CUET UG Geography Booster Test 2-Mode and Data Distribution

15mm is the mode because it represents the maximum occurrence or frequency at a particular point in the dataset. While other averages look at totals or physical positions, the mode is concerned with the highest recurrence. Since 15mm appeared 12 times—more than any other daily rainfall measure—it matches the precise statistical definition of the mode.

This matching question connects statistical concepts with their operational definitions. The Mode (1) identifies the value with the maximum frequency (B). The Median (2) represents the middle-ranking value in a sorted dataset (A). The Mean (3) is the arithmetic average of all observations (C). The Range (4) is calculated as the difference between the highest and lowest values (D). Therefore, the correct matching is 1-B, 2-A, 3-C, 4-D.

Both statements are correct. Statement I is true because looking through a messy, unsorted list of raw numbers makes it easy to miscount or miss recurring values entirely. Statement II is true because sorting the list automatically groups identical numbers into adjacent rows. This visual layout allows researchers to see immediately which value repeats the most, simplifying the process of identifying the mode.

The correct term is frequency identification. Once an ungrouped dataset is sorted into an ascending or descending order, the researcher must scan the list to count how many times each value appears. This process of frequency identification is what allows the researcher to pinpoint the exact number that features the maximum recurrence, which is defined as the mode.

Determining a distribution type from raw data follows a clear step-by-step workflow. First, the unorganized raw numbers must be sorted in ascending order (2) to line up identical values. Next, the researcher scans these groups to identify the single highest frequency block (1). Finally, because there is only one clear peak with no ties, the researcher can conclude that the series is unimodal (3). This establishes 2, 1, 3 as the correct sequence.

Both statements are correct. Statement I is true because counting the numbers in the dataset shows that 61 appears three times, while every other score appears only once. Statement II is true because for a dataset to be classified as unimodal, it must have exactly one peak. The fact that no other values repeat or tie with 61 confirms that this dataset has a single mode and is unimodal.

This matching question connects different distribution types with their defining frequency characteristics. A Unimodal distribution (1) has one value with the highest frequency (B). A Bimodal distribution (2) has two values that share the highest frequency (D). A Trimodal distribution (3) has three values that share the highest frequency (A). A No Mode distribution (4) occurs when no value repeats in the dataset (C). Therefore, the correct matching is 1-B, 2-D, 3-A, 4-C.

This dataset is an example of a trimodal distribution. The lengths 4cm, 6cm, and 8cm each appear 15 times, creating three separate frequency peaks that tie for the highest count in the series. Because the dataset has exactly three distinct modes, it is classified as trimodal.

The correct term is without mode. In statistical analysis, a mode requires at least one value to repeat more often than the others to create a frequency peak. If every number in a dataset appears exactly once, there are no peaks to measure. The standard statistical designation for this layout is a series without a mode.

Statement II is correct. A dataset is classified as a series without a mode when no values repeat and every number appears exactly once, leaving no frequency peaks. Statement I is incorrect because containing the number zero has nothing to do with this classification. A list of numbers like 10, 20, 30, 40 lacks a mode because no numbers repeat, even though it contains no zeroes.

This graph visually represents a normal distribution curve. When a continuous dataset is plotted and shows observations clustering around the center average with fewer cases at the extreme ends, it forms a symmetrical bell shape. This specific graphical representation is known as a normal curve.

The correct term is bell-shaped curve. The structural symmetry of a normal distribution means that data concentrations are highest in the exact middle and decrease evenly as you move toward either extreme edge. When this frequency pattern is plotted on a graph, it forms a classic, smooth bell shape.

Arranging these options from most recognized in the text to irrelevant follows the examples provided in the textbook. The text explicitly names intelligence scores (1) and student achievements (2) as classic examples of human traits that form normal distributions. Conversely, randomized non-human anomalies (3) are irrelevant to a discussion focused on human trait distributions. This establishes 1, 2, 3 as the correct sequence.

This matching question connects common examples of normal distributions with their respective human trait categories. Intelligence (1) represents a cognitive human trait score distribution (C). Student achievement (2) represents an educational performance distribution (B). Height (3) represents a physical growth distribution (A). Body weight (4) represents a physical body weight distribution (D). Therefore, the correct matching is 1-C, 2-B, 3-A, 4-D.

Both statements are correct. Statement I is true because symmetry requires that the left side of a graph mirror the right side perfectly. As you move away from the center toward either extreme, the number of observations must decrease at the exact same rate on both sides. Statement II is true because this balanced decrease on both sides naturally causes data to cluster around the central middle value, creating the peak of the bell curve.

This dataset displays a symmetrical distribution. The lengths cluster heavily around the target center value (50cm) and decrease at the exact same rate as you move toward either the lower extreme (49cm) or the upper extreme (51cm). Because the frequencies decrease evenly on both sides of the center peak, the distribution is perfectly balanced and symmetrical.

The provided passage explicitly states this reason in the second sentence: "The mean, median and mode are the same score because a normal distribution is symmetrical." This matches Option C word-for-word, confirming that because the graph is perfectly balanced and splits evenly down the middle, all three central metrics land on the exact same center spot.

The final sentence of the passage explicitly states: "The score with the highest frequency occurs in the middle of the distribution..." This matches Option C, confirming that because a normal distribution forms a bell shape, its tallest peak—which represents the mode or highest frequency—sits right in the center of the graph.

Arranging the zones of a normal curve from most frequent to least frequent follows the downward slope of the bell shape from the center out to the edges. The highest frequency of observations sits at the absolute peak of the graph, which represents scores exactly at the central mean (1). Moving slightly away from the center, the curve begins to slope downward, representing a slightly lower frequency for scores slightly above or below the mean (2). The lowest frequency sits at the outer edges of the graph, representing the very high and very low extreme scores (3). This establishes 1, 2, 3 as the correct sequence.

Statement I is entirely correct because a normal distribution curve forms a bell shape that peaks in the middle, showing that most observations concentrate heavily around the central mean. Statement II is incorrect because the term "rare extreme scores" means those values occur infrequently. If extreme scores occurred frequently, the graph would flatten or flare out at the edges, which contradicts the symmetrical, downward-sloping structure of a normal curve.