**Statistics**

**Question 1.The blood groups of 30 students of class VIII are recorded as followsA, 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, ORepresent 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 required frequency distribution table is

From the above table, we have The most common blood group is O. The rarest blood group is AB.

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

**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:**

Here, the observation with minimum and maximum values are 2 and 32 respectively.

∴ The class intervals are as follows:

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

The required frequency distribution table is

From the above table we observe that:

(i) 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.

(ii) 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**

**(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:**

Here, 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) Since, the relative humidity is high during the rainy season, so, the data appears to be taken in the rainy season.

(iii) Range = (Highest observation) – (Lowest observation) = 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**

**(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) Here, 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) From the above 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**

**(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) Here, 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 required frequency distribution table is

(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**

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

**Solution:**

The required frequency distribution table is

**Question 7.The value of π upto 50 decimal places is given below3.14159265358979323846264338327950288419716939937510**

**(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 required frequency distribution table

(ii) The most frequently occurring digits are 3 and 9 and the least frequently 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(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) Here, 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 required frequency distribution table is

(ii) Number of children who watched television for 15 or more hours in a week = 2.

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

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