Worksheet Solution: Data Handling - Mathematics (Maths) Class 7

Q.1. Find the mode of the following data:
24, 26, 23, 26, 22, 25, 26, 28
Ans: Arranging the given data with the same value together, we get
22, 23, 24, 25, 26, 26, 26, 28
Here, 26 occurs the greatest number of times i.e. 3 times
Thus, the required mode = 26.

Q.2. Find the median of the following data:
8, 6, 10, 12, 14
Ans: Let us arrange the given data in increasing order,
6, 8, 10, 12, 14
n = 5 (odd)
Median = (n + 1/2)^th term = 3^rd term = 10
Thus, the required median = 10.

Q.3. A fair die is rolled, find the probability of getting a prime number.
Ans: Number on a die = 1, 2, 3, 4, 5, 6
n(S) = 6
Prime numbers = 2, 3, 5
n(E) = 3
Probability = n(E) / n(S) = 3 / 6 = 1 / 2
Thus the required probability = 1 / 2.

Q.4. Find the mean of the first 5 multiples of 3.
Ans: Five multiples of 3 are 3, 6, 9, 12 and 15
Mean =  
= 45 / 5
= 9

Q.5. Find the mean and median of first five prime numbers.
Ans: First five prime numbers are: 2, 3, 5, 7 and 11
Mean =
= 28 / 5
= 5.6

Q.6. A bag contains 5 white and 9 red balls. One ball is drawn at random from the bag. Find the probability of getting
(a) a white ball
(b) a red ball
Ans: Total number of balls = 5 + 9 = 14 balls
(a) Number of white ball = 5
n(E) = 5
Probability of getting white ball = n(E)/n(S) = 5 / 14
(b) Number of red balls = 9
n(E) = 9
Probability of getting white ball = n(E)/n(S) = 9 / 14

Q.7. Find the range of the following data:
21, 16, 30, 15, 16, 18, 10, 24, 26, 20
Ans: Greatest number 30
Smallest number = 10
Range = 30 – 10 = 20

Q.8. Find the average of the numbers 8, 13, 15.
Ans: Average = Sum of the numbers / Total number of terms
= 8 + 13 + 15 / 3
= 36/3
= 12

Q.9. Find the median of the following data:
20, 14, 6, 25, 18, 13, 19, 10, 9, 12
Ans: Arranging the given data in increasing order, we get
6, 9, 10, 12, 13, 14, 18, 19, 20, 25
n = 10 (even)

Thus, the required median = 13.5

Q.10. The following bar graph shows the number of books sold by a publisher during the five consecutive years. Read the bar graph and answer the following questions:
(i) About how many books were sold in 2008, 2009 and 2012 years?
(ii) In which years were 575 books were sold?
(iii) In which years were the minimum number of books sold?

Ans:
(i) 
(ii) In the year of 2012, maximum number of books i.e. 575 were sold.
(iii) Minimum number of books i.e. 150 were sold in the year 2008.

Q.11. The marks obtained (out of 10) by 80 students in a class test are given below:
Find the mode of the above data.
Ans: In the given frequency distribution table, we find that the observation 7 has maximum frequency, i.e., 20
Hence, the required mode = 7.

Q.12. State true of false.
(i) A data set may have more than one mode.
(ii) The data set 4, 8, 11, 7, 5, 0 has the mode 0.
(iii) The median can be value which is not equal to any of the observation.
(iv) It is impossible to get a sum of 14 of the numbers on both dice when a pair of dice is thrown together
(v) Mean of the observations can be lesser than each of the observations.
(vi) Mean of a data set is the value which divides the value into two equal parts.
(vii) The value of median changes if the value in a data set are arranged in ascending order instead of descending order.
(viii) Rolling the number 7 on a standard die is an impossible event.
(ix) Mean of the data is always from the given data.
(x) Mode of the data is always from the given data.
Ans: (i) - True
(ii) - False
(iii) - False
(iv) - True
(v) - False
(vi) - False
(vii) - False
(viii) - True
(ix) - False
(x) - True

Q.13. A batsman scored the following number of runs in six innings:
36, 35, 50, 46, 60, 55
Calculate the mean runs scored by him in an inning
Ans: 47

Q.14. Fill in the blanks:
(i) The difference between the highest and lowest values of observations in a set of data is called the_________
(ii) The representation of numbers using bars of uniform width, the length of the bars depicting the frequency is called the_________
(iii) When the raw data is arranged in ascending or descending order, it forms an_________
(vi) The probability of getting 1 in tossing of coin is_________
(v) The outcomes which have equal chances of occurrence are called_________.
(vi) Different forms of central tendency are _________and__________
(vii) On dividing the sum of observation by total number of observations, we obtain the_________
(viii) The possible results of an experiment are called_________
(ix) The measure of chance of happening something is called_________
(x) The probability of getting a tail in a throw of a dice is_________.
Ans: (i) - Range
(ii) - Bar graph
(iii) - array
(iv) - 0
(v) - equally likely
(vi) -  Mean, median and Mode
(vii) - mean
(viii) - outcomes
(ix) - probability
(x) - 0

Q.15. The mean of 5 numbers is 25. If the four numbers 16, 26, 31, 32. Find the fifth numbers.
Ans: 20