Class 7 Maths Chapter 4 HOTS Questions - Data Handling

Q1: Tell whether the following statement is true or false:
(a) The Mode is always present as one of the numbers in the given data.
Ans:
The statement given above is true.
Because Mode,
Mode is determined as the value of the variable which is present most frequently.
Hence, the Mode is always one of the numbers present in the data.

(b) The Mean is one of the numbers present in the data.
Ans:
The above statement which is given above is false.
Because the Mean may or may not be the one of the numbers present in the data.

(c) The Median is always present as one of the numbers in the data.
Ans:
The statement given above is true.
Because the median is,
The value of the middle-most observation of the data while arranged in ascending or in descending order.
Hence, the median is always one of the numbers present in a data

(d) The data 6, 13, 9, 4, 3, 8, 9, and 12 have a mean of 9.
Ans:
Mean is equal to = Sum of all given observations divided by the total no of observations.
= (6 + 4 + 3 + 8 + 9 + 12 + 13 + 9) divided by 8
= (64/8)
= 8
Hence, the above-given statement is false.

Q2:There are six marbles present in a box ranging with numbers from 1 to 6 marked on each one of them.
(a) What is the major probability of drawing a marble with the number 2?
Ans:
From the above question, it is given that
There are six marbles in the box where numbers from 1 to 6 are marked.
The probability of drawing a marble with the number 2 is = the number of favourable outcomes divided by the number of possible outcomes
= (1/6)

(b) What is the major probability of drawing a marble with the number 5?
Ans:
From the above question, it is given that
There are six marbles in the box where numbers from 1 to 6 are marked.
Probability of drawing a marble with the number 5 = Number of favourable outcomes divided by the number of possible outcomes
= (1/6)

Q3: Let x, y, and z denote three observations. The final Mean of these observations is
(i) (x × y × z)/3 (ii) (x + y + z)/3
(iii) (x – y – z)/3 (iv) (x × y + z)/3
Ans:
The correct answer is (ii) (x + y + z)/3
Explanation – The average or the Arithmetic Mean or the Mean of the given data is the Sum of all of these observations divided by the number of observations.

Q4: Which measures of the central tendency get affected in the extreme observations of both of these ends of a data arranged in the descending order are removed?
(i) Mean and mode
(ii) Mean and Median
(iii) Mode and Median
(iv) Mean, Median and Mode
Ans: (i) 

Q5: The median of the following data: 3, 4, 5, 6, 7, 3, 4 is
(a) 5
(b) 3
(c) 4
(d) 6
Ans: (c)
When the given data is arranged in an ascending or descending order, then the middle observation present is known as the median of the data.
So, now arrange the given observation into an ascending order which is 3, 3, 4, 4, 5, 6, 7
Therefore, the number 4 is the middle observation, and it is the median of the above-given data. 

Q6: Kajal earned scores of 97, 73 and 88, respectively, in her first three exams. So If she scored the number 80 in her fourth examination, then her average score becomes
(i) increased by 1
(ii) increased by 1.5
(iii) decreased by 1
(iv) decreased by 1.5
Ans: (d)
From the above question,
Kajal earned scores in her last 3 exam = 97, 73, 88
Then, the Mean would be = (97 + 73 + 88 +)/3
Mean = 86 marks
Kajal earned the score in her 4 exam = 97, 73, 88, 80
Then, Mean is = (97 + 73 + 88 + 80)/4
Mean = 84.5 marks
Then, her average score becomes 86 – 84.5 = 1.5, decreased by 1.5 

Q7: Which of these following has the same mean, median and Mode?
(i) 6, 2, 5, 4, 3, 4, 1
(ii) 4, 2, 2, 1, 3, 2, 3
(iii) 2, 3, 7, 3, 8, 3, 2
(iv) 4, 3, 4, 3, 4, 6, 4
Ans: (iv)
Mean of the given data is given as = (4 + 3 + 4 + 3 + 4 + 6 + 4)/7
= 4
Mode is the observation that generally occurs most frequently in the data, which is 4.
When the given data is arranged in an ascending or descending order, then the middle observation is said to be the median of the given data.
Arranging the given data as 3, 3, 4, 4, 4, 4, 6.
So, the Median is 4. 

Q8: On tossing a coin, the outcome generated is
(i) only head
(ii) only tail
(iii) neither head nor tail
(iv) either head or tail
Ans: (d)

Q9: The Mean of three numbers is denoted as 40. All three numbers are different natural numbers. If the lowest number is 19, then what could be the highest possible number of the remaining two numbers?
(a) 81
(b) 40
(c) 100
(d) 71
Ans: (a)
From the above question, it is given that,
The Mean of the three numbers is 40.
The lowest number is = 19
Let us assume that the other two numbers be P, Q.
Then,
The Mean = (P + Q + 19)/3
40 = (P + Q + 19)/3
By cross multiplication, we receive,
120 = P + Q + 19
120 – 19 = P + Q
Now, P + Q = 101
So, 81 + 20 = 101
Therefore, the highest number is 81 

Q10: Tell whether these following statements are certain to happen, impossible to happen, or can happen but not certain.
(a) You are older today than yesterday.
Ans:
It is certain to happen.

(b) A tossed coin will land heads up.
Ans:
It can happen but not certain.

(c) A die, when tossed, shall land up with eight on its top.
Ans:
It is impossible as there are only six faces present on a die, and these faces are marked as the numbers 1, 2, 3, 4, 5, and 6.

(d) The next traffic light seen will be green.
Ans:
It can happen but not certain.

(e) Tomorrow will be a cloudy day.
Ans:
It can happen but not certain.

Q11: A coin is flipped to decide which of the two teams starts the game. What is the probability that team A will start?
Ans:
A coin has two faces. One is named head, and the other one is named Tail.
Now, one team can choose either a Head or a Tail.
The probability of team A starting the first= number of favourable outcomes/
Number of possible outcomes
= ½

Q12: The number of trees present in different parts of a city is 33, 48,33, 34, 33, 34, 33 and 24. The Mode of the following data is 
(a) 24 
(b) 34 
(c) 33 
(d) 48
Ans: (c)
Mode is the observation which occurs most frequently in the data.

Q13: The range of these data is: 18, 12, 21, 6, 17, 8, 4, 13 is
(a) 17
(b) 12
(c) 8
(d) 15
Ans: (a)
The major difference between the highest and the lowest observations in the given data is called its range.
The range is defined as = Highest – lowest
= 21 – 4
= 17

Q14: Out of these five brands of chocolates in the shop, a boy has to purchase the brand that is most liked by the children. What measure of the central tendency would be most appropriate if any of the given data is provided to him?
(a) Mean
(b) Mode
(c) Median
(d) Any of the three
Ans: (b)
Mode is the observation that frequently occurs in the data.

Q15: Which measure of the central tendency best represents the data of the most popular politician after their debate?
(i) Mean
(ii) Median
(iii) Mode
(iv) Any of the above
Ans: (c)
Mode is the observation that generally occurs most frequently in the data.