Students often refer to Kerala Syllabus 9th Standard Maths Textbook Solutions Chapter 15 Statistics Extra Questions and Answers Notes to clear their doubts.
Kerala SCERT Class 9 Maths Chapter 15 Solutions Statistics
Statistics Class 9 Kerala Syllabus Questions and Answers
Kerala State Syllabus 9th Standard Maths Chapter 15 Statistics Solutions Questions and Answers
Class 9 Maths Chapter 15 Kerala Syllabus – Average
Intext Questions And Answers
Question 1.
Take some numbers and calculate the arithmetic means. Calculate the excess or deficit of each of the numbers from the mean and add them up separately. Are the sums equal? Can you explain the reason for this?
Answer:
Let’s consider some numbers 10, 15, 20, 25, 30
Arithmetic mean = \(\frac{10+15+20+25+30}{5}=\frac{100}{5}\) = 20
Now calculate the excess or deficit of each of the number from the mean.
| Numbers | Excess of the number from 20 | Deficit of the number from 20 |
| 10 | 20 – 10 = 10 | |
| 15 | 20 – 15 = 5 | |
| 20 | ||
| 25 | 25 – 20 = 5 | |
| 30 | 30 – 20 = 10 |
Sum of excess of the number from 20 = 10 + 5 = 15
Sum of deficit of the number from 20 = 10 + 5 = 15
Here, the sum of excess of the numbers from the mean and deficit of the numbers from the mean are equal. Because the mean act as a balance between the values of the numbers.
Class 9 Maths Kerala Syllabus Chapter 15 Solutions – Tables
Textual Questions And Answers
Question 1.
In a T20 match, 51 runs were scored in the first 5 overs
i) What is the mean run rate then?
ii) If this run rate is maintained, what is the total they can expect?
Answer:
i) To find the mean run rate, we divide the total runs scored by the number of overs:
Mean Run Rate = \(\frac{\text { Total Runs Scored }}{\text { Overs Bowled }}\) = \(\frac{51}{5}\) = 10.2 runs per over
ii) Expected Total = Mean Run Rate × Total Overs
= 10.2 × 20
= 204 runs
Question 2.
The table below shows the children in a class grouped according to their marks in a math test:
i) What is the mean marks of the class?
ii) How many got less marks than the mean?
iii) How many got more marks than the mean?
Answer:
| Marks | Children | Total Mark |
| 2 | 1 | 2 × 1 = 2 |
| 3 | 2 | 3 × 2 = 6 |
| 4 | 5 | 4 × 5 = 20 |
| 5 | 4 | 5 × 4 = 20 |
| 6 | 6 | 6 × 6 = 36 |
| 7 | 11 | 7 × 11 = 77 |
| 8 ‘ | 10 | 8 × 10 = 80 |
| 9 | 4 | 9 × 4 = 36 |
| 10 | 2 | 10 × 2 = 20 |
| Total | 45 | 297 |
Mean mark = \(\frac{297}{45}\) = 6.6
i) Children who got mark less than mean is = 1 + 2 + 5 + 4 + 6 = 18
ii) Children who got mark more than mean is = 11 + 10 + 4 + 2 = 27
Question 3.
The details of rubber sheets a farmer got during a month are shown below:
i) How many kilograms of rubber did he get a day on average in this month?
Answer:
| Rubber(kg) | Days | Total Rubber (kg) |
| 09 | 3 | 9 × 3 = 27 |
| 10 | 4 | 10 × 4 = 40 |
| 11 | 3 | 11 × 3 = 33 |
| 12 | 3 | 12 × 3 = 36 |
| 13 | 5 | 13 × 5 = 65 |
| 14 | 6 | 14 × 6 = 84 |
| 16 | 6 | 16 × 6 = 96 |
| Total | 30 | 381 |
Average Quantity of rubber per day = \(\frac{381}{30}\) = 12.77 kg
ii) The price of a kilogram of rubber is 175 rupees. How much did he get a day on average this month from rubber?
Answer:
If the price is Rs. 175 per kg, then average income per day = 12.77 × 175
= Rs.2234.75
Question 4.
The table below shows the days in a month sorted according to the amount of rainfall in a locality:
What is the mean rainfall per day during this month?
Answer:
| Rainfall (mm) | Days | Total Rainfall (mm) |
| 54 | 3 | 54 × 3 = 162 |
| 56 | 5 | 56 × 5 = 280 |
| 58 | 6 | 58 × 6 = 348 |
| 55 | 3 | 55 × 3 = 165 |
| 50 | 2 | 50 × 2 = 100 |
| 47 | 4 | 47 × 4 = 188 |
| 44 | 5 | 44 × 5 = 220 |
| 41 | 2 | 41 × 2 = 82 |
| Total | 30 | 1545 |
The average of the rain fall per day during that month = \(\frac{\text { Total rain fall }}{\text { Number of days }}=\frac{1545}{30}\) = 51.5 m
Textual Questions And Answers
Question 1.
The table below shows the children in a class, grouped according to their heights:
What is the mean height?
Answer:
| Height (cm) | Number of children | Class Mark | Total Height |
| 148 – 152 | 8 | 150 | 1200 |
| 152 – 156 | 10 | 154 | 1540 |
| 156 – 160 | 15 | 158 | 2370 |
| 160 – 164 | 10 | 162 | 1620 |
| 164 – 168 | 7 | 166 | 1162 |
| Total | 50 | 7892 |
Mean height = \(frac{\text { Total height }}{\text { Number of children }}\)
= \(\frac{7892}{50}\)
= 157.84 cm
Question 2.
The table below shows the classification of teachers in a university based on their ages:
Calculate the mean age of the teachers
Answer:
| Age | Number of teachers | Class Mark | Total Age |
| 25-30 | 06 | 27.5 | 165 |
| 30-35 | 14 | 32.5 | 455 |
| 35-40 | 18 | 37.5 | 675 |
| 40-45 | 20 | 42.5 | 850 |
| 45-50 | 05 | 47.5 | 237.5 |
| 50-55 | 04 | 52.5 | 210 |
| 55-60 | 03 | 57.5 | 172.5 |
| Total | 70 | 2765 |
Mean age = \(\frac{\text { Total age }}{\text { Number of persons }}\)
= \(\frac{2765}{70}\)
= 39.5
Question 3.
The classification of a group of children according to their weights is given in the table below:
Calculate the mean weight.
Answer:
| Weight (kg) | Number of children | Class Mark | Total Weight |
| 21-23 | 4 | 22 | 88 |
| 23-25 | 7 | 24 | 168 |
| 25-27 | 8 | 26 | 208 |
| 27-29 | 6 | 28 | 168 |
| 29-31 | 3 | 30 | 90 |
| 31-33 | 1 | 32 | 32 |
| Total | 29 | 754 |
Mean Weight = \(=\frac{\text { Total Weight }}{\text { Number of children }}\)
= \(\frac{754}{29}\)
= 26
Statistics Class 9 Extra Questions and Answers Kerala Syllabus
Question 1.
The daily wages of workers of a factory are given below. Find the average daily wage.
| Daily wages | Number |
| 500 | 3 |
| 600 | 7 |
| 700 | 10 |
| 900 | 8 |
| 1000 | 2 |
Answer:
| Daily wages | Number | Total Wages |
| 500 | 3 | 1500 |
| 600 | 7 | 4200 |
| 700 | 10 | 7000 |
| 900 | 8 | 7200 |
| 1000 | 2 | 2000 |
| Total | 30 | 21900 |
Average daily wage = \(\frac{21900}{30}\) = 730
Question 2.
The table shows the students in a class sorted according to their marks in an exam
i) The average marks is 6 .How many students got 8 marks?
ii) How many students are there in the class?
Answer:
| Mark | Students | Total mark |
| 3 | 2 | 6 |
| 4 | 4 | 16 |
| 5 | 5 | 25 |
| 6 | 6 | 36 |
| 7 | 7 | 49 |
| 8 | X | 8x |
| 9 | 2 | 18 |
| 10 | 1 | 10 |
| Total | 27 + x | 160 + 8x |
i) Average mark = \(\frac{\text { Total Mark }}{\text { Number of Students }}\)
6 = \(\frac{160+8 x}{27+x}\)
6(27 + x)= 160 + 8x
162 + 6x = 160 + 8x
2x = 2
x = 1
Therefore only one student got 8 marks ii) Total Number of students in the class = 27 + x = 27 + 1 = 28
Question 3.
A table categorizing the workers in an office on the basis of their salary is given below.
| Salary (Rs) | Number of workers |
| 15000 -18000 | 1 |
| 18000 – 21000 | 3 |
| 21000 – 24000 | 5 |
| 24000 – 27000 | 4 |
| 27000 – 30000 | 1 |
| 30000-33000 | 1 |
Find the mean of salary.
Answer:
| Salary (Rs) | Number of workers | Class interval | Total salary |
| 15000- 18000 | 1 | 16500 | 16500 |
| 18000-21000 | 3 | 19500 | 58500 |
| 21000-24000 | 5 | 22500 | 112500 |
| 24000 – 27000 | 4 | 25500 | 102000 |
| 27000 – 30000 | 1 | 28500 | 28500 |
| 30000 – 33000 | 1 | 31500 | 31500 |
| Total | 15 | 349500 |
Mean income = \(=\frac{\text { Total salary }}{\text { Number of workers }}\)
= \(\frac{349500}{15}\)
= 23,300
Therefore the mean salary of the workers = 23,300
Question 4.
The table below shows the daily wages of the workers in a firm. Calculate the mean daily wage.
| Daily wage (Rs) | Number of workers |
| 450 – 550 | 7 |
| 550 – 650 | 8 |
| 650 – 750 | 10 |
| 750 – 850 | 10 |
| 850 – 950 | 9 |
| 950 -1050 | 6 |
Answer:
| Daily wages (Rs) | Number of workers | Class interval | Total salary |
| 450-550 | 7 | 500 | 3500 |
| 550-650 | 8 | 600 | 4800 |
| 650 – 750 | 10 | 700 | 7000 |
| 750-850 | 10 | 800 | 8000 |
| 850-950 | 9 | 900 | 8100 |
| 950- 1050 | 6 | 1000 | 6000 |
| Total | 50 | 37,400 |
Mean value = \(\frac{\text { Total salary }}{\text { Number of workers }}\)
= \(\frac{37,400}{50}\)
= 748
Therefore the mean daily wage = 748