The mean and median of same data are 24 and 26 respectively. The value of mode is :a)26b)23c)25d)30Correct answer is option 'D'. Can you explain this answer?

Question

Answer

As we know,

3 median= mode + 2median

3×26=mode+(2×24)

78=mode+48

mode=78-48=30

so, mode=30

Answer

Answer

Given:
- Mean = 24
- Median = 26
- Mode = ?

Mean:
- The mean is the average of all the values in the data set.
- To find the mean, we sum up all the values and divide it by the total number of values.
- In this case, the mean is given as 24.

Median:
- The median is the middle value of a data set when it is arranged in ascending order.
- If there are an odd number of values, the median is the middle value.
- If there are an even number of values, the median is the average of the two middle values.
- In this case, the median is given as 26.

Mode:
- The mode is the value that appears most frequently in a data set.
- It is possible for a data set to have multiple modes if multiple values have the same highest frequency.
- The mode can be determined by looking at the frequency distribution of the data set.
- In this case, the mode is not given.

Explanation:
- Since the mode is not given, we need to find it based on the given mean and median.
- We know that the median is the middle value of the data set, and in this case, it is given as 26.
- The mean is the average of all the values in the data set, and it is given as 24.
- Since the median is higher than the mean, it indicates that there are some higher values in the data set.
- This means that the mode must be a value higher than both the mean and median in order to balance out the distribution of values.
- Among the given options, the only option higher than both the mean and median is option 'D' (30).
- Therefore, the correct answer is option 'D' (30) for the mode.

Summary:
- The mean of the data set is 24 and the median is 26.
- Since the median is higher than the mean, the mode must be a value higher than both the mean and median.
- Among the given options, the only value higher than both the mean and median is 30, so the mode is 30.

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