MCQ
Measures of central tendency: mean, median and mode MCQ - Practice Questions with Answers
Solve 15 Measures of central tendency: mean, median and mode questions for RAS/RPSC preparation.
Practice questions
Q1Assertion: The arithmetic mean of 10, 20, 30 and 40 is 25, so the mean must always be one of the observations. Reason: Mean is found by dividing the sum of observations by their count.
The calculation is correct: the sum is 100 and the count is 4, so the mean is 25. But 25 is not one of the listed observations. The study note warns that mean need not be an actual observation; it is a calculated centre. Median for an even number of observations can also be a value not present in the original data. Mode is different because it must be a value or category that actually occurs.
Q2Assertion: In the data 1, 2, 3 and 4, there is no mode. Reason: Mode is the value that occurs most often.
The assertion is correct because each value in 1, 2, 3 and 4 occurs exactly once. There is no single value with the highest frequency. The reason is also correct because mode is defined as the value that occurs most often. Since the definition directly tells us why this data set has no mode, the reason properly explains the assertion. This is different from bimodal data, where two values tie for the highest frequency.
Q3In the frequency table x: 10, 20, 30, 40 and f: 2, 3, 4, 1, what is the arithmetic mean?
For a frequency table, the mean is not found by averaging only the x-values. Each value must first be multiplied by its frequency. Here Σf = 2 + 3 + 4 + 1 = 10, and Σfx = 10×2 + 20×3 + 30×4 + 40×1 = 240. Therefore the arithmetic mean is 240/10 = 24. This also shows a common CET trap: the mean can be a calculated value that is not printed in the table.
Q4The scores of five candidates are 10, 12, 13, 15 and 100. Which measure best represents the typical score if the extreme value should not distort the answer?
After ordering, the data is already 10, 12, 13, 15 and 100, so the middle value is 13. The mean is 150/5 = 30, which does not describe the usual score well because four values lie between 10 and 15 while one value is extremely high. The study note specifically treats median as more stable for skewed data, income-like data, marks with one very high score, and other cases where an extreme value should not dominate.
Q5Which statement is incorrect about mode?
Mode is the value or category that occurs most often. It is based on frequency, not on the middle position. Averaging two middle values is the rule for median when the number of observations is even. The note also states that a data set can have no mode or more than one mode, and that mode can be applied to categories such as a most preferred subject or most common ticket category.
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More questions
6Which statement is incorrect about mode and frequency tables?
7Match the situation with the most suitable measure of central tendency.
8In a frequency table, values x are 10, 20, 30 and 40 with frequencies 2, 3, 4 and 1 respectively. What is the mean?
9A grouped frequency table has four classes with frequencies 6, 12, 14 and 8. At CET level, which class is the median class?
10Match the situation with the most suitable measure: 1. Equal-share value from total marks; 2. Middle value in skewed income data; 3. Most sold shoe size; 4. Test result with 40% and 60% section weights.
11Which statement correctly describes the arithmetic mean for individual observations?
12For the frequency table x: 5, 10, 15 and f: 1, 4, 1, which set of values is correct?
13Find the median of the observations 25, 8, 12, 20 and 17.
14A test gives 40% weight to Section A and 60% weight to Section B. A candidate scores 50 in Section A and 70 in Section B. What is the weighted mean score?
15Match each clue with the correct measure: 1. Uses every observation and is sensitive to extremes; 2. Requires arranging data first; 3. Looks for the highest frequency; 4. Multiplies values by given importance.