Home › Kerala SSLC (Class 10) › Mathematics › Statistics › For a set of numbers in arithmetic sequence, whi…
For a set of numbers in arithmetic sequence, which statement about the mean and median is true?
AThe mean is always greater than the median
BThe median is always greater than the mean
CTheir relationship depends on the common difference's sign
DThe mean and median are always equal
Answer & Solution
Correct answer: D. The mean and median are always equal
1. In an arithmetic sequence the values are symmetric about the central term(s).
2. The mean averages the endpoints, which equals the centre by symmetry.
3. The median picks the central value(s), also the centre by symmetry.
4. So mean and median coincide for any arithmetic sequence.
5. The unit lists this as a result to prove (Question 3 on page 245).
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
Related questions
A number measuring how far the data are spread from the mean is the standard:A histogram is pulled out towards the low values, so the distribution is described as:The value that appears most often in a data set is the:Fifty weights are added together and the total divided by fifty. The result is the:On a box plot, the two ends of the rectangular box are marked by:A box plot is built from the minimum, maximum, median and the two:The third quartile of a data set is the same as the percentile numbered:The median of a data set is the same as the percentile numbered: