CBSE Class 10 Maths HOTs Statistics Set 07

Say True (T) or False (F).

Question. Mean of first 'n' natural numbers is \( \frac{1}{2}[n + 1] \).
Answer: T

Question. Median is the point of intersection of two ogives of same data.
Answer: T

Question. Mode of data can be negative also.
Answer: F

Question. There is no relation between Mean, Median and Mode.
Answer: F

Question. Sum of deviation of all observations from mean is always zero.
Answer: T

Question. Mean and median of first eleven natural number is 6.
Answer: T

Question. Statistics can not deal with numerical information.
Answer: F

Question. Mode of first ten natural numbers is 5.
Answer: F

Question. Most stable measure of central tendency is mean.
Answer: F

Question. We can not calculate median of grouped data.
Answer: F

Question. If each observation of same discrete data is decreased by \( k \) then mean will also be decreased by \( k \).
Answer: T

Question. If each observation is increased by \( p \) then median will also be increased by \( p \) (always).
Answer: T

Question. Mean, median and mode are measure of central tendency.
Answer: T

Question. If mode of data is \( 12k \) and mean is \( 15k \) then median will be \( 14k \).
Answer: T

Question. Difference of two successive class marks is known as class size.
Answer: T

Fill in the Blank.

Question. Mean of first 5 odd natural numbers is ___________.
Answer: 5

Question. Median of first 100 natural numbers is ___________.
Answer: 50.5

Question. Mode of observation 3, 1, 2, 3, 4, 4 is ___________.
Answer: 4

Question. Median is the point of intersection of ___________.
Answer: ogives

Question. Emperical formula for mode = ___________.
Answer: 3 median - 2 mean

Question. Data is the plural name of latin word ___________.
Answer: Datum

Question. Mean of \( n \) observation is \( \bar{x} \), if each observation is multiplied by \( k \) then mean of new set of observations will be __________.
Answer: \( k\bar{x} \)

Question. If mean is subtracted from \( n \) observations, now sum of deviations obtained is ___________.
Answer: zero

Question. If mean of 1, 2, 3, ... \( n \) is \( \frac{6n}{11} \) then value of \( n \) is ___________.
Answer: 11

Question. The mean of first \( m \) natural numbers is ___________.
Answer: \( \frac{m + 1}{2} \)

Question. Class mark of any class interval is ___________.
Answer: \( \frac{\text{Lower limit + upper limit}}{2} \)

Question. Median in case of number of observations \( n \) is even is given by formula ___________.
Answer: \( \frac{1}{2} \left[ \left( \frac{n}{2} \right)^{th} \text{ observation} + \left( \frac{n}{2} + 1 \right)^{th} \text{ observation} \right] \)

Question. Cumulative frequency polygon is known as ___________.
Answer: Ogive

Question. Median of first 50 even natural numbers is ___________.
Answer: 51

Question. Mean of 5 numbers is 18. If one more number is added into group such that mean of new group become 20, then new number is ___________.
Answer: 30

MCQs with more than one correct options.

Question. Which of the following relation is empirical formula
(a) Mode = 3 Median - 2 Mean
(b) 2 Mean = 3 Median - Mode
(c) Median = 2 Mode - 3 Mean
(d) 3 Median = Mode + 2 Mean
Answer: (a), (b) & (d)

Question. Which of following are ways of graphical representation of data :
(a) Frequency Polygon
(b) Bargraph
(c) Histogram
(d) None of the options
Answer: (a), (b) & (c)

Question. Which is not possible to calculate graphically
(a) Mean
(b) Median
(c) Mode
(d) None of the options
Answer: (a) & (d)

Question. We can calculate mean of regular group data by the methods of :
(a) Assumed mean method
(b) Step deviation number
(c) Graphical Method
(d) None of the options
Answer: (a) & (b)

Question. Mean of first eleven natural number is equal to :
(a) 7
(b) 6
(c) 5
(d) equal to their median
Answer: (b) & (d)

Question. In a group distribution table which of following can be in the same group (same class-interval)
(a) Mean
(b) Median
(c) Mode
(d) None of the options
Answer: (a), (b), (c)

Question. It is possible to calculate median by :
(a) Empirical formula
(b) Histogram
(c) Ogives
(d) Bargraph
Answer: (a) & (c)

Question. Median of discrete data is calculated by arranging the observation
(a) Ascending order
(b) descending order
(c) No need to arrange
(d) None of the options
Answer: (a) & (b)

Question. Statistics deals with :
(a) Data
(b) Quality
(c) Quantity
(d) None of the options
Answer: (a), (c)

Question. Which of the following is not a curve :
(a) Histogram
(b) Bargraph
(c) Less than ogive
(d) More than ogive
Answer: (a) & (b)