NCERT Solutions for Class 9 Maths Chapter 14 Statistics Exercise 14.2

Exercise 14.2

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?

Ans: From the question we can observe that the students having blood group $A$ are $9$, students having blood group $B$ are $6$, students having blood group $AB$ are $3$ and the students having blood group $O$ are $12$.

Its table will be of the form:

From the table we can observe that the blood group $O$ is the most common and the blood group $AB$ is the rarest.

2. The distance (in km) of $40$ engineers from their residence to their place of work were found as follows: 

\[\begin{align} & \mathbf{5}\text{ }\mathbf{3}\text{ }\mathbf{10}\text{ }\mathbf{20}\text{ }\mathbf{25}\text{ }\mathbf{11}\text{ }\mathbf{13}\text{ }\mathbf{7}\text{ }\mathbf{12}\text{ }\mathbf{31}\text{ }\mathbf{19}\text{ }\mathbf{10}\text{ }\mathbf{12}\text{ }\mathbf{17}\text{ }\mathbf{18}\text{ }\mathbf{11}\text{ }\mathbf{32}\text{ }\mathbf{17}\text{ }\mathbf{16}\text{ }\mathbf{2}\text{ }\mathbf{7}\text{ }\mathbf{9}\text{ }\mathbf{7}\text{ }\mathbf{8}\text{ }\mathbf{3}\text{ }\mathbf{5}\text{ }\mathbf{12}\text{ }\mathbf{15}\text{ }\mathbf{18}\text{ } \\ & \mathbf{3}\text{ }\mathbf{12}\text{ }\mathbf{14}\text{ }\mathbf{2}\text{ }\mathbf{9}\text{ }\mathbf{6}\text{ }\mathbf{15}\text{ }\mathbf{15}\text{ }\mathbf{7}\text{ }\mathbf{6}\text{ }\mathbf{12} \\ \end{align}\]

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 feature do you observe from this tabular representation?

Ans: The grouped frequency distribution table with class size $5$ for the given data will be:

From the table representation above, we can observe that most of the engineers from their residence to the place they work lies below and between the range of $15-20$.

3. The relative humidity (in %) of a certain city for a month of $30$ days was as follows: 

\[\begin{align} & \mathbf{98}.\mathbf{1}\text{ }\mathbf{98}.\mathbf{6}\text{ }\mathbf{99}.\mathbf{2}\text{ }\mathbf{90}.\mathbf{3}\text{ }\mathbf{86}.\mathbf{5}\text{ }\mathbf{95}.\mathbf{3}\text{ }\mathbf{92}.\mathbf{9}\text{ }\mathbf{96}.\mathbf{3}\text{ }\mathbf{94}.\mathbf{2}\text{ }\mathbf{95}.\mathbf{1}\ \ \mathbf{89}.\mathbf{2}\text{ }\mathbf{92}.\mathbf{3}\text{ }\mathbf{97}.\mathbf{1}\text{ }\mathbf{93}.\mathbf{5}\text{ }\mathbf{92}.\mathbf{7}\text{ }\mathbf{95}.\mathbf{1}\text{ } \\ & \mathbf{97}.\mathbf{2}\text{ }\mathbf{93}.\mathbf{3}\text{ }\mathbf{95}.\mathbf{2}\text{ }\mathbf{97}.\mathbf{3}\text{ }\mathbf{96}.\mathbf{2}\text{ }\mathbf{92}.\mathbf{1}\text{ }\mathbf{84}.\mathbf{9}\text{ }\mathbf{90}.\mathbf{2}\text{ }\mathbf{95}.\mathbf{7}\text{ }\mathbf{98}.\mathbf{3}\text{ }\mathbf{97}.\mathbf{3}\text{ }\mathbf{96}.\mathbf{1}\text{ }\mathbf{92}.\mathbf{1}\text{ }\mathbf{89} \\ \end{align}\]

(i). Construct a grouped frequency distribution table with classes $84-86,86-88$ etc.

Ans: The grouped frequency distribution table with classes $84-86,86-88$ and so on will be of the form:

(ii). Which month or season do you think this data is about?

Ans: As, the humidity is very high in percentage, hence the data could be of the monsoon season in the month of June – July.

(iii). What is the range of this data?

Ans: The range of the data can be calculated by $Range=Maximum\ value-Minimum\ value$

$\Rightarrow 99.2-84.9=14.3$

4. The heights of 50 students, measured to the nearest centimetres, have been found to be as follows: 

\[\begin{align} & \mathbf{161}\text{ }\mathbf{150}\text{ }\mathbf{154}\text{ }\mathbf{165}\text{ }\mathbf{168}\text{ }\mathbf{161}\text{ }\mathbf{154}\text{ }\mathbf{162}\text{ }\mathbf{150}\text{ }\mathbf{151}\text{ }\mathbf{162}\text{ }\mathbf{164}\text{ }\mathbf{171}\text{ }\mathbf{165}\text{ }\mathbf{158}\text{ }\mathbf{154}\text{ } \\ & \mathbf{156}\text{ }\mathbf{172}\text{ }\mathbf{160}\text{ }\mathbf{170}\text{ }\mathbf{153}\text{ }\mathbf{159}\text{ }\mathbf{161}\text{ }\mathbf{170}\text{ }\mathbf{162}\text{ }\mathbf{165}\text{ }\mathbf{166}\text{ }\mathbf{168}\text{ }\mathbf{165}\text{ }\mathbf{164}\text{ }\mathbf{154}\text{ }\mathbf{152}\text{ } \\ & \mathbf{153}\text{ }\mathbf{156}\text{ }\mathbf{158}\text{ }\mathbf{162}\text{ }\mathbf{160}\text{ }\mathbf{161}\text{ }\mathbf{173}\text{ }\mathbf{166}\text{ }\mathbf{161}\text{ }\mathbf{159}\text{ }\mathbf{162}\text{ }\mathbf{167}\text{ }\mathbf{168}\text{ }\mathbf{159}\text{ }\mathbf{158}\text{ }\mathbf{153}\text{ }\mathbf{154}\text{ }\mathbf{159} \\ \end{align}\]

(i). Represent the data given above by a grouped frequency distribution table, taking the class intervals as $160-165,165-170$, etc. 

Ans: The grouped frequency distribution table, taking the class intervals as $160-165,165-170$, etc will be of the form:

(ii). What can you conclude about their heights from the table?

Ans: We can conclude from the table that almost $70%$ of the students have height less than $165cm$.

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: 

\[\begin{align} & \mathbf{0}.\mathbf{03}\text{ }\mathbf{0}.\mathbf{08}\text{ }\mathbf{0}.\mathbf{08}\text{ }\mathbf{0}.\mathbf{09}\text{ }\mathbf{0}.\mathbf{04}\text{ }\mathbf{0}.\mathbf{17}\text{ }\mathbf{0}.\mathbf{16}\text{ }\mathbf{0}.\mathbf{05}\text{ }\mathbf{0}.\mathbf{02}\text{ }\mathbf{0}.\mathbf{06}\text{ }\mathbf{0}.\mathbf{18}\text{ }\mathbf{0}.\mathbf{20}\text{ }\mathbf{0}.\mathbf{11}\text{ }\mathbf{0}.\mathbf{08}\text{ }\mathbf{0}.\mathbf{12}\text{ } \\ & \mathbf{0}.\mathbf{13}\text{ }\mathbf{0}.\mathbf{22}\text{ }\mathbf{0}.\mathbf{07}\text{ }\mathbf{0}.\mathbf{08}\text{ }\mathbf{0}.\mathbf{01}\text{ }\mathbf{0}.\mathbf{10}\text{ }\mathbf{0}.\mathbf{06}\text{ }\mathbf{0}.\mathbf{09}\text{ }\mathbf{0}.\mathbf{18}\text{ }\mathbf{0}.\mathbf{11}\text{ }\mathbf{0}.\mathbf{07}\text{ }\mathbf{0}.\mathbf{05}\text{ }\mathbf{0}.\mathbf{07}\text{ }\mathbf{0}.\mathbf{01}\text{ }\mathbf{0}.\mathbf{04} \\ \end{align}\]

(i). Make a grouped frequency distribution table for this data with class intervals as \[\mathbf{0}.\mathbf{00}\mathbf{0}.\mathbf{04},\text{ }\mathbf{0}.\mathbf{04}\mathbf{0}.\mathbf{08}\], and so on.

Ans: The grouped frequency distribution table for this data with class intervals as $0.00-0.04,\ 0.04-0.08$, and so on will be of the form:

(ii).For how many days, was the concentration of sulphur dioxide more than $0.11$ parts per million?

Ans: From the table we can observe that the concentrations of sulphur dioxide that are more than $0.11$ are $0.12-0.16,\ 0.16-0.20$ and $0.20-0.24$. Hence, the number of days the concentration is more than $0.11$ will be –

$2+4+2=8\ days$.

6. Three coins were tossed $30$ times simultaneously. Each time the number of heads occurring was noted down as follows: 

\[\mathbf{0}\text{ }\mathbf{1}\text{ }\mathbf{2}\text{ }\mathbf{2}\text{ }\mathbf{1}\text{ }\mathbf{2}\text{ }\mathbf{3}\text{ }\mathbf{1}\text{ }\mathbf{3}\text{ }\mathbf{0}\text{ }\mathbf{1}\text{ }\mathbf{3}\text{ }\mathbf{1}\text{ }\mathbf{1}\text{ }\mathbf{2}\text{ }\mathbf{2}\text{ }\mathbf{0}\text{ }\mathbf{1}\text{ }\mathbf{2}\text{ }\mathbf{1}\text{ }\mathbf{3}\text{ }\mathbf{0}\text{ }\mathbf{0}\text{ }\mathbf{1}\text{ }\mathbf{1}\text{ }\mathbf{2}\text{ }\mathbf{3}\text{ }\mathbf{2}\text{ }\mathbf{2}\text{ }\mathbf{0}\]

Prepare a frequency distribution table for the data given above.

Ans: From the given data, the frequency distribution table will be in the form: 

7. The value of $\pi $ up to $50$ decimal places is given below: \[\mathbf{3}.\mathbf{14159265358979323846264338327950288419716939937510}\]

(i). Make a frequency distribution of the digits from $0\ to\ 9$ after the decimal point.

Ans: The frequency distribution table of the digits from $0\ to\ 9$ after the decimal point will be of the form:

(ii). What are the most and the least frequently occurring digits?

Ans: The most frequently occurring digits are $3$ and $9$ with frequency $8$ and the least frequently occurring digit is $0$.

8. Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows: 

\[1\ \ \mathbf{6}\text{ }\mathbf{2}\text{ }\mathbf{3}\text{ }\mathbf{5}\text{ }\mathbf{12}\text{ }\mathbf{5}\text{ }\mathbf{8}\text{ }\mathbf{4}\text{ }\mathbf{8}\text{ }\mathbf{10}\text{ }\mathbf{3}\text{ }\mathbf{4}\text{ }\mathbf{12}\text{ }\mathbf{2}\text{ }\mathbf{8}\text{ }\mathbf{15}\text{ }\mathbf{1}\text{ }\mathbf{17}\text{ }\mathbf{6}\text{ }\mathbf{3}\text{ }\mathbf{2}\text{ }\mathbf{8}\text{ }\mathbf{5}\text{ }\mathbf{9}\text{ }\mathbf{6}\text{ }\mathbf{8}\text{ }\mathbf{7}\text{ }\mathbf{14}\text{ }\mathbf{12}\]

(i). Make a grouped frequency distribution table for this data, taking class width $5$ and one of the class intervals as $5-10$.

Ans: The grouped frequency distribution table for the data given taking class width $5$ and one of the class intervals as $5-10$ will be of the form:

(ii). How many children watched television for $15$ or more hours a week?

Ans: From the table above, we can observe that the number of children who watched television for $15$ or more hours a week is $2$.

9: A company manufactures car batteries of a particular type. The lives (in years) of $40$ such batteries were recorded as follows: 

\[\begin{align} & \mathbf{2}.\mathbf{6}\text{ }\mathbf{3}.\mathbf{0}\text{ }\mathbf{3}.\mathbf{7}\text{ }\mathbf{3}.\mathbf{2}\text{ }\mathbf{2}.\mathbf{2}\text{ }\mathbf{4}.\mathbf{1}\text{ }\mathbf{3}.\mathbf{5}\text{ }\mathbf{4}.\mathbf{5}\text{ }\mathbf{3}.\mathbf{5}\text{ }\mathbf{2}.\mathbf{3}\text{ }\mathbf{3}.\mathbf{2}\text{ }\mathbf{3}.\mathbf{4}\text{ }\mathbf{3}.\mathbf{8}\text{ }\mathbf{3}.\mathbf{2}\text{ }\mathbf{4}.\mathbf{6}\text{ }\mathbf{3}.\mathbf{7}\text{ }\mathbf{2}.\mathbf{5}\text{ }\mathbf{4}.\mathbf{4}\text{ }\mathbf{3}.\mathbf{4}\text{ }\mathbf{3}.\mathbf{3}\text{ } \\ & \mathbf{2}.\mathbf{9}\text{ }\mathbf{3}.\mathbf{0}\text{ }\mathbf{4}.\mathbf{3}\text{ }\mathbf{2}.\mathbf{8}\text{ }\mathbf{3}.\mathbf{5}\text{ }\mathbf{3}.\mathbf{2}\text{ }\mathbf{3}.\mathbf{9}\text{ }\mathbf{3}.\mathbf{2}\text{ }\mathbf{3}.\mathbf{2}\text{ }\mathbf{3}.\mathbf{1}\text{ }\mathbf{3}.\mathbf{7}\text{ }\mathbf{3}.\mathbf{4}\text{ }\mathbf{4}.\mathbf{6}\text{ }\mathbf{3}.\mathbf{8}\text{ }\mathbf{3}.\mathbf{2}\text{ }\mathbf{2}.\mathbf{6}\text{ }\mathbf{3}.\mathbf{5}\text{ }\mathbf{4}.\mathbf{2}\text{ }\mathbf{2}.\mathbf{9}\text{ }\mathbf{3}.\mathbf{6} \\ \end{align}\]Construct a grouped frequency distribution table for this data, using class intervals of size \[\mathbf{0}.\mathbf{5}\] starting from the intervals \[\mathbf{2}-\mathbf{2}.\mathbf{5}\].

Ans: The grouped frequency distribution table for the given data using the class intervals of size $0.5$ starting from the intervals $2-2.5$.

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Exercise 14.2

Opting for the NCERT solutions for Ex 14.2 Class 9 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 14.2 Class 9 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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