# Free Data Handling 03 Practice Test - 7th grade

### Question 1

Given below is the table of the marks of 10 students. For getting promoted to section A, a student has to score more marks than the average. Can you tell me from the given options, which student will not be promoted to Section A?

NameMarksNameMarksPavani79Ajit77Goutham81Kushagra73Deepthi68Manish94Pavan85Satyam81Akash62Sarosh80

Pavani

Sarosh

Deepthi

Goutham

#### SOLUTION

Solution :C

We know that,

Average=Sum of all observationsTotal number of observations

Average marks = 79+81+68+85+62+77+73+94+81+8010 = 78010 = 78.Students who scored less marks than the average, won't be promoted to section A. So, from the given options, only Deepthi has lesser marks than 78.

### Question 2

Median is defined as:

the data which is the largest in a data set.

the data which lies in the middle of an organised data set.

same as mean.

the observation that occurs most frequently.

#### SOLUTION

Solution :B

Median is defined as the data which lies in the middle of an organised data set. Median refers to the value which lies in the middle of the data (when arranged in an increasing or decreasing order) with half of the observations above it and the other half below it.

### Question 3

Which of the following is always equal to one of the observations in the data set?

Median

Mode

Both median & mode

Mean

#### SOLUTION

Solution :B

Mean and Range may or may not be equal to any of the observations from the data set. Median is one of the observations if the number of observations is odd. If it's even, median also won't be equal to one of the observations. But mode is always equal to one of the observations.

### Question 4

In the game of ludo, you start your move if you get 6 after throwing the dice for the first time. What is the probability that you will start your move after the first throw?

13

14

15

16

#### SOLUTION

Solution :D

The probability of getting digit '6' (from the digits 1,2,3,4,5,6) after throwing the dice for the first time

=Number of favourable outcomesTotal number of outcomes = 16

Here the total number of outcomes is 6 and the number of favourable outcomes is 1 as the value of '6' is there for one time.

### Question 5

Find the difference between the median and the mode of the following data set:

1 6 45 4 33 12 19 6 56 25 13 9

12.5

12

6.5

6

#### SOLUTION

Solution :C

Arranged data set is:

1 4 6 6 9 12 13 19 25 33 45 56

Median: The middle most value after arranging the given data.

Here, the number of observations is 12, which is an even number. So, we take the average of the two observations in the middle to find the value of median.Median = 12+132 = 12.5. (Mean of the 6th and 7th observation)

Mode: The observation that occurs most often in the data set.

We can find 6 two times in the data set. This is the most repeated value in the data set. The value of the mode is 6.

i.e., Mode = 6.

Difference between median and mode of the given data set = 12.5-6 = 6.5.

### Question 6

What is the probability of getting an ACE from a deck of well-shuffled cards if the total number of cards are 52 and there are 4 ACEs in it?

113

413

213

313

#### SOLUTION

Solution :A

Probability of getting ACE from a deck of shuffled cards =Number of favourable outcomesTotal number of outcomes = 452 = 113.

### Question 7

If the X- axis represents various fruits purchased and the Y-axis represents sales(in kgs), then match the following.

1-a , 2-b , 3-d , 4-c , 5-e

1-c , 2-d , 3-b , 4-e , 5-a

1-d , 2-c , 3-a , 4-b , 5-e

1-b , 2-c , 3-e , 4-a , 5-d

#### SOLUTION

Solution :B

As seen from the graph,

the quantity of apples sold = 5 kg,

the quantity of mangoes sold= 15 kg,

the quantity of bananas sold = 20 kg,

the quantity of pineapples sold = 10 kg and

the quantity of papayas sold = 25 kg.

Thus, 1 - c, 2 - d, 3 - b, 4 - e, 5 - a is correct.

### Question 8

There are 50 students in a class and the average mark scored by the class in Maths is 65 out of 100. The total marks scored by all the students except Karan and Arjun is 3080. If the marks scored by Karan & Arjun are same. What is the mark scored by Arjun?

75

80

85

90

#### SOLUTION

Solution :C

Average =Total marksTotal number of student

65=3080+Marks scored by Arjun+ Marks scored by Karan50.

Since marks scored by Arjun = Marks scored by Karan

Marks scored by Arjun + Marks scored by Karan = 2 × Marks scored by Arjun.

So, 65 × 50 = 3080 + 2 × Marks scored by Arjun.

So, marks scored by Arjun =3250−30802=1702=85 marks.

### Question 9

Find the range of following set of integers:

-2 , 5 , 12, -10, 0, -9 , -13, 1, 4 , 2 , 9, -8

#### SOLUTION

Solution :A

The difference between the highest and lowest observations is called range.

Largest integer = 12.

Smallest integer = -13.

Range = 12-(-13) = 25.

### Question 10

There is a data set with 1000 observations. Out of these observations, the observation that occurs most frequently is 9, which occurs 13 times. After taking 20 more observations, it was observed that 13, which was not there in the observations before, occurred 19 out of 20 times and 9 occurred only 1 out of 20 times. What is the mode in these 1020 observations?

#### SOLUTION

Solution :In the 1000 observations, 9 will be the mode.

In 1020 observations, frequency of 9 = 13 + 1 = 14

In 1020 observations, frequency of 13 = 19

So, mode of the observations = 13.