UGC NET Questions (Paper – 1)

This option is correct because the mode is defined as the value that appears most often in a data set. It focuses on frequency rather than magnitude or order. In many practical situations, the mode represents the most common or popular value. Therefore, the most frequent value is called the mode.

Option A:
The mean is the arithmetic average of all values in the data set. It is obtained by summing all observations and dividing by the count. It does not specifically represent the most frequent value, so it is not the correct term here.

Option B:
The median is the middle value when the data are arranged in order. It divides the data into two equal halves but does not necessarily correspond to the most frequent observation. Hence, median is not the right answer.

Option C:
The range measures the spread of the data by subtracting the smallest value from the largest. It does not identify any particular value in terms of frequency. Therefore, range is unrelated to the notion of "most frequently occurring value."

Option D:
The mode is the observation with the highest frequency in the data. Datasets can have one mode, multiple modes or sometimes no mode if all values occur equally. Since the question focuses on the most frequent value, mode is the accurate term.

Statements A, B and C provide standard definitions of mean, median and mode. Statement E is also correct because in skewed distributions extreme values can distort the mean, making the median more representative. Statement D is false since equality of mean, median and mode holds only for certain symmetric distributions and not for every data set. Therefore, the combination A, B, C and E only is correct.

Option A:
Option A is correct as it collects all the accurate statements while leaving out D, which overgeneralises the equality of the three measures.

Option B:
Option B is incomplete because it omits E and therefore ignores the practical guidance on skewed data.

Option C:
Option C is wrong since it includes D, the false assertion about universal equality.

Option D:
Option D is wrong because it includes D and omits A, losing a core definition while keeping a false rule.

Statements A, B and E state standard facts about central tendency. A is correct because mean can lie left or right of the median in skewed distributions or coincide in symmetric cases. B is correct for perfectly symmetric unimodal distributions such as the normal distribution. E is correct since the median position splits an ordered data set into two halves with equal counts. C is false because mean and median need not always be equal, and D is false because mode may be non-unique or even absent, so A, B and E only is the correct combination.

Option A:
Option A is correct since it includes all and only the true statements: A about relative positions of mean and median, B about equality in symmetric unimodal distributions and E about the median’s partition property. It excludes C and D, both of which overstate what must always happen.

Option B:
Option B is incorrect because it adds C, which wrongly claims that median always equals mean for any data set. Including C introduces a false universal statement about equality of mean and median.

Option C:
Option C is wrong as it includes C again, making the set A, B, C, E contain one false member. A correct combination must consist entirely of true statements, so this option cannot be chosen.

Option D:
Option D is incorrect because it includes D, which asserts that the mode must always be unique. In reality, a distribution may be bimodal, multimodal or have no mode, so adding D makes this option incorrect.