Tables in Statistics

||\text{Relative Frequency} = \dfrac{\text{Frequency}}{\text{Total frequency}} \times 100||

||\begin{gather}\text{Cumulative}\\\text{Relative Frequency}\end{gather}=\dfrac{\text{Cumulative frequency}}{\text{Total frequency}}\times100||

1. Determine the data

   In this distribution, the values of the ages are |12,| |13,| |14,| |15,| |16,| |17,| and |18| years old.

2. Determine the frequency of each data value

   To do so, the number of times each value occurs in the distribution is recorded in the table. A tally table (compilation table) can be used if needed.

   We then add them all together and find that there are |40| data values.

3. Calculate the cumulative frequency of each data value, as needed

   To find the cumulative frequency of a certain value, we add its frequency to the frequencies of all the preceding values.

   For the 1st row, which is the row with a value of |12| years, the cumulative frequency of people is equal to the frequency, which is |5.| For the 2nd row, the cumulative frequency equals |5+8,| or |13.| For the 3rd row, the cumulative frequency equals |13+7,| or |20.| The rest of the column is filled in the same way.

   There is no total to fill in for this column. However, we must make sure that the cumulative frequency of the last value correctly equals the total number of employees.

4. Calculate the relative frequency of each data value, as needed

   This is determined using the relative frequency formula for each value. Here is an example of how this is calculated for the value |14.|
   ||\begin{align}\text{Relative Frequency}&= \dfrac{\text{Frequency}}{\text{Total frequency}} \times 100\\ &=\dfrac{7}{40} \times 100\\ &= 17.5\ \%\end{align}||
   The total of this column should always equal |100\%.|

5. Calculate the cumulative relative frequency of each data value, as needed

   This is determined by using the cumulative relative frequency formula for each value. Here is an example of how this is calculated for the value |16.|
   ||\begin{align}\begin{gathered}\text{Cumulative}\\\text{Relative Frequency}\end{gathered}&= \dfrac{\text{Cumulative frequency}}{\text{Total frequency}} \times 100\\&=\dfrac{34}{40} \times 100\\ &\approx 85.0\ \%\end{align}||
   There is no total to fill in for this column. However, we must make sure that the cumulative relative frequency of the last value equals |100\%.|

1. Determine the classes by finding the class interval

   We separate the data into |6| classes. To find the class interval, we take the range of the distribution and divide it by the desired number of classes.
   ||\begin{align}\text{Class Interval}&=\dfrac{\text{Range of the distribution}}{\text{Number of classes}}\\ &=\dfrac{17.3-12.1}{6}\\&=\dfrac{5.2}{6}\\&=0.8\overline{6}\end{align}||
   The class interval is |0.8\overline{6}.| We choose a class interval of |1| and begin the classes at |12.|

2. Determine the frequency of each class

   To do so, we count the number of data in each class.

   Note: The data value |15.0| is placed in the class |[15,16[| and not in the |[14,15[| class.

   Then, we add up the data and find that there are indeed a total of |20| data values.

4. Calculate the relative frequency of each class, as needed

   This is done using the relative frequency formula for each class. Here is an example of how this is calculated for the |[15, 16[| class.
   ||\begin{align}\text{Relative Frequency}&= \dfrac{\text{Frequency}}{\text{Total frequency}} \times 100\\ &=\dfrac{7}{20} \times 100\\ &= 35\ \%\end{align}||
   This column should always have a total of |100\ \%.|