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Practice each question, then open the answer or worked solution.
Some integers are marked on a board. What is the range of these integers?
(a) 31 (b) 37 (c) 20 (d) 3
Solution:-
(b) 37
The difference between the highest and lowest observations in a given data is called its Range.
Range = Highest – lowest
= 20 – (- 17)
= 20 + 17
= 37
On tossing a coin, the outcome is
(a) only head
(b) only tail
(c) neither head nor tail
(d) either head or tail
Solution:-
(d) either head or tail
The mean of three numbers is 40. All the three numbers are different natural numbers. If the lowest is 19, what could be the highest possible number of the remaining two numbers?
(a) 81 (b) 40 (c) 100 (d) 71
Solution:-
(a) 81
From the question it is given that,
The mean of three numbers is 40.
Lowest number = 19
Let us assume the other two numbers be P, Q.
Then,
Mean = (P + Q + 19)/3
40 = (P + Q + 19)/3
By cross multiplication we get,
120 = P + Q + 19
120 – 19 = P + Q
Then, P + Q = 101
So, 81 + 20 = 101
Therefore, the highest number is 81
Khilona earned scores of 97, 73 and 88, respectively, in her first three examinations. If she scored 80 in the fourth examination, then her average score will be
(a) increased by 1 (b) increased by 1.5
(c) decreased by 1 (d) decreased by 1.5
Solution:-
(d) decreased by 1.5
From the question,
Khilona earned scores in 3 exam = 97, 73, 88
Then, Mean = (97 + 73 + 88 +)/3
Mean = 86 marks
Khilona earned scores in 4 exam = 97, 73, 88, 80
Then, Mean = (97 + 73 + 88 + 80)/4
Mean = 84.5 marks
Then, her average score will be 86 – 84.5 = 1.5, decreased by 1.5
Which measure of central tendency best represents the data of the most popular politician after a debate?
(a) Mean (b) Median (c) Mode (d) Any of the above
Solution:-
(c) Mode
Mode is the observation that occurs most frequently in the data.
Which of the following has the same mean, median and mode?
(a) 6, 2, 5, 4, 3, 4, 1 (b) 4, 2, 2, 1, 3, 2, 3
(c) 2, 3, 7, 3, 8, 3, 2 (d) 4, 3, 4, 3, 4, 6, 4
Solution:-
(d) 4, 3, 4, 3, 4, 6, 4
Mean of the given data = (4 + 3 + 4 + 3 + 4 + 6 + 4)/7
= 4
Mode is the observation that occurs most frequently in the data i.e. 4.
When the given data is arranged in ascending (or descending) order, then the middlemost observation is the median of the data.
Arranging the given data, 3, 3, 4, 4, 4, 4, 6.
So, the median is 4.
In Questions 17 to 31, fill in the blanks to make the statements true.
The difference between the highest and the lowest observations of a data is called _________.
Solution:-
The difference between the highest and the lowest observations of a data is called range.
The mean of a data is defined as _________.
Solution:-
The average or Arithmetic Mean or mean of a given data is defined as Sum of all observations by the Number of observations.
In a set of observations, the observation that occurs the most often is called _________.
Solution:-
Mode
Mode is the observation that occurs most frequently in the data.
In a given data, arranged in ascending or descending order, the middle most observation is called _________.
Solution:-
Median.
When the given data is arranged in ascending (or descending) order, then the middlemost observation is the median of the data.