# Class 9 Maths NCERT Solution for statistics part 1

In this page we have NCERT book Solutions for Class 9th Maths:statistics for EXERCISE 1 . Hope you like them and do not forget to like , social share and comment at the end of the page.

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 number of students who have a certain type of blood group is called frequency of the blood group

The below Frequency distribution is prepared

 Blood Group Frequency A 9 B 6 O 12 AB 3

We can clearly see from the frequency distribution table that blood group AB is the rarest and blood group O is the most common.

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 feature do you observe from this tabular representation?

Solution:

It is given that a grouped frequency distribution table of class size 5 has to be constructed. Therefore, the class intervals will be 0 − 5, 5 − 10, 10 − 15, 15 −20…

By observing the data given as above, a grouped frequency distribution table can be constructed as follows.

 Class (Distance) Frequency 0-5 5 5-10 11 10-15 11 15-20 9 20-25 1 25-30 1 30-35 2

It can be observed that there are very few engineers whose homes are at more than or equal to 20 km distance from their work place. Most of the engineers have their workplace up to 15 km distance from their homes.

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

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

(iii)  What is the range of this data?

Solution:

Class intervals will be as follows 84 - 86, 86 - 88, and 88 - 90... ...

 Relative humidity Frequency in days 84-86 1 86-88 1 88-90 2 90-92 2 92-94 7 94-96 6 96-98 7 98-100 4

ii) Since relative humidity is high so the data must be of a month of rainy season.

(iii)    Range of data = maximum value - minimum value

= 99.2 - 84.9

= 14.3

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 the class intervals as 160 - 165, 165 - 170, etc.

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

Solution:

Class intervals will be as follows 160 - 165, 165 - 170, etc.

 Heights Frequency 150-155 12 155-160 9 160-165 14 165-170 10 170-175 5

It is clear from the table, out of 50 students, 35 are below 165 cm.  So 50%of the students are below 165cm

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 0.2 0.11 0.08 0.12 0.13 0.22 0.07 0.08 0.01 0.1 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

Frequency distribution

 Interval Frequency .00-.04 4 .04-.08 9 .08 - .12 9 .12- .16 2 .16-.20 4 .20-.24 2

ii)The concentration of sulphur dioxide was more than 0.11 parts per million for 8 days.

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

Frequency table

 Number  of heads Frequency 0 6 1 10 2 9 3 5

Question 7:

The value of π up to50 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:

 Digits Frequency 0 2 1 5 2 5 3 8 4 4 5 5 6 4 7 4 8 5 9 8

(ii)    From the above table the least frequency is 2 of digit 0, and the maximum frequency is 8 of digit 3 and 9. So, the most frequently occurring digits are 3 and 9 and the least occurring digit is 0.

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 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) Frequency table

 Number of hours Frequency 0-5 10 5-10 13 10-15 5 15-20 2

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

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 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 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 intervals 2 − 2.5.

Solution:

Frequency distribution

 Lives of battery Number of batteries 2-2.5 2 2.5 -3.0 6 3.0 – 3.5 14 3.5-4.0 11 4.0 -4.5 4 4.5 – 5.0 3