Question

A data set of n observations has mean 2 x. While another data set of 2n observations has mean x . Then the mean of the combined data set of 3n observations will be :

Answer 1

(a) RangeThe measure of dispersion which is easiest to understand and easiest to
calculate is the range. Range is defined as:
Range = Largest observation – Smallest observation
(b) Mean Deviation
(i) Mean deviation for ungrouped data:
For n observation x1
, x2
, ..., xn
, the mean deviation about their mean x is
given by
M.D ( x ) =
| | i
x x
n
−
(1)
Mean deviation about their median M is given by
M.D (M) =
| M | i
x
n
−
(2)
(ii) Mean deviation for discrete frequency distribution
Let the given data consist of discrete observations x1
, x2
, ... , xn
occurring with
frequencies f
1
, f
2
, ... , f
n
, respectively. In this case


M.D ( x ) =
| | | |
N
i i i i
i
f x x f x x
f
− −
=

(3)
M.D (M) =
| M |
N
i i f x −
(4)
where N = i
f .
(iii) Mean deviation for continuous frequency distribution (Grouped data).
M.D ( x ) =
| |
N
i i f x x −
(5)
M.D (M) =
| M |
N
i i f x −
(6)
where xi
are the midpoints of the classes, x and M are, respectively, the mean
and median of the distribution.