A shopkeeper is recording the stock of shoes he has in his shop:

How can we find the mode of the discrete data?

A. Determine the modal size of the shoes.
B. Calculate the mean from the given data.
C. Find the median without using the cumulative frequency.



Answer :

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.