# Class 9 NCERT Solutions- Chapter 14 Statistics – Exercise 14.2

**Problem 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.**

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**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?**

**Solution:**

Frequency:- No. of students having the same blood group.

Blood Group No. of Students A 9 B 6 AB 3 O 12 Total30 Most common blood group (highest frequency blood group) :- O

Rarest blood group (least frequency blood group) :- AB.

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

**5 3 10 20 25 11 13 7 12 31**

**19 10 12 17 18 11 32 17 16 2**

**7 9 7 8 3 5 12 15 18 3**

**12 14 2 9 6 15 15 7 6 12**

**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? **

**Solution:**

Grouped frequency distribution table of class size 5:

Distance (in Kms) Frequency 0-5 5 5-10 11 10-15 11 15-20 9 20-25 1 25-30 1 30-35 2 Total40 We observe that, most of the engineers live within 20 kms from their place of work. Only 4 employees out of 40 employees are living in between 20 and 35 kms from their place of work.

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

**98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1**

**89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3**

**96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89**

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

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

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

**Solution:**

(i)grouped frequency distribution table with classes 84 – 86, 86 – 88, etc….

Relative humidity (in %) Frequency 84-86 1 86-88 1 88-90 2 90-92 2 92-94 7 94-96 6 96-98 7 98-100 4 Total 30

(ii)In the most of days the humidity is very high, so this data should be from rainy season.

(iii)range of the data = maximum value in the data – minimum value in the data= 99.2 – 84.9

= 14.3

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

**161 150 154 165 168 161 154 162 150 151**

**162 164 171 165 158 154 156 172 160 170**

**153 159 161 170 162 165 166 168 165 164**

**154 152 153 156 158 162 160 161 173 166**

**161 159 162 167 168 159 158 153 154 159**

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

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

**Solution:**

(i)grouped frequency distribution table with classes 160 – 165, 165 – 170, etc…

Height (in cm) Frequency 150-155 12 155-160 9 160-165 14 165-170 10 170-175 5 Total50

(ii)from the above table we can tell that height of most of the students (35 students) is less than 165 cms.

**Problem 5: A study was conducted to find out the concentration of sulphur dioxide in the air in**

**2020-21 parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:**

**0.03 0.08 0.08 0.09 0.04 0.17**

**0.16 0.05 0.02 0.06 0.18 0.20**

**0.11 0.08 0.12 0.13 0.22 0.07**

**0.08 0.01 0.10 0.06 0.09 0.18**

**0.11 0.07 0.05 0.07 0.01 0.04**

**(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.**

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

**Solution:**

(i)grouped frequency distribution table with classes 0.00 – 0.04, 0.04 – 0.08, etc..

Concentration of sulphur dioxide in air

(in ppm)

Frequency 0.00-0.04 4 0.04-0.08 9 0.08-0.12 9 0.12-0.16 2 0.16-0.20 4 0.20-0.24 2 Total 30

(ii)concentration of sulphur dioxide was more than 0.11 parts per million for 8 days. ((2 + 4 + 2) days).

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

**0 1 2 2 1 2 3 1 3 0**

**1 3 1 1 2 2 0 1 2 1**

**3 0 0 1 1 2 3 2 2 0**

**Prepare a frequency distribution table for the data given above**

**Solution:**

Frequency distribution table:

No. of heads Frequency 0 6 1 10 2 9 3 5 Total30

**Problem 7: The value of **π** upto 50 decimal places is given below:**

**3.14159265358979323846264338327950288419716939937510**

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

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

**Solution:**

(i)frequency distribution table:-

Digit Frequency 0 2 1 5 2 5 3 8 4 4 5 5 6 4 7 4 8 5 9 8 Total 50

(ii)most frequently occurring digits : 3 & 9 (both occurred 8 times)least frequently occurring digits : 0 (occurred only twice).

**Problem 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 6 2 3 5 12 5 8 4 8**

**10 3 4 12 2 8 15 1 17 6**

**3 2 8 5 9 6 8 7 14 12**

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

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

**Solution:**

(i)grouped frequency distribution table with class width 5 :

No. of hours frequency 0-5 10 5-10 13 10-15 5 15-20 2 Total 30

(ii)from the above table, we can tell that only 2 children watched television for 15 or more hours a week.

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

**2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5**

**3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7**

**2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8**

**3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4**

**4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6**

**Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 – 2.5.**

**Solution:**

Grouped frequency distribution table with class intervals of size 0.5 starting from the interval 2 – 2.5:

life of battery (in years) Frequency 2-2.5 2 2.5-3 6 3-3.5 14 3.5-4 11 4-4.5 4 4.5-5 3 Total40