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Question 1. Give five examples of data that you can collect from your day-to-day life?

Answer. Five examples from day-to-day life: 

1. The number of students enrolled in our class.

2. The number of fans in our school.

3. The cost of electricity in our home in the past two years. 

4. Election results data found on television or in publications. 

5. The Educational Survey data on literacy rates.

Question 2. Classify the data in Q.1 above as primary or secondary data?

Answer. The term "primary data" refers to information obtained by the investigator with a specific goal in mind. Examples 1, 2, and 3 have primary data.

Secondary data is information that has been acquired from a source that has already stored the data. Examples 4 and 5 have secondary data.

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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?

Answer. For the given data, "frequency" is the measure of the number of pupils that have the same blood group. The frequency is represented as follows in the frequency distribution table:

The blood group O is the most common. 

The blood group AB is the rarest and has the lowest frequency.

Question 2. The distances (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?

Answer. Due to the massive amount of data, we generate a grouped frequency distribution table with a class size of 5. The intervals between classes will be 0-5, 5-10, 10-15, and so on. In the table of grouped frequency distributions, the data is presented as follows:

There are no overlaps between the classes in the above table. It's also interesting to note that 36 of the 40 engineers live less than 20 kilometres from each other.

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?

Answer. (i) Since the given data is rather large, we generate a grouped frequency distribution table of class size 2. 

Therefore, the class intervals will be 84-86, 86-88, 88-90, 90-92 and so on. As in grouped frequency distribution table, the data is displayed as follows:

(ii) The data shows that the humidity in the city is extremely high. Since humidity is usually found to be high during the rainy season, the data below must be about the wet season. 

(iii) A data's range is defined as the greatest value of the data minus the minimum value of the data.

= 99.2 - 84.9 

= 14.3

Question 4. The heights of 50 students, measured to the nearest centimetres, were 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?

Answer. (i) A grouped frequency distribution table can be used to represent the data in the question, using class intervals of 160–165, 165–170, and so on, as follows:

(ii) The number of days with sulphur dioxide concentration greater than 0.11 parts per million = 2+4+2 = 8.

Question 6. Three coins were tossed 30 times simultaneously. The number of times heads occurred 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.

Answer. The frequency distribution of the data in the question is shown in the table below:

Question 7. The value of π up to 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?

Answer. (i) The frequency distribution of the digits 0 to 9 following the decimal point is summarised in the table below:

(ii) The digit with the lowest frequency is the one that appears the least. The frequency of 0 is 2 because it appears twice. As a result, 0 is the least common digit. 

The digit that appears the most frequently is the one with the highest frequency. It has an eight-fold frequency since the numbers 3 and 9 appear eight times. As a result, the numbers three and nine are the most frequently used.

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?

Answer. (i) The data in the question's grouped frequency distribution table is given below, with a class width of 5 and one of the class intervals set to 5–10:

(ii) We may extrapolate from the data that two children watched television for at least 15 hours per week.