph depicts the number of boys and girls in each section of class VII

(B) Number of boys in class VII A = 15

Number of boys in class VII B = 30

Number of boys in class VII C = 20

Number of boys in class VII D = 20

Number of boys in class VII E = 25

Total number of boys = 15 + 30 + 20 + 20 + 25

= 110

(C) In section A and D number of girls are greater than number of boys

∵ in both sections bar of girls is larger than bar of boys

(D) In section B number of boys is maximum

there are 30 boys in B section

(E) In section C number of girls is least

there are only 15 girls in C section

(A)

(B) Readers of library is maximum on Thursday

As

Magazine + newspaper reader = 550 + 300

= 850

Which is maximum among all days

(C) Mean number on magazine readers =

Total number of magazine readers

Is 100 + 150 + 200 + 200 + 250 + 300

= 1200

Mean = = 200

(A)

This graph depicts the total number of students and among them how many are present in each class

(B) Class VIII has maximum number of students

∵ there are total 95 students in the class which is maximum among all classes

(C) It is minimum in X class

As there is only one student absent

(63-62)

(D) in class IX

Total number of students = 70

Total number of present students = 65

Ratio

70:65 = 13:14

(E) In class VI

Total number of students = 90

Total number of present students = 81

Absent students = 90-81 = 9

Percentage of absent student is

Percentage of absent student is

= 10%

(A)

(B) The sale is maximum on Saturday

∵ 60 mobile set are sold which is maximum among al days

(C) Min sale = 27(Friday)

Max sale = 60(Saturday)

Ratio = 27:60

= 9:20

(D) Average sale of week =

Total number of sales

Is 50 + 45 + 30 + 55 + 27 + 60

= 267

Mean = = 44.5

(E) On 4 days the sale was above average sale

On Monday, Tuesday, Thursday, Saturday

(A)

(B) Average height of 1 storey =

Sum of all 3 heights of each storey

= 4.15 + 4.15 + 3.93 = 12.23

Average = = 4.076

(C) the city with maximum skyscrapers is Mumbai

Percentage =

Percentage = = 90%

(D) Range = Maximum height – lowest height

= 249m-156

= 93m

(E) For median arrange heights in ascending order

156,170,170,170,180,181,184,193,249,249

Median of even number terms is mean of and term

Median of even number terms is mean of 5^thand 6^th term

Median = mean of 180 and 181

Median = = 180.5

(A)

(B) Total marks of Soni = 86 + 89 + 90 + 82 + 75 + 82

= 504

Percentage of Soni =

Percentage of Soni =

= 84%

(C) Total marks of Kunal = 72 + 81 + 92 + 96 + 64 + 85

= 490

Percentage of Soni =

Percentage of Soni =

= 81.66%

(D) Percentage of Soni = 84%

Percentage of Kunal = 81.66%

∴ Soni has got 3.33% more marks

(E) There are 3 subjects in which Soni got more marks than Kunal

Subjects are English, Hindi, S. Science

(F) Soni got more marks in S. Science

Difference = 75-64 = 11 marks

(G) Difference of marks of Kunal and Soni is minimum in maths

Difference = 92-90 = 2 marks

Kunal got 2 more marks than soni

(A)

(B) Students in class VII = total number of boys + girls

Number of boys = 12 + 16 + 8 + 17 + 11 + 30

= 94

Number of girls = 15 + 24 + 10 + 19 + 27 + 21

= 116

Total number of students in class VII = 116 + 94

= 210

(C) Most preferred club by boys is electronics

They have maximum strength of 30 boys in it

(D) Least preferred club by girls is Yoga

They have minimum strength of only 10 girls in it

(E) Yoga and dramatics is the club where difference of boys and girls is least

Number of boys in yoga = 8

Number of girls in yoga = 10

Difference = 10-8 = 2

Number of boys in Dramatics = 17

Number of girls in Dramatics = 19

Difference = 19-17 = 2

(F) Fine arts is the club where difference of boys and girls is Maximum

Number of boys in Fine arts = 11

Number of girls in Fine arts = 27

Difference = 27-11 = 16

(A)

(B) Total number of bikes produced in 2008

2700 + 3200 + 6000 + 5000 + 4200

= 21100

Total number of bikes produced in 2007

2800 + 4500 + 4800 + 4800 + 5200

= 22100

In 2007 total output is more than in 2008

(C) Mean production of 2007 =

Mean production in 2007 = = 3683.33

(D) In august the production difference is maximum

Difference = 6000-4800

= 1200

(E) In august of 2008 the production is maximum

6000 motor bikes are produced

(F) in February of 2007 the production was least

2800 motor bikes are produced

(A)

(B) In Town D the growth of population is maximum

Growth = 6300-4600 = 1700

(C) In Town A the growth of population is least

Growth = 3200-2900 = 300

(A)

(B) In 2008 maximum number of tourists arrived on Mussoorie

There were 5800 tourist

(C) In 2009 Least number of tourist arrived al Manali

There were only 4200 tourist

(D) 5 hill station got increase in number of tourist in 2009

Those are Nainital, Shimla, Manali, Mussoorie, Kullu

(A)

(B) Butterscotch is most liked by the boys

13 boys of society like Butterscotch

(C) Sum of Girls = 8 + 12 + 7 + 9 + 10

= 46

There are 46 girls in society

(D) Boys likes chocolate flavour ice-cream are 9

Girls likes chocolate flavour ice-cream are 12

Total children likes chocolate flavour = 12 + 9 = 21

(E) Children likes Strawberry flavour are 3 + 7 = 10

Children likes Vanilla Flavour are 4 + 8 = 12

Ratio = 10:12

= 5:6