UGC NET Questions (Paper – 1)

This option is correct because the arithmetic mean of two numbers is obtained by adding them and dividing by 2. Here, (10 + 20) ÷ 2 = 30 ÷ 2 = 15. This value lies exactly midway between 10 and 20. Therefore, the arithmetic mean is 15.

Option A:
Taking 10 as the mean would ignore the contribution of the larger number 20. The average must be between the two numbers and balanced by both. Since 10 is at the lower end, it cannot be the mean of 10 and 20.

Option B:
A value of 12 is between 10 and 20 but does not satisfy the mean formula. Using (10 + 20) ÷ 2 does not produce 12. Therefore, this number does not represent the correct arithmetic mean.

Option C:
20 is the larger of the two numbers and would be the mean only if both numbers were 20. Because the other number is 10, the mean must lie between 10 and 20, not at the greater endpoint. Thus, 20 is incorrect.

Option D:
The average 15 comes directly from the formula for mean and is equidistant from 10 and 20. It balances the two values, which is the key idea of an arithmetic mean. Hence, this option correctly answers the question.

The mean is calculated by summing all scores and dividing by the number of observations, so every value contributes to its magnitude. As a result, extremely high or low scores can pull the mean toward them, distorting its representation of the typical value. This sensitivity makes the mean less robust in skewed distributions. Because the stem asks for the measure most affected by extreme scores, mean is the correct answer.

Option A:
Median is based on the middle position of ordered scores and is largely unaffected by the exact values of extremes, as long as their positions do not change. It is therefore more robust to outliers than the mean. Hence, median does not match the property described in the stem.

Option B:
Mean provides useful information in symmetric distributions with few outliers but becomes misleading when the data are highly skewed, such as income distributions. In such cases, median or trimmed means are often preferable. The strong impact of extreme scores on mean corresponds to the statement in the question, confirming mean as the appropriate completion.

Option C:
Mode identifies the most frequent score in the distribution and is not calculated using all values. While the presence of outliers can alter frequencies, extreme scores are not inherently more influential than other scores. Thus, mode is not the measure that is most affected by extremes in the sense described.

Option D:
Geometric mean is used mainly for multiplicative processes or growth rates and, although sensitive in its own way, is not the standard measure considered in discussions about the influence of extreme scores on central tendency in basic descriptive statistics. Therefore, geometric mean is not the best answer here.

A normal distribution is a theoretical continuous probability distribution characterised by perfect symmetry about its mean, with the mean, median and mode all equal at the centre. The tails extend infinitely in both directions, and many natural and social phenomena approximate this shape under certain conditions. It plays a central role in inferential statistics because many tests assume normality of errors or variables. Because the stem describes a symmetrical, bell-shaped distribution with coinciding mean, median and mode, normal distribution is the correct term.

Option A:
Skewed distributions are asymmetrical, with one tail longer or fatter than the other, causing the mean, median and mode to separate rather than coincide at the centre. They do not fit the perfectly symmetrical, bell-shaped description given in the stem. Therefore, skewed is not the right answer.

Option B:
Normal distributions are fully described by their mean and standard deviation, and many sampling distributions approach normality under the central limit theorem. This makes them fundamental to constructing confidence intervals and conducting many parametric tests, which aligns with the importance implied in the question.

Option C:
A bimodal distribution has two distinct peaks, representing two modes, and is not necessarily symmetric or bell-shaped in the classic Gaussian sense. As the stem indicates one central peak where the three measures of central tendency coincide, bimodal distribution cannot be the correct completion.

Option D:
A uniform distribution has equal probability across its range, often represented by a rectangular shape rather than a bell. It does not exhibit the central peak and tapering tails characteristic of the normal curve, so uniform is not appropriate here.

Statements A, B and C give the standard description and formula for arithmetic and weighted means. A is correct because the simple mean assigns equal weight to each observation. B and C correctly explain that weighted means use different weights and are computed as the weighted sum divided by the total weight. Statement E is true because if all weights are equal, the weighted mean collapses to the ordinary mean. Statement D is false since a weighted mean, like the arithmetic mean, can lie between observed values and need not coincide with any one observation, so the correct set is A, B, C and E only.

Option A:
Option A is incomplete because it omits C and E and so does not show how weighted means are actually computed or how they relate back to the arithmetic mean when weights are equal. It therefore does not represent all correct statements.

Option B:
Option B is also incomplete as it does not include E, ignoring the simplifying case in which weights are equal, even though it correctly includes A, B and C. The missing link to the arithmetic mean makes it insufficient.

Option C:
Option C is wrong because, although it includes B, C and E, it omits A, which states the key contrast between arithmetic and weighted means, and still does not highlight the equal-weight case as a special instance in context.

Option D:
Option D is correct because it brings together the accurate description of both kinds of means and the proper computation rule, while explicitly excluding D, which incorrectly insists that the mean must be one of the data points. This aligns with the conceptual treatment of averages in NET questions.

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.

The median is the middle value of an ordered distribution such that half of the observations fall below it and half above it. It is particularly useful for skewed distributions or data with extreme values, because it is less affected by outliers than the mean. For ordinal data, the median is often the most appropriate measure of central tendency. Therefore, the measure that divides the distribution into two equal halves is correctly called the median.

Option A:
The mean is the arithmetic average obtained by summing all scores and dividing by the number of observations. While widely used, it is sensitive to extreme values and does not necessarily separate the distribution into two equal halves. Hence, mean is not the correct measure described in the stem.

Option B:
The mode is the value that occurs most frequently in a distribution and can be used for nominal, ordinal or interval data. A distribution may have multiple modes or none clearly defined, and the mode does not guarantee that 50% of cases lie above and 50% below. Thus, mode is not the best completion.

Option C:
Standard deviation measures the average deviation of scores from the mean and expresses the spread or variability in the data, not its central location. It does not divide the distribution into equal halves and therefore does not fit the description given in the question.

Option D:
The median’s reliance on the positional middle of ordered scores, rather than on mathematical averaging, ensures that it always splits the distribution into two equal parts, which matches the stem exactly.