Question
Which of the following statements about the mean,
median, and mode is true when applied to a dataset with a skewed distribution?Solution
In a skewed distribution, the mean is heavily influenced by outliers or extreme values. For example, in a positively skewed distribution (right-skewed), where the tail is extended to the right, the mean will be greater than the median because the extreme high values push the mean to the right. The median, however, represents the middle value and is less affected by the extreme values, making it a more reliable measure of central tendency in skewed data. Therefore, the median is often preferred in the presence of outliers and skewness. The mode, while useful in some cases, does not always represent the center in skewed data and can sometimes be non-representative. Why Other Options Are Incorrect: • A: The mean, median, and mode are not equal in a skewed distribution. This occurs only in symmetric distributions like the normal distribution. • B: In a positively skewed distribution, the mean is greater than the median, not less. • C: While the mode represents the most frequent value, it is not always the most reliable measure of central tendency, particularly in skewed distributions. • E: The mode does not necessarily have to be greater than the median in skewed distributions.
If a man rows at the rate of 14 kmph in still water and his rate against the current is 5 kmph, then the man’s rate along the current is:<...
Speed of boat is 25 km/hr. Speed of the stream is 20% less than speed of boat. Then find time taken by boat to go 90 km downstream?
The ratio of the speed of boats ‘A’ and ‘B’ in still water is 8:9, respectively. The speed of the current is 25% of the speed of boat ‘A’ in...
A boat travels 240 km upstream in 6 hours and 360 km downstream in 6 hours. How long will it take to travel 300 km in still water?
A boat traveled 100 km downstream. The boat's speed in still water is 30 km/h, and the stream's speed is 10 km/h. Calculate the time required for the bo...
A motor boat goes downstream from point A to B ,which is 36 km away from point A, and then returns to A. If actual speed of the boat in still water is 7...
The speed of current is 10 km/hr. If the speed of the boat in still water had been 8 km/hr more than the original speed, then it would take 7 hours to c...
Speed of a boat in still water is 6 times more than the speed of stream. If boat covers 144 km in downstream in 9 hours, then find the time taken by the...
A man takes 10 hours to row 21 km upstream from point A to point B and back to A by boat. If he takes the same time to row 7 km downstream as upstream. ...
A boat covers a distance of 57 km upstream in 9.5 hours. If the boat's speed in still water had been doubled, it would have taken only 2 hours to cover...