PSEB Solutions for Class 9 Maths Chapter 14 Statistics
PSEB 9th Class Maths Solutions Chapter 14 Statistics
Ex 14.1
Question 1.
Give five examples of data that you can collect from your day-to-day life.
Answer:
Five examples of data that can be collected from day-to-day life can be given as below:
- Election results obtained from newspapers or TV
- The number of different kinds of trees grown in our school.
- Amounts of invoices of electricity for last one year at our home.
- The number of students studying in different standards of our school.
- Percentage of marks scored at last examination by the students in our class.
Question 2.
Classify the data in Q. 1 above as primary or secondary data.
Answer:
Among the five data given as the answer to Q. 1, data no.
Primary data:
- The number of different kinds of trees grown in our school.
- Amounts of invoices of electricity for last one year at our home.
- Percentage of marks scored at last examination by the students in our class.
- primary data which we can collect ourselves.
Secondary data:
- Election results obtained from newspapers or TV
- The number of students studying in different standards of our school.
- Secondary data as they are received from the sources of the newspapers or TV or the office of our school.
Ex 14.2
Question 1.
The blood groups of 30 students of Class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,
A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students ?
Answer:
Frequency distribution table
From the frequency distribution table, it is very clear that the most common blood group is O and the rarest blood group is AB.
Question 2.
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?
Answer:
Grouped frequency distribution table
From the frequency distribution table, we can conclude that for the majority of engineers, s i.e., 31 engineers, the distance from their residence to their place to work is 5 km or more than 5 km but less than 20 km. For some engineers, i.e., 5 engineers, this distance is less than 5 km. Still, for some engineers, i.e., 4 engineers, this distance is 20 km or more than 20 km but less than 35 km.
Question 3.
The relative humidity (in %) of a certain city for a month of 30 days was as follows:
(i) Construct a grouped frequency distribution table with classes 84-86, 86 – 88, etc.
Answer:
(ii) Which month or season do you think this data is about ?
Answer:
During 24 days out of 30 days, the relative humidity is 92 % or more than 92 %. This suggests that the data must have been collected during Monsoon.
(iii) What is the range of this data ?
Answer:
Range of the data
= The greatest observation – The least observation
= 99.2 – 84.9
= 14.3
Question 4.
The heights of 50 students, measured to the nearest centimetres, have been found to be as follows:
(i) Represent the data given above by grouped frequency distribution table, taking the class intervals as 160 – 165, 165-170, etc.
Answer:
Grouped frequency distribution table
(ii) What can you conclude about their heights from the table?
Answer:
From the above frequency distribution, we can conclude that the height of 70 % students (35 students) is less than 165 cm while the height of only 10 % students (5 students) is 170 cm or more than that.
Question 5.
A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows :
(i) Make a grouped frequency distribution table for this data with class intervals as 0.00-0.04, 0.04-0.08, and so on.
Answer:
(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?
Answer:
The concentration of sulphur dioxide was more than 0.11 ppm for 8 days (2 + 4 + 2).
Question 6.
Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:
Prepare a frequency distribution table for the data given above.
Answer:
Question 7.
The value of π up to 50 decimal places is given below:
3.1415926535897932384626433832795028 8419716939937510
(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.
Answer:
Frequency distribution table
(ii) Which are the most and the least frequently occurring digits?
Answer:
The most frequently occurring digits are 3 and 9 (8 times each) and the least occurring digit is 0 (2 times).
Question 8.
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5-10.
Answer:
(ii) How many children watched television for 15 or more hours a week?
Answer:
Two children watched television for 15 or more hours a week.
Question 9.
A company manufactures car batteries of a Grouped frequency distribution table particular type. The lives (in years) of 40 such batteries were recorded as follows
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 – 2.5.
Answer:
Ex 14.3
Question 1.
A survey conducted by an organisation for the cause of illness and death among the women between the ages 15-44 (in years) worldwide, found the following figures (in %):
| Causes | Female fatality rate (%) |
| 1. Reproductive health conditions | 31.8 |
| 2. Neuropsychiatric conditions | 25.4 |
| 3. Injuries | 12.4 |
| 4. Cardiovascular conditions | 4.3 |
| 5. Respiratory conditions | 4.1 |
| 6. Other causes | 22.0 |
(i) Represent the information given above graphically.
Answer:
(ii) Which condition is the major cause of women’s ill health and death worldwide?
Answer:
‘Reproductive health conditions’ is the major cause of womens ill health and death worldwide.
(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.
Answer:
‘Malnutrition’ and ‘Lack of necessary medical facilities’ can be considered as two other factors which play a major role in female fatality.
Question 2.
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below:
| Section | Number of girls per thousand bays |
| Scheduled Caste (SC) | 940 |
| Scheduled Tribe (ST) | 970 |
| Non-SC/ST | 920 |
| Backward districts | 950 |
| Non-backward districts | 920 |
| Rural | 930 |
| Urban | 910 |
(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.
Answer:
Question 3.
Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
(i) Draw a bar graph to represent the polling results.
Answer:
Seats won by different political parties
(ii) Which political party won the maximum number of seats?
Answer:
Political party: A won the maximum number of seats.
Question 4.
The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:
| Length (in mm) | Number of leaves |
| 118-126 | 3 |
| 127-135 | 5 |
| 136-144 | 9 |
| 145-153 | 12 |
| 154-162 | .5 |
| 163-171 | 4 |
| 172-180 | 2 |
(i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous.]
(ii) Is there any other suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
Answer:
Making the class intervals continuous, we get the following table:
| Length (in mm) | Number of leaves |
| 117.5-126.5 | 3 |
| 126.5- 135.5 | 5 |
| 135.5-144.5 | 9 |
| 144.5-153.5 | 12 |
| 153.5- 162.5 | 5 |
| 162.5-171.5 | 4 |
| 171.5-180.5 | 2 |
(i) Length of leaves in millimetre
(ii) Yes. The given data can also be represented by ‘Frequency polygon’.
(iii) It is not correct to conclude that the maximum number of leaves are 153 mm long, because even if the frequency of class 145-153 is 12, we do not have the information about the length of each of those 12 leaves individually.
Question 5.
The following table gives the life times of 400 neon lamps:
| Life time (in hours) | Number of lamps |
| 300 – 400 | 14 |
| 400 – 500 | 56 |
| 500 – 600 | 60 |
| 600 – 700 | 86 |
| 700 – 800 | 74 |
| 800 – 900 | 62 |
| 900 – 1000 | 48 |
(i) Represent the given information with the help of a histogram.
Answer:
(ii) How many lamps have a life time of 700 hours or more than 700 hours ?
Answer:
The-frequencies of classes 700-800, 800-900 and 900-1000 are 74, 62 and 48 respectively.
Hence, the life time of 184 (74 + 62 + 48) lamps is 700 hours or more than 700 hours.
Question 6.
The following table gives the distribution of students of two sections according to the marks obtained by them:
Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
Answer:
To draw the frequency polygons of both the sections, we find the class marks of each class and prepare the following tables:
Section A
| Marks | Class mark | Frequency |
| 0-10 | 5 | 3 |
| 10-20 | 15 | 9 |
| 20-30 | 25 | 17 |
| 30-40 | 35 | 12 |
| 40-50 | 45 | 9 |
Section B
| Marks | Class mark | Frequency |
| 0-10 | 5 | 5 |
| 10-20 | 15 | 19 |
| 20-30 | 25 | 15 |
| 30-40 | 35 | 10 |
| 40-50 | 45 | 1 |
Comparing the performance of both the sections from the frequency polygons, we observe that the performance of students of section A is better than the performance of students of section B.
Question 7.
The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:
| Number of balls | Team A | Team B |
| 1-6 | 2 | 5 |
| 7-12 | 1 | 6 |
| 13-18 | 8 | 2 |
| 19-24 | 9 | 10 |
| 25-30 | 4 | 5 |
| 31-36 | 5 | 6 |
| 37-42 | 6 | 3 |
| 43-48 | 10 | 4 |
| 49-54 | 6 | 8 |
| 55-60 | 2 | 10 |
Represent the data of both the teams on the same graph by frequency polygons.
[Hint: First make the class intervals continuous.]
Answer:
Number of runs made by Team A and Team B in first 60 balls.
Question 8.
A random survey of the number of children of various age groups playing in a park was found as follows:
| Age (in years) | Number of children |
| 1-2 | 5 |
| 2-3 | 3 |
| 3-5 | 6 |
| 5-7 | 12 |
| 7-10 | 9 |
| 10-15 | 10 |
| 15-17 | 4 |
Draw a histogram to represent the data above.
Answer:
Children of various age groups playing in a park
Question 9.
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
| Number of letters | Number of surnames |
| 1-4 | 6 |
| 4-6 | 30 |
| 6-8 | 44 |
| 8-12 | 16 |
| 12-20 | 4 |
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.
Answer:
(i) Information regarding the number of surnames having given number of letters
Answer:
(ii) Write the class interval in which the maximum number of surnames lie.
Answer:
The maximum number of surnames lie in the class interval 6-8.
Ex 14.4
Question 1.
The following number of goals were scored by a team in a series of 10 matches:
2, 3. 4, 5, 0. 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.
Question 2.
In a mathematics test given to 15 students, the following marks (out of 100) are recorded :
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data.
Question 3.
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
Question 4.
Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.
Answer:
Here, just by simple observation, it is clearly seen that observation 14 occurs most frequently, i.e., 4 times.
Hence, the mode of the data is 14.
Question 5.
Find the mean salary of 60 workers of a factory from the following table:
Answer:
Question 6.
Give one example of a situation in which
(i) the mean is an appropriate measure of central tendency.
Answer:
For the students studying in the same class, usually their level of knowledge and understanding would be more or less equal. There would be a few student having this level low and there would be a few students having this level high. Their level of knowledge and understanding would be reflected in the marks scored by them at an examination. Hence, the mean of marks scored by them at an examination is an appropriate measure of central tendency.
(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
Answer:
If we consider the monthly income of the people of certain region, the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
MCQ
Multiple Choice Questions and Answer
Answer each question by selecting the proper alternative from those given below each question to make the statement true:
Question 1.
The marks scored by Kavya in 10 tests of Mathematics are 35, 18, 41, 24, 45, 10, 28, 32, 40, 15. Then, the range of the data is …………….. .
A. 45
B. 10
C. 35
D. 28.8
Answer:
C. 35
Question 2.
The average of the observations 3, 4, 5, 8, 12, 10, 13, 16, 18, 11 is …………………. .
A. 100
B. 10
C. 18
D. 3
Answer:
B. 10
Question 3.
The mean of first five odd natural numbers is ……………….. .
A. 3
B. 5
C. 4
D. 25
Answer:
B. 5
Question 4.
The mean of first four even natural numbers is ……………….. .
A. 5
B. 10
C. 20
D. 4
Answer:
A. 5
Question 5.
The mean of first five prime numbers is
A. 28
B. 2.8
C. 5.6
D. 1.4
Answer:
C. 5.6
Question 6.
If the mean of 2x, 5, 3x, 12, 5x, 17 and 6 is 20, then x = ………………….. .
A. 10
B. 20
C. 15
D. 40
Answer:
A. 10
Question 7.
The mean of the following distribution is ………………. .
A. 3.9
B. 7.8
C. 78
D. 39
Answer:
A. 3.9
Question 8.
If the mean of 12, 13, x, 17, 18 and 20 is 16, then x = ………………. .
A. 8
B. 4
C. 16
D. 32
Answer:
C. 16
Question 9.
For a given frequency distribution, n = 20 and Σf<sub>i</sub>x<sub>i</sub> = 140, then X̄ = ………………… .
A. 20
B. 14
C. 7
D. 28
Answer:
C. 7
Question 11.
The median of 14, 6, 2, 13, 9, 15 and 12 is …………………. .
A. 12
B. 10
C. 2
D. 15
Answer:
A. 12
Question 12.
The median of 21, 17, 13, 33, 19, 23 is ………………… .
A. 21
B. 20
C. 33
D. 19
Answer:
B. 20