- The dataset contains 20 observations ranging from 1 to 8 hours.
- Each unique value is counted to determine its frequency within the study hours data.
- The frequencies are: \(f(1)=2, f(2)=3, f(3)=4, f(4)=3, f(5)=4, f(6)=2, f(7)=1, f(8)=1\).
- The completed frequency table is represented as: \(\boxed{\text{Table constructed}}\).
Explanation
- Analyze the dataset
To create the frequency table, we first identify the unique values for "Hours studied" in the provided dataset: {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8}. These values are 1, 2, 3, 4, 5, 6, 7, and 8. The total number of observations is 20. We will count how many times each value appears in the list.
- Count frequencies for each category
Now, we count the occurrences (Frequency) for each value:
- For 1: Appears 2 times.
- For 2: Appears 3 times.
- For 3: Appears 4 times.
- For 4: Appears 3 times.
- For 5: Appears 4 times.
- For 6: Appears 2 times.
- For 7: Appears 1 time.
- For 8: Appears 1 time.
Total count: \(2 + 3 + 4 + 3 + 4 + 2 + 1 + 1 = 20\). This confirms our count matches the dataset size.
- Construct the frequency table
Using the frequencies determined, we construct the table. For the 'Tally' column, we represent each frequency with tally marks, where 5 is written as four vertical bars with a diagonal line through them.
\[ \begin{array}{|l|l|l|} \ \text{Hours studied} & \text{Tally} & \text{Frequency} \\ 1 & || & 2 \\ 2 & ||| & 3 \\ 3 & |||| & 4 \\ 4 & ||| & 3 \\ 5 & |||| & 4 \\ 6 & || & 2 \\ 7 & | & 1 \\ 8 & | & 1 \\ \end{array} \]
Examples
Frequency tables are widely used in data analysis to quickly understand the distribution of a dataset. For example, a teacher might use this to see how many students studied for a specific number of hours before an exam, helping them identify trends or areas where students might need more support. This method simplifies raw data into a readable format for easier decision-making.