Final answer:
The mean and median of same data are 24 and 26 respectively. The value of mode is 26.
Step-by-step explanation:
To find the mode, we need to use the relationship between the mean, median, and mode. The mode is the value that occurs most frequently in a data set. Given that the mean is 24 and the median is 26, we can deduce that the data is negatively skewed. In a negatively skewed distribution, the mean is less than the median, which is less than the mode.
Let’s denote the mode as M. Since the mean is 24 and the median is 26, we have:
Mean = (Sum of all values) / (Number of values)
24 = (Sum of all values) / (Number of values)
Sum of all values = 24 * (Number of values)
Now, let’s assume there are n occurrences of the mode M. Then we have:
Median = M
26 = M
Since M is the mode and it occurs n times, we can express the sum of all values as:
Sum of all values = (n-1)M + M + (n-1)M
We already know that the sum of all values is 24 * (Number of values). Therefore:
24 * (Number of values) = (n-1)M + M + (n-1)M
24 * (Number of values) = 2nM
Now, since M = 26:
24 * (Number of values) = 52n
We also know that M occurs n times in the dataset. Therefore:
Mode = M = 26
This calculation shows that the value of mode is 26.