Questions: Construct a grouped frequency distribution for the data. Use 85-89 for the first class and use width for each subsequent class. Class Frequency 85-89 7 90 - 94 95 5 100 - 104 105 - 109 110 - 114 115 119 8

Solution Steps

Let the data set be defined as: \[ \text{data} = \{85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119\} \] The class intervals are defined as: \[ \text{class\_intervals} = \{(85, 89), (90, 94), (95, 99), (100, 104), (105, 109), (110, 114), (115, 119)\} \]

Create a frequency distribution dictionary to count the number of data points in each class interval: \[ \text{frequency\_distribution} = \{(85, 89): 0, (90, 94): 0, (95, 99): 0, (100, 104): 0, (105, 109): 0, (110, 114): 0, (115, 119): 0\} \]

For each data point \( x \) in the data set, determine which class interval it belongs to and increment the corresponding frequency:

• For \( x \in [85, 89] \), increment frequency of \( (85, 89) \)
• For \( x \in [90, 94] \), increment frequency of \( (90, 94) \)
• For \( x \in [95, 99] \), increment frequency of \( (95, 99) \)
• For \( x \in [100, 104] \), increment frequency of \( (100, 104) \)
• For \( x \in [105, 109] \), increment frequency of \( (105, 109) \)
• For \( x \in [110, 114] \), increment frequency of \( (110, 114) \)
• For \( x \in [115, 119] \), increment frequency of \( (115, 119) \)

After counting, the frequency distribution is summarized as follows: \[ \begin{align_} (85, 89) & : 5 \\ (90, 94) & : 5 \\ (95, 99) & : 5 \\ (100, 104) & : 5 \\ (105, 109) & : 5 \\ (110, 114) & : 5 \\ (115, 119) & : 5 \\ \end{align_} \]

This completes the construction of the grouped frequency distribution for the given data.

Final Answer