PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 14 Statistics Ex 14.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 14 Statistics 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
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 1
From the frequency distribution table, it is very clear that the most common blood group is O and the rarest blood group is AB.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

Question 2.
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 2
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
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 3
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.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

Question 3.
The relative humidity (in %) of a certain city for a month of 30 days was as follows:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 4
(i) Construct a grouped frequency distribution table with classes 84-86, 86 – 88, etc.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 5

(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

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

Question 4.
The heights of 50 students, measured to the nearest centimetres, have been found to be as follows:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 6

(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
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 7

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

(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 :
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 8

(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:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 9

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

(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:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 10
Prepare a frequency distribution table for the data given above.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 11

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

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
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 12

(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).

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

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:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 13
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5-10.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 14

(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.

PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2

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
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 15
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 – 2.5.
Answer:
PSEB 9th Class Maths Solutions Chapter 14 Statistics Ex 14.2 16

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