Mean
MEAN (AVERAGE): Mean [Ungrouped Data] – Mean of n observations, x1, x2, x3 … xn, is
MEAN [Grouped Data]: The mean for grouped data can be found by the following three methods:
(i) Direct Mean Method:
Class Mark = UpperClassLimit+LowerClassLimit upon 2
(ii) Assumed Mean Method: In this, an arbitrary mean ‘a’ is chosen which is called, ‘assumed mean’, somewhere in the middle of all the values of x.
…[where di = (xi – a)]
(iii) Step Deviation Method:
….. [where ui=dih , where h is a common divisor of di]
Median
Median is a measure of central tendency which gives the value of the middle-most observation in the data.
…where[l = Lower limit of median class; n = Number of observations; f = Frequency of median class; c.f. = Cumulative frequency of preceding class; h = Class size]
Mode
(i) Ungrouped Data: The value of the observation having maximum frequency is the mode.
(ii) Grouped Data:
…where[l = Lower limit of modal class; f1 = Frequency of modal class; f0 = Frequency of the class preceding the modal class; f2 = Frequency of the class succeeding the modal class; h = Size of class interval. c.f. = Cumulative frequency of preceding class; h = Class size]
Mode = 3 Median – 2 Mean
Median = Mode+2Mean upon 3
Mean = 3Median−Mode upon 2
The topics discussed in this chapter are as follows:
- Ungrouped Data
- Grouped Data
- Frequency and Class Interval
- Mean, Median and Mode
- Ogive
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NCERT Solutions for Chapter 14: Statistics
Also Check
Chapter 1: Real Numbers
Chapter 2: Polynomials
Chapter 3: Pair of Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progression
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry
Chapter 9: Some Applications of Trigonometry
Chapter 10: Circle
Chapter 11: Constructions
Chapter 12: Areas Related to Circles
Chapter 13: Surface Areas and Volume
Chapter 15: Probability
Check out Frequently Asked Questions (FAQs) for Chapter 14: Statistics
Cumulative frequency curve is also called
The relationship between mean, median and mode for a moderately skewed distribution is
Mode and mean of a data are 12k and 15A. Median of the data is
⇒ 12k = 3 median – 2 × 15k
⇒ 42k = 3 median
⇒ Median = 14k