## Chapter 14 Statistics Exercise 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?

Blood group O is the most common and blood group AB is the rarest among the students.

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?

From the above table we observe that:
• Frequencies of class intervals 5 - 10 and 10 - 15 are equal, i.e., 11 each. It shows that maximum number of engineers have their residences at 5 to 15 km away from their work place.
• Frequencies of class intervals 20 - 25 and 25 - 30 are also equal, i.e., 1 each. It shows that minimum number of engineers have their residences at 20 to 30 km away from their work place.

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?
:

ii) Since, the relative humidity is high, so, the data appears to be taken during the rainy season.
iii) Range = Highest observation - Lowest observation
Range = 99.2 – 84.9
= 14.3

Question 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?

i) As the lowest observation is 150 therefore we will start the class intervals with 150 i.e. 150 - 155.
As the highest observation is 173 therefore we will end the class intervals with 175 i.e. 170 - 175.

ii) From the frequency distribution table, we can conclude that more than 50% of the students are shorter than 165 cm.

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?

i)

ii) The concentration of sulphur dioxide was more than 0.11 ppm 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.

Question 7: The value of Ï€ 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?

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

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?

i)

ii) Only 2 children watched television for 15 hours or more in a 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 interval 2 - 2.5.