# Free Data Handling Subjective Test 01 Practice Test - 7th grade

### Question 1

Find the mode of 2, 14, 16, 12, 14, 14, 16, 14, 10, 14, 18, 14. [1 MARK]

#### SOLUTION

Solution :Given Data is: 2, 14, 16, 12, 14, 14, 16, 14, 10, 14, 18, 14.

Arranging the observations in the ascending order.

2, 10, 12, 14, 14, 14, 14, 14, 14, 16, 16, 18.

Clearly, the most repeated observation is 14.

⇒ 14 is mode.

### Question 2

Find the mean of 9, 10, 8, 9, 12, 10. [2 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Result: 1 MarkMean=Sum of all observationTotal number of observation

Mean=9+10+8+9+12+106=9.66.

The mean is 9.66.

### Question 3

The runs scored by 11 players in a cricket match are 12, 32, 43, 32, 12, 32, 12, 32, 36, 54,11. Find the mode of the runs scored by the players. [2 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Result: 1 Mark

Given runs are, 12, 32, 43, 32, 12, 32, 12, 32, 36, 54,11.

Arranging the numbers in ascending order:

11, 12, 12, 12, 32, 32, 32, 32, 36, 43, 54.

Mode of a set of observations is the observation which occurs most often.

Clearly, here, 32 runs are scored by most of the batsman.

So, the mode of the observation is 32.

### Question 4

Find the mean of first five multiples of 5. [2 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Solution: 1 MarkFirst five multiples of 5 are 5,10,15, 20 and 25.

Mean=Sum of all observationTotal number of observation

Mean=5+10+15+20+255=15

### Question 5

Marks obtained by students out of 20 in a class test are written on the board. What is the range of the marks?

12 ,14 , (-1), (-6), 15, 0, 8, 2. [2 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Result: 1 Mark

Range is defined as the difference between the highest and the lowest observation.

Here, after arranging marks in ascending order : ( -6 ),( -1 ) , 0 , 2, 8 , 12 , 14 , 15.

Lowest observation: (-6)

Highest observation: 15

Range = Highest observation - Lowest observation

Range = 15 - (-6) = 21

### Question 6

Calculate the Mean, Median, Mode of the following data: 5,10,10,12, 13

Are these three equal? [3 MARKS]

#### SOLUTION

Solution :Mean, Median, Mode: Each 1 Mark

Mean=Sum of all observationTotal number of observation

⇒Mean=5+10+10+12+135=505=10

Median is the middle most observation of the given observations.

⇒Median=10

The mode is the most repeated observation of the given observations.

⇒Mode=10

Hence, for this observation, Mean, Median, Mode are equal.

### Question 7

Given below are the weights of 9 different students of class 10^{th}: 54 kg , 56 kg , 54 kg , 57 kg , 54 kg , 52 kg , 54 kg , 55 kg , 59 kg. Find the mode and median of the given observations. [3 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Result: 1 Mark

Given,

Weights of 9 different students : 54kg, 56kg , 54kg , 57kg , 54kg , 52kg , 54kg , 55kg , 59kg

Arranging the data in ascending order,

52kg, 54kg, 54kg, 54kg, 54kg, 55kg, 56kg, 57kg, 59kg

Median is the middle most observation of the given observations

⇒ Median = 54kg

Mode is the most repeated observation of the given observations

Clearly, 54kg is the most repeated observation

⇒ Mode = 54kg

### Question 8

Following cards are facing down: [3 MARKS]

Find the probability of drawing:

1. Vowel

2. Consonant

#### SOLUTION

Solution :Formula: 1 Mark

Application: 1 Mark

Calculation: 1 MarkHere, we have 8 cards A, E, I, O, U, B, G, H

Vowels = A, E, I, O, U

⇒ Number of vowel cards = 5

So, probability of drawing vowel

P(E)=No.of vowelsTotal number of cards=58

Consonants = B, G, H

⇒ Number of Consonant cards = 3

Probability of drawing consonant:

P(E)=No.of consonantsTotal number of cards=38

### Question 9

The ages in years of 10 teachers of a school are:

34, 43, 31, 56, 37, 28, 25, 35, 40, 42

(i) What is the range of the ages of the teachers?

(ii) What is the mean age of these teachers? [3 MARKS]

#### SOLUTION

Solution :Formulas: 1 Mark

Each part: 1 Mark

(i) Arranging the ages in ascending order, we get:

25, 28, 30, 34, 35, 37, 40, 42, 43, 56

We find that the age of the oldest teacher is 56 years and the age of the youngest teacher is 25 years.

Range of the ages of the teachers = (56 - 25) years = 31 years

(ii) Mean age of the teachers:

=25+28+30+34+35+37+40+42+43+5610 years

=37010 years=37 years

### Question 10

Following table shows the points of each player scored in four games:

PlayerGameGameGameGame1234Suraj10161410Abhijit8046Harshith13Did not118Play

Based on the above table answer the following questions:

(i) Find the mean to determine Suraj's average number of points scored per game.

(ii) To find the mean number of points per game of Harshith, would you divide the total points by 3 or by 4? Why?

(iii) Abhijit played in all the four games. How would you find the mean?

(iv) Who is the best performer? [4 MARKS]

#### SOLUTION

Solution :Solution: 1 Mark each

(i) Suraj's average number of points.

Mean=Sum of all observationTotal number of observation

Mean=10+16+14+104=504

⇒Mean=12.5

(ii) To find the mean number of points per game of Harshith, mean should be divided by 3 because he played in only 3 games.

Mean=Sum of all observationTotal number of observation

Mean=13+11+83=323

⇒Mean=10.66

(iii) For Abhijit's game mean is:

Mean=Sum of all observationTotal number of observation

Mean=8+0+4+64=184

⇒Mean=4.5

(iv) Comparing everybody's mean score, Suraj has highest mean.

⇒ Suraj is best performer.

### Question 11

There are 10 marbles in a box which are marked with first 10 multiples of 2.

(a) What is the probability of drawing a multiple of 4?

(b) What is the probability of drawing a multiple of 6? [4 MARKS]

#### SOLUTION

Solution :Formula: 1 Mark

Steps: 1 Mark

Answer: Each part 1 MarkFirst 10 multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

⇒ Numbers of multiples of 2 = 10

In these number which are multiples of 4 are 4, 8,12,16, 20

⇒ Numbers of multiples of 4 = 5

In these number which are multiples of 6 are 6,12,18

⇒ Numbers of multiples of 6 = 3

i) Probability of drawing a multiple of 4 is:

P(E)=Numbers of multiples of 4Total numbers of marbles

⇒P(E)=510=12.

ii) Probability of drawing a multiple of 6 is:

P(E)=Numbers of multiples of 6 Total numbers of marbles

⇒P(E)=310

### Question 12

Sale of English and Hindi books in the years 1995, 1996, 1997 and 1998 are given below:

Years1995199619971998English350400450620Hindi500525600650

Draw a double bar graph and answer the following questions:

(a) In which year was the difference in the sale of the two language books least?

(b) Can you say that the demand for english books increased? Justify. [4 MARKS]

#### SOLUTION

Solution :Double Bar graph: 2 Marks

Answers: 1 Mark each

Double bar graph:

(a) In the year 1998, the difference in the sale of the two language books was least.

(b) Yes, the demand for English books increased. From the graph, it is evident that the difference in the demand for English books from 1995 to 1998 is 620 - 350 = 270.

Whereas for Hindi books the difference is 650 - 500 = 150.

Comparatively, the demand for English books increased.

### Question 13

The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:

DayMonTueWedThursFriSatSunRainfall0.012.22.10.020.55.51.0(in mm)

(i) Find the range of the rainfall in the above data.

(ii) Find the mean rainfall for the week.

(iii) On how many days was the rainfall less than the mean rainfall? [4 MARKS]

#### SOLUTION

Solution :Range: 1 Mark

Mean: 2 Marks

Answer: 1 Mark

(i) Range = Highest observation - Lowest observation

Range = 20.5 - 0.0 = 20.5

(ii) Mean=Sum of all observationTotal number of observation

Mean=0.0+12.2+2.1+0.0+20.5+5.5+1.07

Mean=41.37=5.9

(iii) On Mon, Wed, Thurs, Sat, and Sun the rainfall was less than mean rainfall i.e. 5.9 mm.

⇒ On 5 days the rainfall was less than the mean rainfall.

### Question 14

(a) The profits of a soft drink firm during certain months of a year are given alongside. Draw a Bar graph. [4 MARKS]

MonthsProfits (in thousands)January2.4February1.8March3.0April4.0May5.2June4.0July2.0

(b) The following bar graph shows the number of men and women visiting a sports complex. Can you spot the day when the number of men was equal to the number of women and on which day is the number of women 20 more than the number of men?

#### SOLUTION

Solution :(a) 2 Marks

(b) 2 Marks

Scale : x - axis - Months

y - axis - Profits in thousands - 1 cm = 1 Thousand

(b)

Here, the height of the bar graph gives us the number of men and women. For Thursday, the height of both the graphs is same. So, on Thursday, the number of men was equal to the number of women.

On Monday the number of women is 20 more than the number of men. (No. of men = 40 , No. of women = 60)

### Question 15

(a) The number of boys taking part in different extracurricular activities is shown in the table given below. Represent the data on a bar graph. [4 MARKS]

ActivitiesNo. of boysScouts25Debate13Science Club7Inst. Music30S.U.P.W15

(b) What is the difference between the number of mangoes sold on Sunday and the number of custard apples sold on Wednesday?

#### SOLUTION

Solution :(a) Scale: 1 Mark

Bar graph: 1 Mark

(b) Solution: 2 Marks

(a) Scale: x axis - extracurricular activities

y axis - Number of boys; 1 cm = 5 units

(b) Number of mangoes sold on Sunday = 85Number of custard apples sold on Wednesday = 20

Difference = 65