1   Give five examples of data that you can collect from day to day life.

Solution :

In our day to day life, we can collect the following data.$\\$ 1. Number of females per $1000$ males in various states of our country$\\$ 2. Weights of students of our class$\\$ 3. Production of wheat in the last $5$ years in our country$\\$ 4. Number of plants in our locality$\\$ 5. Rainfall in our city in the last $12$ months.

2   Classify the data in $Q1$ above as primary or secondary data.

Solution :

The information which is collected by the investigator himself with a definite objective in his mind is called as $\text{primary data}$ whereas when the information is gathered from a source which already had the information stored, it is called as $\text{secondary data.}$$\\$ It can be observed that the data in $1, 3,$ and $5$ is secondary data and the data in $2$ and $4$ is primary data.

3   The blood groups of 30 students of Class VIII are recoded 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 :

It can be observed that $9$ students have their blood group as $A, 6$ as $B, 3$ as $AB,$ and $12$ as $O.$ Therefore, the blood group of $30$ students of the class can be represented as follows.$\\$ It can be observed clearly that the most common blood group and the rarest blood group among these students is $O$ and $AB$ respectively as $12$ (maximum number of students) have their blood group as $O,$ and $3$ (minimum number of students) have their blood group as $AB.$

4   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 :

The given data is very large. So, we construct a group frequency of class size $5$.$\\$ Therefore the class interval will be $0-5,5-10,10-15$ and so on.$\\$ The data is represented in table as:$\\$ The classes in the table are not overlapping. Also, $36$ out of $40$ Engineers have their houses below $20km$ distance.

5   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 :

(i) A grouped frequency distribution table of class size $2$ has to be constructed. The class intervals will be $84-86, 86-88,$ and $88-90, ...$ By observing the data given above, the required table can be constructed as follows:$\\$ (ii) It can be observed that the relative humidity is high. Therefore, the data is about a month of rainy season.$\\$ (iii) Range of data = Maximum value - Minimum value$\\$ $= 99.2 - 84.9 = 14.3$