Name: Measures of Central Tendency
Uploaded: 2019-07-19
Duration: 11 min 23 s
Description: There are three main measures of central tendency: the mode, the median, and the mean. Each of these measures describes a different indication. Learn more.

Question

Find the range, mean deviation about the mean, as well as median for the series:

20, 28, 40, 12, 30, 15, 50 .

Accepted Answer

Range

Arranging the given data in ascending order we have $12, 15, 20, 28, 30, 40, 50$

Maximum observation $= 50$

Minimum observation $= 12$

So, Range $=$ Maximum observation $-$ Minimum observation

$= 50 - 12$

$= 38$

Calculation of Mean Deviation about Mean

Mean $= \frac{Sum of all observations}{Number of observations}$

$= \frac{12 + 15 + 20 + 28 + 30 + 40 + 50}{7}$

$= \frac{195}{7}$

$x_{i}$ $12$ $15$ $20$ $28$ $30$ $40$ $50$

$|x_{i} - \bar{x}|$ $\frac{111}{7}$ $\frac{90}{7}$ $\frac{55}{7}$ $\frac{1}{7}$ $\frac{15}{7}$ $\frac{85}{7}$ $\frac{155}{7}$ $Σ |x_{i} - \bar{x}| = \frac{512}{7}$

So, M.D about mean $= \frac{Σ |x_{i} - \bar{x}|}{n}$

$= \frac{\frac{512}{7}}{7}$

$= \frac{512}{49}$

Calculation of Mean Deviation about Median

Here, number of observations $n = 7$ (odd)

So, Median $= M_{d}$

$= (\frac{n + 1}{2}) th$ observation

$= (\frac{7 + 1}{2}) th$ observation

i.e $4 th$ observation $= 28$

$x_{i}$ $12$ $15$ $20$ $28$ $30$ $40$ $50$

$|x_{i} - M_{d}|$ $16$ $13$ $8$ $0$ $2$ $12$ $22$ $Σ |x_{i} - M_{d}| = 73$

So, M.D about median $= \frac{Σ |x_{i} - M_{d}|}{n}$

$= \frac{73}{7}$

Size $(x_{i})$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$
Frequency $(f_{i})$	$3$	$3$	$4$	$14$	$7$	$4$	$3$	$4$

Size	$20$	$21$	$22$	$23$	$24$
Frequency	$6$	$4$	$5$	$1$	$4$

$x_{i}$	$15$	$21$	$27$	$30$	$35$
$f_{i}$	$3$	$5$	$6$	$7$	$8$

Find the range, mean deviation about the mean, as well as median for the series: $20, 28, 40, 12, 30, 15, 50 .$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the range, mean deviation about the mean, as well as median for the series: 20,28,40,12,30,15,50.

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the range, mean deviation about the mean, as well as median for the series: $20, 28, 40, 12, 30, 15, 50 .$