Which data set has the highest standard deviation (without doing calculations)? A) 1,2,3,4 B) 1,1,1,4 C) 1,2,2,4 D) 4,4,4,4

Question

asked Dec 3, 2020 221k views

1 Answer

Cyclomarc · Answer 1 · 2020-12-08T07:38:20+0000

Answer:

B)1,1,1,4

Explanation:

A.1,2,3,4

Mean=
$\bar x=(1+2+3+4)/(4)=2.5$

x
$x-\bar x$
$(x-\bar x)^2$

1 -1.5 2.25

2 -0.5 0.25

3 0.5 0.25

4 1.5 2.25

$\sum(x-\bar x)^2=2.25+0.25+0.25+2.25=5$

B.

Mean=
$\bar x=(1+1+1+4)/(4)=1.75$

$(x-\bar x)^2$

0.5625

5.0625

$\sum(x-\bar x)^2=0.5626+0.5625+0.5625+5.0625=6.75$

C.

Mean=
$\bar x=(1+2+2+4)/(4)=2.25$

$(x-\bar x)^2$

1.5625

0.0625

3.0625

$\sum (x-\bar x)=1.5625+0.0625+0.0625+3.0625=4.75$

D.
$Mean=\bar x=(4+4+4+4)/(4)=4$

$(x-\bar x)^2$

0

$\sum (x-\bar x)^2=0+0+0+0=0$

We know that

S.D is directly proportional to
$\sum (x-\bar x)^2$ .

When
$\sum (x-\bar x)^2$ is highest then the S.D is also highest.

We can see that the value of
$\sum (x-\bar x)^2$ is highest in option B.

Therefore, S.D of the date set of option B is highest.