Master Central Tendency: Quick Questions on Mean, Median, Mode for Class 10
Understanding the central measures of tendency—mean, median, and mode—is a key part of learning statistics in Class 10 Mathematics. These measures help us summarise and analyse data by identifying the central or typical value in a dataset. Whether you're calculating the average score of a cricket match, finding the most common number in a list, or determining the middle value in a set of numbers, these concepts are incredibly useful in everyday life. To help you practise and master these ideas, we’ve put together a list of very short answer-based questions. These questions are designed to test your understanding and improve your problem-solving skills quickly and engagingly. Let’s dive in and explore the world of central measures of tendency!
Q1: If the value of each observation in the data is increased by 2, then the median of the new data __________
(A) increases by 2
(B) increases by 2n
(C) remains same
(D) decreases by 2
Answer: (C) remains same
Q2: If the value of each observation in a dataset is multiplied by 3, then the mean of the new dataset:
(A) increases by 3
(B) is multiplied by 3
(C) remains the same
(D) is divided by 3
Answer: (B) is multiplied by 3
Q3: If the value of each observation in a dataset is decreased by 5, then the mode of the new dataset:
(A) decreases by 5
(B) increases by 5
(C) remains the same
(D) is multiplied by 5
Answer: (A) decreases by 5
Q4. The middle observation of data sorted in ascending order is called the ________.
Answer: median
Q5. The median and mode, respectively, of a frequency distribution are 26 and 29, then its mean is ____.
Answer: 24.5
∵ Mode = 3Median - 2Mean
29 = 3(26) - 2Mean
2Mean = 78 - 29 = 49
Mean = 24.5
Q6. In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. Write the class interval.
Answer: Lower Class Limit (LCL) = 10 - h/2 = 10 - 6/2 = 10 - 3 = 7
Upper Class Limit (UCL) = 10 + h/2 = 10 + 6/2 = 10 + 3 = 13
∴ CI = 7 - 13
Q7. A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s and seven 10’s. The mode of this set of numbers is _________.
Answer: 8 occurs maximum times, i.e. eight times.
∴ Mode = 8.
Q8. For finding the popular size of readymade garments, which central tendency is used?
Answer: Mode is the best measure.
Q9. If the difference of the mode and the median of a data is 24, then what is the difference of the median and the mean?
Answer: Mode - Median = 24
∵ Mode = 3Median - 2Mean
Mode = 1Median + 2Median - 2Mean
Mode - Median = 2(Median - Mean)
24 = 2(Median - Mean)
⇒ Median - Mean = 24/2 = 12
Q10. A dataset of five positive integers has a unique mode of 7, a median of 9, and an arithmetic mean of 11. What is the greatest possible value in the set?
Answer: The largest number is 22.
Let the five numbers in ascending order be: a,b,9,c, d
Since mode is 7, it must occur two times. Thus a = b = 7
Thus the sorted number is 7, 7, 9, c, d
Sum of observations = 5 × Mean = 5 × 11 = 55
⇒ 7 + 7 + 9 + c + d = 55
⇒ c + d = 55 - 23 = 32
Thus, c has to have a minimum value, and d has the maximum value. c can't be less than 9.
If c = 9, the dataset is bimodal (Question says it is unimodal.)
Thus c must be 10.
and d = 32 - 10 = 22
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