## NCERT solutions for class 9 Maths

**Statistics**

**Chapter 14**

**Exercise 14.2**

**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?**

**Solution:**

The most common blood group is O. The rarest blood group is AB.

**Ex 14.2 Question 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:**

The class intervals are:

0 – 5, 5 – 10, 10 – 15, 15 – 20, 20 – 25, 25 – 30, 30 – 35

The required frequency distribution table is

According to distribution table, most of the engineers are living with in the 20km from the place of work.Only few are living on longer distance.

**Ex 14.2 Question 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:**

The lowest value of observation = 84.9

The highest value of observation = 99.2

So, class intervals are 84 – 86, 86 – 88, 88 – 90, ……. , 98 – 100

(i) Thus, the required frequency distribution table is

(ii) These data is related to raainy season beacuse the relative humidity is more.

(iii) Range = (Maximum humidity) – (Minimum humidity) = 99.2 – 84.9 = 14.3

**Ex 14.2 Question 4.**

**The heights of 50 students, measured to the nearest centimeters 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 class intervals as 160 – 165, 165 – 170 etc.**

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

**Solution:**

(i) The lowest value of the observation = 150

The highest value of the observation = 173

∴ Class intervals are 150 – 155, 155 -160, …, 170 – 175.

The required frequency distribution table is

(ii) More than 50% of the students have height less than 165 cm.

**Ex 14.2 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**

**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 day’s was the the concentration of sulphur dioxide more than 0.11 parts per million ?**

**Solution:**

(i) The lowest value of the observation = 0.01

The highest value of the observation = 0.22

∴ Class intervals are 0.00 – 0.04, 0.04 – 0.08,……., 0.20 – 0.24

The frequency distribution table

(ii) In 8 days , the concentration of sulphur dioxide was more than 0.11 parts per million.

**Ex 14.2 Question 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:**

The frequency distribution table

**Ex 14.2 Question 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) The frequency distribution table

(ii) 3 and 9 are the most occurring digits and 0 is the least frequently occurring digit.

**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**

**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) The lowest value of the observation = 1 and the highest value of the observation = 17

∴ Class intervats are 0 – 5, 5 – 10 ., 15 – 20

The frequency distribution table is

(ii) Only 2 children watched television for 15 or more hours a week.

**Ex 14.2 Question 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:**

Here, the lowest value of the observation = 2.2

and the highest value of the observation = 4.6

∴ Class intervals are 2.0 – 2.5, 2.5 – 3.0, …., 4.5 – 5.0

The required frequency distribution table is