Students often refer to SSLC Maths Textbook Solutions and Class 10 Maths Chapter 13 Statistics Important Extra Questions and Answers Kerala State Syllabus to clear their doubts.
SSLC Maths Chapter 13 Statistics Important Questions and Answers
Statistics Class 10 Extra Questions Kerala Syllabus
Statistics Class 10 Kerala Syllabus Extra Questions
Question 1.
What is the median of the following data?
21, 6, 14, 9, 5
(a) 9
(b) 8
(c) 5
(d) 11
Answer:
(a) 9
Question 2.
What is the mean of the first 10 natural numbers?
(a) 10
(b) 5
(c) 6
(d) 5.5
Answer:
(d) 5.5
Question 3.
The median of 17 observations, which are in arithmetic sequence, is 21. What does it mean?
(a) 9
(b) 18
(c) 15
(d) 21
Answer:
(d) 21
Question 4.
Read the two statements given below.
Statement 1: The scores 10, 18, 14, 20, 12, 16 have a mean and median equal.
Statement 2: The numbers form an arithmetic sequence when arranged in order.
Choose the correct answer from those given below.
(a) Statement 1 is true, and Statement 2 is false.
(b) Statement 1 is false, and Statement 2 is true.
(c) Both statements are true, and Statement 2 is the correct reason for Statement 1.
(d) Both statements are true, but Statement 2 is not the correct reason for Statement 1.
Answer:
(c) Both statements are true, and Statement 2 is the correct reason for Statement 1.
Question 5.
Read the two statements given below.
Statement 1: The numbers 7, 10, 13, 16, 19 have median = mean.
Statement 2: The numbers form an arithmetic sequence with a common difference of 3.
Choose the correct answer from those given below.
(a) Statement 1 is true, and Statement 2 is false.
(b) Statement 1 is false, and Statement 2 is true.
(c) Both statements are true, and Statement 2 is the correct reason for Statement 1.
(d) Both statements are true, but Statement 2 is not the correct reason for Statement 1.
Answer:
(c) Both statements are true, and Statement 2 is the correct reason for Statement 1.
Question 6.
The weights of 11 players of a football team are given in kilograms:
55, 65, 56, 70, 62, 54, 64, 58, 68, 65, 60
Find the median of the weights of players.
Answer:
Arrange the given weights in ascending order,
54, 55, 56, 58, 60, 62, 64, 65, 65, 68, 70
Median is the middle value.
Therefore median = 62
Question 7.
Find the median of the first 9 even numbers.
Answer:
The first 9 even numbers in ascending order are 2, 4, 6, 8, 10, 12, 14, 16, 18
Median is the middle value.
Therefore, median = 10.
Question 8.
The weights of 7 pupils in a class are given (in kilograms). Find the median weight.
35, 43, 38, 45, 32, 44, 42
Answer:
Arrange the given weights in ascending order
32, 35, 38, 42, 43, 44, 45
The median is the middle value.
Therefore median = 42
Question 9.
The scores of 10 students in an examination are given below.
30, 28, 25, 32, 20, 36, 24, 33, 27, 38
Calculate the median score.
Answer:
Arrange the given scores in ascending order
20, 24, 25, 27, 28, 30, 32, 33, 36, 38
Here, we have two middle values.
So, the median is their average.
Median = \(\frac{28+30}{2}\) = 29
Question 10.
The ages of 8 teachers in a school are given. Calculate the mean and median age.
27, 41, 32, 53, 40, 38, 51, 30
Answer:
Mean = \(\frac{27+41+32+53+40+38+51+30}{8}\)
= \(\frac {312}{8}\)
= 39
Arrange the ages in ascending order
27, 30, 32, 38, 40, 41, 51, 53
Median = \(\frac{38+40}{2}\) = 39
Question 11.
The algebraic form of an arithmetic sequence is 3n + 2. What is the median of the first 21 terms of this sequence?
Answer:
21 is an odd number.
So, \(\frac{21+1}{2}=\frac{22}{2}\) = 11
11th term is the median.
Median = 3 × 11 + 2 = 33 + 2 = 35
Question 12.
There are 10 workers in a small-scale unit. Three of them have a a daily wage of 500 rupees, and the others have 800 rupees.
(a) What is the median wage of the workers?
(b) How many workers have a wage below the median wage?
Answer:
Arranging in ascending order, the wages will be 500, 500, 500, 800, 800, 800, 800, 800, 800, 800
(a) The median wage is 800.
(b) Three.
Question 13.
The daily wages of 99 workers in a factory is shown in the table.
(a) If the workers are arranged based on their daily wages, at what position does the median wage fall?
(b) What is the median class?
(c) Find the median of the wages.
Answer:
(a)
Here n = 99, an odd number
\(\frac{99+1}{2}=\frac{100}{2}\) = 50
So, the 50th worker’s wage is the median wage.
That is, the median wage falls at the position.
(b) 800-900 is the median class
(c) Class width = 900 – 800 = 100
Number of workers in the median class = frequency of the class = 25
Length of the subdivision = \(\frac {100}{25}\) = 4
Wage of 42nd worker = \(\frac{800+804}{2}\) = 802
Wage of 50th worker = 802 + (50 – 42) × 4
= 802 + 32
= 834
Question 14.
The table below shows the students of a maths club sorted according to their heights.
(a) When the heights are written in ascending order, the height of which student is taken as the median height?
(b) Find the median height.
Answer:
(a)
Here total number of students = 25, which is an odd number.
So, there is only one middle value = \(\frac{25+1}{2}=\frac{26}{2}\) = 13
So, the height of the 13th student is the median height.
(b) Median class is 140-150
Width of median class = 150 – 140 = 10
Number of students in this median class = 10
So, the width of the subdivisions = \(\frac {10}{10}\) = 1
Height of 10th student = \(\frac{140+141}{2}\) = 140.5
Height of the 13th student = 140.5 + (13 – 10) × 1
= 140.5 + 3
= 143.5
Therefore, the median height = 143.5
Question 15.
The table below shows, children of a class sorted according to their scores in an examination.
(a) If the children are arranged in the ascending order of their scores, then what will be the assumed score of the 14th child?
(b) Compute the median score.
Answer:
(a) The cumulative frequency table is,
The total number is 45, which is odd
\(\frac{45+1}{2}=\frac{46}{2}\) = 23
So, the 23rd child has the median score.
The 14th child is in the class 20-30.
The class width = 30 – 20 = 10.
Number of students belonging to this class = 10
So, the width of the subdivision = \(\frac {10}{10}\) = 1
Score of 14th students = \(\frac{20+21}{2}\) = 20.5
(b) Median score = Score of 23rd student
= 20.5 + (23 – 14) × 1
= 20.5 + 9
= 29.5
Only one temperature below 26 is 25.
Question 16.
The number of people who get vaccinated at various ages at a community health centre is listed below.
(a) At what age limit does the median occur? What is the age of the 49th person vaccinated in the camp if all are arranged in ascending order of age?
(b) Calculate the median age.
Answer:
(a) n = 109 (odd number)
\(\frac{109+1}{2}\)th person comes in the middle.
The cumulative frequency table is
The
55th person comes in the middle.
This belongs to the class 40-60.
Thus, the Median comes in the age limit of 40-60.
(b) Class width is 20.
The number of people in the median class is 40.
Width of a subdivision = \(\frac{20}{40}=\frac{1}{2}\)
The age of 49th person is \(\frac{40+40.5}{2}\) = 40.25
∴ Median age = Age of 55th person
= 40.25 + (55 – 49) × 0.5
= 40.25 + 6 × 0.5
= 43.25