Question

Which of the following data sets has the largest standard deviation?

101, 104, 106, 108, 111
668.5, 668.7, 668.8, 668.9
1001, 1002, 1003, 1004, 1005
22, 23, 24, 25, 26

Answer 1

Answer:

111

668.9

1005

26

these are the greater than those numbers

Answer 2

Answer:

The largest standard deviation is 3.81 . It is option(1) 101, 104, 106, 108, 111.

Step-by-step explanation:

Given: four sets of numbers.

To find: The data set with largest standard deviation.

Solution:

Standard deviation is the measure of dispersion of a set of values.

If the standard deviation is low then the data are clustered round mean and if the standard deviation is high then the data are more spread out.

The formula to find standard deviation is SD, σ = √∑($x_{i}-$μ)²/n-1

where σ is standard deviation, $x_{i}$ is each value, μ is the mean, and N total number of values.

First we need to find the mean of each set .

(1) Mean μ =(101+104+106+108+111)/5

                 = 530/5 = 106.

$x_{i} -$μ: 101-106=-5, 104-106= -2, 106-106=0, 108-106=2, 111-106=5.

∑($x_{i} -$μ)²: (-5)²+(-2)²+0+2²+5² = 25+4+4+25 = 58.

SD = √58/(5-1) = √58/4= √14.5 = 3.81.

(2)Mean = (668.5+668.7+668.8+668.9)/4 = 2674.9/4 = 668.73

$x_{i}-$μ: 668.5-668.7=(-.2), 668.7-668.7=0, 668.8-668.7=0.1,668.9-668.7= .2

∑($x_{i} -$μ)²= (-.2)²+0+(.1)²+(.2)²=0.04+0.01+0.04=0.09

SD= √0.09/(4-1)=√0.09/3=0.03.

(3) Mean = (1001+1002+1003+1004+1005)/5 =5015/5 = 1003.

$x_{i}-$μ: 1001-1003=(-2), 1002-1003=(-1), 1003-1003=0, 1004-1003=1, 1005-1003=2.

∑($x_{i} -$μ)² =4+1+0+1+4= 10.

SD = √10/(5-1) = √10/4= √2.5 = 1.58

(4) Mean= 22+23+24+25+26/5= 120/5= 24.

$x_{i} -$μ: 22-24=(-2), 23-24=(-1), 24-24=0, 25-24=1, 26-24=2

∑($x_{i} -$μ)²= 4+1+0+1+4= 10

SD = √10/(5-1) = √10/4 = √2.5 =1.58

Therefore the largest standard deviation is 3.81

The correct option is (1) 101, 104, 106, 108, 111.

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