Data Handling Test

Result

Data Handling Test - 10

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Question 1

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Directions: Study the given table and answer the following question.

The table shows the population of towns A, B and C in different years:

Years	Town A	Town B	Town C
2011	14,000	45,050	36,540
2012	15,600	46,850	35,980
2013	18,900	47,650	36,000
2014	23,500	50,500	36,500
2015	25,600	51,500	37,000

Which town has the minimum average population over the given years?

A

B

C

All three towns have the same average population.

Solution

Average population of town A over all the years

=
= 97,600 ÷ 5

= 19,520

Average population of town B over all the years

=

= = 48,310

Average population of town C over all the years

=

= = 36,404

So, town A has the minimum average population over the given years.

Question 2

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Directions: Study the given table and answer the following question.

The table shows the population of towns A, B and C in different years:

Years	Town A	Town B	Town C
2011	14,000	45,050	36,540
2012	15,600	46,850	35,980
2013	18,900	47,650	36,000
2014	23,500	50,500	36,500
2015	25,600	51,500	37,000

What is the difference between the total population of all three towns in 2012 and that in 2015?

20,620

17,690

16,540

15,670

Solution

Total population of all three towns in 2012

= 15,600 + 46,850 + 35,980 = 98,430

Total population of all three towns in 2015

= 25,600 + 51,500 + 37,000 = 1,14,100

So, the required difference

= 1,14,100 - 98,430 = 15,670

Question 3
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The weights (in kg) of 12 employees in a company are:

87, 58, 96, 74, 56, 57, 67, 68, 49, 88, 82, 70

(a) What is the mean weight of the employees?
(b) How many employees weigh less than the mean weight?

A
70 kg; 10

B
71 kg; 7

C
73 kg; 8

D
74 kg; 9

Solution

Mean weight =

=

= kg

(b) Weights less than the mean weight (71 kg):
58, 56, 57, 67, 68, 49, 70
So, 7 employees weigh less than the mean weight.
Question 4
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Find the mode and median of the following observations:

13, 19, 32, 31, 29, 21, 51, 14, 53, 29, 42, 71

A
Mode = 51, Median = 29

B
Mode = 29, Median = 51

C
Mode = 29, Median = 30

D
Mode = 31, Median = 14

Solution

In the given data, 29 occurs the highest number of times.

So, Mode = 29

To find the median, the numbers need to be arranged in ascending order:

13, 14, 19, 21, 29, 29, 31, 32, 42, 51, 53, 71

Total terms = 12

Since the number of terms is even, therefore the median is the average of the ()^th and the ()^th term.

term= 6^th term = 29

(6 + 1)^thterm = 7^thterm = 31

Average = = 30

So, Median = 30
Question 5
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The mean of 13 observations was found to be 41. Later on, it was detected that an observation 111 was misread as 11. Now, the correct mean of the observations would be

A
48.7

B
51.2

C
60.3

D
65.8

Solution

Incorrect mean = 41

Incorrect sum of 13 observations = (41 × 13) = 533

Now, 111 was written as 11.

Correct sum of 13 observations = 533 - 11 + 111 = 633

Correct mean = = 48.69 = 48.7
Question 6
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If the average of 9, 15, 18, 16, a and 25 is 18, then find the value of a.

A
25

B
27

C
31

D
15

Solution

Average = 18

So,

83 + a =

a = 108 - 83

a = 25

Question 7

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Find the mode(s) of the following data:

Size	1	21	8	17	4	6	16
Frequency	15	51	16	67	98	98	51

1

17 Both 21 and 16

Both 4 and 6

Solution

Mode is the observation which has the highest frequency.

According to the given data, each of 4 and 6 has a frequency of 98, which is the highest.

So, option 4 is the answer.

Question 8
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The average height of 7 students is 75 cm. When one student is excluded, the average height of remaining students becomes 72.5. Find the height of the excluded student.

A
70 cm

B
90 cm

C
80 cm

D
100 cm

Solution

Average height of 7 students = 75 cm

So, the sum of the heights of 7 students = 75 × 7 = 525

Average after one student is excluded = 72.5 cm

Total height of 6 students = 72.5 × 6 = 435 cm

So, height of the excluded student = 525 - 435 = 90 cm
Question 9
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Find the median of the given numbers:

101, 87, 96, 105, 36, 78, 47, 96, 65, 68, 38, 115, 116, 158

A
85.7

B
91.5

C
101.2

D
105.6

Solution

Numbers written in ascending order:

36, 38, 47, 65, 68, 78, 87, 96, 96, 101, 105, 115, 116, 158

Number of terms = 14, which is even

So, median would be the average of the ()^th and the ()^th term, i.e. 7^thand 8^th terms.

7^thterm = 87

8^th term = 96

So, average = = 91.5

Median = 91.5
Question 10
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Directions: Study the given data and answer the following question.

The given bar graph shows the number of students with different favourite subjects:

What is the total number of students who have English as their favourite subject and Science as their favourite subject?

A
9

B
8

C
10

D
11

Solution

Number of students who have English as favourite subject = 4

Number of students who have Science as favourite subject = 7

Total number of students = 4 + 7 = 11
Question 11
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Directions: Study the given data and answer the following question.

The given bar graph shows the number of students with different favourite subjects:

Which subject is the favourite of the highest number of students?

A
Science

B
Maths

C
English

D
Arts

Solution

Science is the favourite subject of 7 students, which is the highest.
Question 12
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Directions: Study the given data and answer the following question.

The given bar graph shows the number of students with different favourite subjects:

What is the average of number of students who have Maths as their favourite subject and English as their favourite subject?

A
5

B
6

C
7

D
8

Solution

Number of students with Maths as their favourite subject = 6

Number of students with English as their favourite subject = 4

Average == 5
Question 13
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Directions: Study the given data and answer the following question.

The given bar graph shows the number of students with different favourite subjects:

What is the ratio of the number of students who have Arts as their favourite subject to the number of students who have Maths as their favourite subject?

A
7 : 4

B
4 : 7

C
2 : 1

D
1 : 2

Solution

Number of students who have Maths as their favourite subject = 6

Number of students who have Arts as their favourite subject = 3

So, required ratio = 3 : 6 = 1 : 2
Question 14
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Directions: Study the given data and answer the following question.

The given bar graph shows the number of girls and boys who play different sports:

Which sport is played by the highest number of girls?

A
Tennis

B
Basketball

C
Soccer

D
Can't say

Solution

Number of girls who play basketball = 45

Number of girls who play tennis = 20

Number of girls who play soccer = 50

Soccer is played by 50 girls, which is the highest.
Question 15
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Which of the following statements is correct?

A
Median of data may or may not be from the given data.

B
Mean of data is always from the given data.

C
Mean, median and mode are always the same for given data.

D
Mean of data can't be from the given data.

Solution

Statement 1: Median of data may or may not be from the given data. This is correct.

For example, for an even number of terms, we have to find the average of the two middle terms in the given data.
Data: 13, 12, 11, 10
So, median = Average of 12 and 11 = 11.5, which is not present in the data

For an odd number of terms, the median is the middle term in the data.

Data: 13, 12, 12, 11, 10

So, median = Middle term = 12, which is present in the data

Statement 2: Mean of data is always from the given data. This is false.
For example: 13, 18, 13, 14, 13, 16, 14, 21, 13

Mean = (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15, which is not present in the data.

Statement 3: Mean, median and mode are always same for given data. This is false.
The median is the middle value: 13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5^th term
13, 13, 13, 13, 14, 14, 16, 18, 21
So, median = 14

Mode is the term that is repeated more often than any other, so 13 is the mode.

It can be seen that all the values are different.

Statement 4: Mean of data can't be from the given data. This is false.
13, 18, 13, 14, 13, 16, 14, 21, 22
Mean = (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 22) ÷ 9 = 16, which is present in the data.
Mean of data is the average and it can or cannot take a value from the given data.
Question 16
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The choices of 49 students in a class for the categories of games they like are as follows:

A, R, S, P, D, R, S, P, A, R, D, S, P, A, P, S, P, D, R, R, S, A, D, A, P, S, R, A, S, R, P, A, D, R, P, S, P, D, R, A, S, R, P, D, A, A, R, A, D

where A stands for Action games, R stands for Racing games, P stands for Puzzle games, D stands for Dice games and S stands for Strategy games.

Which two categories of games are liked by the same number of students?

A
Action & Racing

B
Racing & Puzzle

C
Action & Puzzle

D
None of the above

Solution

Number of students who like Action games = 11

A, R, S, P, D, R, S, P, A, R, D, S, P, A, P, S, P, D, R, R, S, A, D, A, P, S, R, A, S, R, P, A, D, R, P, S, P, D, R, A, S, R, P, D, A, A, R, A, D

Number of students who like Racing games = 11

A, R, S, P, D, R, S, P, A, R, D, S, P, A, P, S, P, D, R, R, S, A, D, A, P, S, R, A, S, R, P, A, D, R, P, S, P, D, R, A, S, R, P, D, A, A, R, A, D

Number of students who like Puzzle games = 10

A, R, S, P, D, R, S, P, A, R, D, S, P, A, P, S, P, D, R, R, S, A, D, A, P, S, R, A, S, R, P, A, D, R, P, S, P, D, R, A, S, R, P, D, A, A, R, A, D

Number of students who like Dice games = 8

A, R, S, P, D, R, S, P, A, R, D, S, P, A, P, S, P, D, R, R, S, A, D, A, P, S, R, A, S, R, P, A, D, R, P, S, P, D, R, A, S, R, P, D, A, A, R, A, D

Number of students who like Strategy games = 9

A, R, S, P, D, R, S, P, A, R, D, S, P, A, P, S, P, D, R, R, S, A, D, A, P, S, R, A, S, R, P, A, D, R, P, S, P, D, R, A, S, R, P, D, A, A, R, A, D

Therefore, Action games and Racing games are liked by the same number of students.

Question 17

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Rahul collected the data regarding the ages of different students in his school and prepared the following table:

Ages (Years)	Number of students
0-5	20
5-10	25
10-15	30
15-20	28

A student is to be selected randomly from his school for annual athletic meet. The probability of selection is the highest for students in the age group ________ years.

10 - 15

0 - 5

5 - 10

15 - 20

Solution

The probability of selection is the highest for students in the age group 10 - 15 years because there are more students in this group than any other.

Question 18
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Shelly has five balls, numbered 2, 5, 6, 7 and 8. She makes a random two-digit number with them. What is the probability that the number made is odd?

A

B

C

D

Solution

Total two-digit numbers that can be formed with the given digits (2, 5, 6, 7 and 8) are:

22, 25, 26, 27, 28, 52, 55, 56, 57, 58, 62, 65, 66, 67, 68, 72, 75, 76, 77, 78, 82, 85, 86, 87, 88

Odd numbers among them are:

25, 27, 55, 57, 65, 67, 75, 77, 85, 87.

So, required probability =

=
Question 19
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A pack consists of candies of four different colours, viz. blue, pink, green and yellow. The probability of selecting a blue candy is , that of selecting a pink candy is and that of selecting a green candy is . What is the probability of selecting a yellow candy from the packet?

A

B

C

D

Solution

Probability of selecting a blue candy + Probability of selecting a pink candy + Probability of selecting a green candy + Probability of selecting a yellow candy = 1

Probability of selecting a yellow candy = 1 - ()

=

=

=
Question 20
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Rahul rolls two dice simultaneously. Each dice has faces numbered 7, 8, 9, 10, 11 and 12. Upon rolling, what is the probability that the numbers appearing on the top faces add up to 15?

A

B

C

D

Solution

Total number of possible outcomes for the first die = 6

Total number of possible outcomes for the second die = 6

So, total number of possible outcomes = 6 × 6 = 36

Now, for the numbers on the top faces to add up to 15, there are two cases:

First - 7, Second - 8

or

First - 8, Second - 7

So, required probability = =
Question 21
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The graph shown below gives the number of female employees which left the organization in five different years. What is the ratio of the females that left the organization in 1997 to total number of females that have left.

A
1 : 11

B
1 : 10

C
1 : 9

D
1 : 8

Solution

Number of females that left the organization in 1997 = 10

Number of females that left in total in 5 years = 15 + 20 + 10 + 25 + 20 = 90

So the required ratio = 10 : 90

= 1 : 9
Question 22
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The heights (in cm) of 7 students in a particular class are:

132, 121, 142, 123, 121, 131, 140

Which of the following options contains the three values for the data in ascending order?

A
Mode < Median < Mean

B
Median < Mean < Mode

C
Mode < Mean < Median

D
Mean < Mode < Median

Solution

Arrangement of heights (in cm) of 7 students in ascending order is:

121, 121, 123, 131, 132, 140, 142

Sum of heights of all students = 910

Mean = = = 130

Now, number of students is 7 (odd).

Therefore, median = ()^thterm = 4^thterm = 131
Also, 121 appears more times than any other number.

Therefore, mode = 121

Hence, Mode < Mean < Median.
Question 23
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Directions For Questions

Directions: In a school the tests are held every month. From April 2010 to December 2010, a student of class VIII appeared for each of the monthly tests. The aggregate marks obtained by him in each test is represented in the line-graph given below. Study the graph and answer the given question.
Marks obtained by a student in monthly tests held from April 2010 to December 2010.
Maximum aggregate marks in a monthly test = 150

...view full instructions

What is the average of marks scored in monthly tests from July to December?

A
121

B
120

C
117

D
116

Solution

Average marks obtained from July to December = = 120
Question 24
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Directions: Study the given data and answer the following question.

The given bar graph shows marks scored by students from class VIII to class XII in an Olympiad test.

Boys from which class scored more marks than the average marks scored by the girls from all the classes?

A
X

B
IX

C
VIII

D
XI

Solution

Average marks scored by girls from all classes = = = 74
Marks scored by boys from class VIII = 90

Clearly, boys from class VIII scored more marks than the average marks scored by the girls from all the classes.
Question 25
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Directions: Study the given data and answer the following question.

The given bar graph shows the number of candidates applying to different colleges:

What is the difference between the average number of boys and average number of girls who applied to the five colleges?

A
150

B
400

C
300

D
280

Solution

Average number of boys = = 3100

Average number of girls = = 2800

Therefore, required difference = 3100 - 2800 = 300