Class 7 Maths Chapter 4 Question Answers - Data Handling

Q1. Define the following terms:
(i) Mean
(ii) Mode
(iii) Median
(iv) Range
Ans:
(i) Mean: The average or Arithmetic Mean or mean of a given data is defined as:
Mean = Sum of all observations  / Number of observations
(ii) Mode: It is the observation that occurs most frequently in the data.
(iii) Median: When the given data is arranged in ascending (or descending) order, then the middle most observation is the median of the data.
(iv) Range: The difference between the highest and lowest observations in a given data is called its Range.

Q2.   Find mean of first 15 natural numbers.
Ans: 
We know that;
the first 15 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Unknown:
The mean of first 15 natural numbers.
Mean = Sum of all observations  / Number of observations
= 1 + 2  + 3 +4 + 5 + 6 + 7 + 8 + 9 + 10 +11 +12 +13 +14 + 15 / 15
= 120/15
= 8
Mean = 8

Q3. If the median of 46, 64, 88, 40, x, 76, 35, 91, 56, 30 and 91 is 58 find the value of x .
Ans:
We know that the median of 46, 64, 88, 40, x, 76, 35, 91, 56, 30 and 91 is 58 .
Unknown:
The value of x.
Steps: 
Let us arrange the data in ascending order, we have,
30, 35, 40, 46, 56, x, 64, 76, 88, 91, 91
x is put after 56 as it is given that the median is 58 .
By observation, we can find that the data provided are 11 numbers and their count is odd.
Median is the middle number and it is x here.
∴ x = 58

Q4. A dice was thrown 20 times and the following were the outcomes:
2, 3, 3, 2, 2, 5, 4, 6, 5, 1, 4, 2, 6, 6, 6, 1, 6, 4, 3, 6 .
Prepare a frequency table and calculate the mode of the above data.
Ans: 
The frequency table for the scores will be as shown below:
From Table 1 we observe that,
Mode = 6 ( ∵Most frequently occurring number on Dice)

Q5. The marks obtained by five students of class VIII in quarterly and half-yearly examinations, 2010 in Mathematics (out of 50 ) are given below.
Represent the data given in Table 2 with the help of a double bar graph.
Ans: 
The following graph in Figure 1 shows the Double Bar graph for given data:

Q6. There are 15 boys and 20 girls in a class. what is the probability of 
(a) boy secures first position in the class 
(b) girl secures first position in the class?
Ans: 
Given that,
Number of boys in the class =15
Number of girls in the class  = 20
Total number of students in class  = Number of Boys in class + Number of Girls in class
= 15 + 20
= 35
Therefore, the total number of students in the class = 35
(a) Steps to find the probability of a boy securing first position in the class:
Boy securing first position in class = Number of Boys in Class / Total Number of Students in Class
= 15/35
= 3/7
∴ Boy securing first position in class = 3/7
(b) Steps to find the probability of a girl securing first position in the class:
Girl securing first position in class = Number of girls in class / Total number of students in class
= 20 / 35
= 4/7
∴ Girl securing first position in class = 4/7