A coin was tossed 20 times successively. Each time the number of heads occurring was noted down as follows:
$\begin{array}{l}
0,1,1,2,0,1,2,0,0,1,2,2,0,2,1,0,1,1, \
0,2
\end{array}$
Prepare a frequency distribution table for the given data.
Answer (2)
Count occurrences of each outcome: 0 heads (7 times), 1 head (8 times), 2 heads (5 times).
Create a frequency distribution table.
Present the data in a table with 'Number of Heads' and 'Frequency' columns.
The frequency distribution table is:
Number of Heads
Frequency
0
7
1
8
2
5
Explanation
Understand the problem and provided data We are given a set of data representing the number of heads obtained when tossing two coins 20 times. Our goal is to organize this data into a frequency distribution table, which will show how many times each possible outcome (0 heads, 1 head, or 2 heads) occurred.
Count the frequency of each outcome First, we need to count the number of times each outcome (0, 1, and 2 heads) appears in the given data set: 0, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0, 1, 1, 0, 2
Determine the frequencies Let's count the occurrences of each outcome:
0 heads: 1, 2, 3, 4, 5, 6, 7 times
1 head: 1, 2, 3, 4, 5, 6, 7, 8 times
2 heads: 1, 2, 3, 4, 5 times
Construct the frequency distribution table Now we can create the frequency distribution table. The table will have two columns: 'Number of Heads' and 'Frequency'.
Present the frequency distribution table The frequency distribution table is as follows:
Number of Heads
Frequency
0
7
1
8
2
5
Final Answer The frequency distribution table shows the number of times each possible outcome (0, 1, or 2 heads) occurred in the 20 coin tosses.
Examples
Frequency distribution tables are useful in many real-life scenarios. For example, if you were tracking the number of customers visiting a store each day, you could create a frequency distribution table to see how many days had a certain number of customers. This could help you understand trends and make staffing decisions. Similarly, in a classroom, a teacher could use a frequency distribution table to show the distribution of grades on a test.
The frequency distribution table based on the results from 20 coin tosses shows that 0 heads occurred 7 times, 1 head occurred 8 times, and 2 heads occurred 5 times. This table helps visualize the distribution of outcomes in the experiment. It provides insights into the likelihood of each result when tossing a coin.
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