Step 1: Understanding the Concept:
The mode of a set of data is the value that appears most frequently.
Step 2: Key Formula or Approach:
1. Tally the frequency of each number in the dataset.
2. Identify the number with the highest frequency.
Step 3: Detailed Explanation:
The given dataset is: 8, 7, 9, 3, 9, 5, 4, 5, 7, 5.
Let's count the occurrences of each number:
- 3: appears 1 time
- 4: appears 1 time
- 5: appears 3 times
- 6: appears 0 times
- 7: appears 2 times
- 8: appears 1 time
- 9: appears 2 times
The number 5 appears most often (3 times).
Step 4: Final Answer:
The mode of the dataset is 5.
| Class | 0 – 15 | 15 – 30 | 30 – 45 | 45 – 60 | 60 – 75 | 75 – 90 |
|---|---|---|---|---|---|---|
| Frequency | 11 | 8 | 15 | 7 | 10 | 9 |
Let the Mean and Variance of five observations $ x_i $, $ i = 1, 2, 3, 4, 5 $ be 5 and 10 respectively. If three observations are $ x_1 = 1, x_2 = 3, x_3 = a $ and $ x_4 = 7, x_5 = b $ with $ a>b $, then the Variance of the observations $ n + x_n $ for $ n = 1, 2, 3, 4, 5 $ is
Find the mean of the following distribution:
\[\begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Class-interval} & 11-13 & 13-15 & 15-17 & 17-19 & 19-21 & 21-23 & 23-25 \\ \hline \text{Frequency} & \text{7} & \text{6} & \text{9} & \text{13} & \text{20} & \text{5} & \text{4} \\ \hline \end{array}\]