Question

Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows
 \[\begin{array}{*{20}{c}}
  0&1&2&2&1&2&3&1&3&0 \\
  1&3&1&1&2&2&0&1&2&1 \\
  3&0&0&1&1&2&3&2&2&0
\end{array}\]
Prepare a frequency distribution table for the data given above.

Answer 1

Hint: Three coins were tossed 30 times simultaneously. The number of heads occurring was noted as above. As we can see there are 30 outcomes (numbers) of head occurring. For this we need to draw frequency distribution. There are four possibilities of the number of heads that are 0, 1, 2 and 3.

Complete step-by-step answer:
Now, as we can see in the data that there are four possibilities of heads occurring.
 \[\begin{array}{*{20}{c}}
  0&1&2&2&1&2&3&1&3&0 \\
  1&3&1&1&2&2&0&1&2&1 \\
  3&0&0&1&1&2&3&2&2&0
\end{array}\]
We need to note the frequency for each possibility.
The four possibilities are 0, 1, 2 and 3.
For 0, count how many times that zero heads are there in the given data.
 \[ \Rightarrow \] 6 times of zero heads.
For 1, count how many times that one head is there in the given data.
 \[ \Rightarrow \] We have 10 times of one head.
For 2, count how many times that two heads are there in the given data.
 \[ \Rightarrow \] We have 9 times of two heads.
For 3, count how many times that three heads are there in the given data.
 \[ \Rightarrow \] We have 5 times of three heads.
Using this we can write frequency distribution table:

Number of Heads	Frequency
0	6
1	10
2	9
3	5
Total	=30

Note: Since they give the only outcomes of head occurring while tossing three coins simultaneously. Simply count the number of outcomes for each possibility (number of heads), and note those values in the tabular column as we did above. The frequency of an observation tells you the number of times the observation occurs in the data.