Alright, let's go through the problem systematically and solve it step-by-step.
1. Find the Mode of the Discrete Data:
- The mode is the value that appears most frequently in a data set.
- Let's list out the shoe sizes: 6, 7, 7, 8, 8, 8, 9, 9, 10.
- Let's count the occurrences of each value:
- Size 6 appears 1 time.
- Size 7 appears 2 times.
- Size 8 appears 3 times.
- Size 9 appears 2 times.
- Size 10 appears 1 time.
- Since size 8 appears the most frequently (3 times), the mode is 8.
2. Determine the Modal Size of the Shoes:
- From the above step, we have already determined that the modal size is 8.
3. Calculate the Mean from the Given Data:
- The mean (average) is calculated by adding all the values together and then dividing by the number of values.
- List of shoe sizes: 6, 7, 7, 8, 8, 8, 9, 9, 10.
- Sum of shoe sizes = 6 + 7 + 7 + 8 + 8 + 8 + 9 + 9 + 10 = 72.
- Number of shoe sizes = 9.
- Mean = Sum of shoe sizes / Number of shoe sizes = 72 / 9 = 8.
4. Find the Median Without Using the Cumulative Frequency:
- The median is the middle value when the data is arranged in ascending order.
- The data is already sorted: 6, 7, 7, 8, 8, 8, 9, 9, 10.
- Since there are 9 values (an odd number), the median is the middle value.
- The middle value is the 5th value (since it's the middle of 9 values).
- Counting to the 5th value: 6, 7, 7, 8, 8 (5th value).
- Therefore, the median is 8.
Summary:
- The mode of the shoe sizes is 8.
- The mean of the shoe sizes is 8.
- The median of the shoe sizes is 8.
