Chapter 3 Data Handling Ex 3.2 Solutions
Question - 1 : - The scores in mathematics test (out of 25) of 15 students is as follows:
19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20
Find the mode and median of this data. Are they same?
Answer - 1 : -
Arranging the givenscores in an ascending order, we get
5, 9, 10, 12, 15, 16,19, 20, 20, 20, 20, 23, 24, 25, 25
Mode,
Mode is the value ofthe variable which occurs most frequently.
Clearly, 20 occursmaximum number of times.
Hence, mode of thegiven sores is 20
Median,
The value of themiddle-most observation is called the median of the data.
Here n = 15, which isodd.
Where, n is the numberof the students.
∴median = value of ½ (n+ 1)th observation.
= ½ (15 + 1)
= ½ (16)
= 16/2
= 8
Then, value of 8th term= 20
Hence, the median is20.
Yes, both the valuesare same.
Question - 2 : - The runs scored in a cricket match by 11 players is as follows:
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Find the mean, mode and median of this data. Are the three same?
Answer - 2 : -
Arranging the runsscored in a cricket match by 11 players in an ascending order, we get
6, 8, 10, 10, 15, 15,15, 50, 80, 100, 120
Mean,
Mean of the given data= Sum of all observations/ Total number of observations
= (6 + 8 + 10 + 10 +15 + 15 + 15 + 50 + 80 + 100 + 120)/ 11
= 429/11
= 39
Mode,
Mode is the value ofthe variable which occurs most frequently.
Clearly, 15 occursmaximum number of times.
Hence, mode of thegiven sores is 15
Median,
The value of themiddle-most observation is called the median of the data.
Here n = 11, which isodd.
Where, n is the numberof players.
∴median = value of ½ (n+ 1)th observation.
= ½ (11 + 1)
= ½ (12)
= 12/2
= 6
Then, value of 6th term= 15
Hence, the median is15.
No, these three arenot same.
Question - 3 : - The weights (in kg.) of 15 students of a class are:
38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
(i) Find the mode and median of this data.
(ii) Is there more than one mode?
Answer - 3 : -
Arranging the given weights 15 students of a class in an ascending order, we get
32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50
(i) Mode and Median
Mode,
Mode is the value of the variable which occurs most frequently.
Clearly, 38 and 43 both occurs 3 times.
Hence, mode of the given weights are 38 and 43.
Median,
The value of the middle-most observation is called the median of the data.
Here n = 15, which is odd.
Where, n is the number of the students.
∴median = value of ½ (n + 1)th observation.
= ½ (15 + 1)
= ½ (16)
= 16/2
= 8
Then, value of 8th term = 40
Hence, the median is 40.
(ii) Yes, there are 2 modes for the given weights of the students.
Question - 4 : - Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
Answer - 4 : -
Arranging the givendata in an ascending order, we get
= 12, 12, 13, 13, 14,14, 14, 16, 19
Mode,
Mode is the value ofthe variable which occurs most frequently.
Clearly, 14 occursmaximum number of times.
Hence, mode of thegiven data is 14.
Median,
The value of themiddle-most observation is called the median of the data.
Here n = 9, which isodd.
Where, n is the numberof the students.
∴median = value of ½ (9+ 1)th observation.
= ½ (9 + 1)
= ½ (10)
= 10/2
= 5
Then, value of 5th term= 14
Hence, the median is14.
Question - 5 : - Tell whether the statement is true or false:
(i) The mode is always one of the numbers in a data.
(ii) The mean is one of the numbers in a data.
(iii) The median is always one of the numbers in a data.
(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.
Answer - 5 : -
(i)The statement is givenabove is true.
Because, Mode is thevalue of the variable which occurs most frequently in the given data.
Hence, mode is alwaysone of the numbers in a data.
(ii)The statement is givenabove is false.
Because, mean is maybe or may not be one of the number in a data.
(iii)The statement is givenabove is true.
Because, median is thevalue of the middle-most observation in the given data while arranged inascending or descending order.
Hence, median isalways one of the numbers in a data
(iv)Mean = Sum of allgiven observations/ number of observations
= (6 + 4 + 3 + 8 + 9 +12 + 13 + 9)/8
= (64/8)
= 8
Hence, the givenstatement is false.