Process to Find Standard Deviation

Finding Mean

100

Find the mean of the data set:

{42, 75}

Mean = 58.5

-100 Points

200

Find the mean of the data set:

{27, 68, 91}

Mean = 62

-200 Points

300

Find the mean of the data set:

{15, 42, 73, 88}

Mean = 54.5 

-300 Points

400

Find the mean of the data set: 

{24, 37, 52, 68, 91}

Mean = 54. 4

-400 Points

500

Find the mean of the data set: 

{5, 10, 15, 20, 25, 30}

Mean = 17.5

+500 Points

Difference of Inputs from Mean Squared

100

Compute (x_i-x)²

{30, 40}

Mean = 35

(30-35)²=(-5)²=25

(40-35)²=(5)²=25

200

What is the (x_i-x)² of the following numbers from a data set if the mean is 59?

{61, 54}

(61-59)²=(2)²=4

(54-59)²=(-5)²=25

300

Compute (x_i-x)²

{10, 2, 8, 4, 6}

Mean = 6

(10-6)²=(4)²=16

(2-6)²=(-4)²=16

(8-6)²=(2)²=4

(4-6)²=(-2)²=4

(6-6)²=(0)²=0

400

Compute (x_i-x)²

{5, 9, 1, 4,}

Mean = 4.75

(5-4.75)²=(0.25)²=0.0625 or 1/16

(9-4.75)²=(4.25)²=18.0625 or 289/16

(1-4.75)²=(-3.75)²=14.0625 or 225/16

(4-4.75)²=(-0.75)²=0.5625 or 9/16

500

Compute (x_i-x)²

{68, 32, 91}

Mean= 191/3

[68-(191/3)]²=169/9

[32-(191/3)]²=9025/9

[91-(191/3)]²=6724/9

Sum or Difference

100

What is the sum of the following:

{2, 3, 1}

Sum of 2 + 3 + 1=6

200

Find the sum.

{1, 3, 5, 2}

Sum = 11

-200 Points

300

Find the sum:

 {10, 2, 11, 12, 2}

Sum= 37

400

Find the difference:

{3, 5}

5-3

Difference=2

500

Find the difference:

{1.2, 0.7}

Difference=0.5

12-7=5

1.2-0.7=0.5

What is the divisor?

100

In order to find the standard deviation of the data set, what number represents the count of inputs to divide by when finding population standard deviation?

{42, 75}

Population applies to the whole group, so we must use the count of responses in the whole data set; 2.

200

What number should we divide by if asked to calculate the population standard deviation?

{27, 68, 91}

3 because 3 numbers make up this whole response group

300

What number is the divisor if asked to calculate the sample standard deviation:

{15, 42, 73, 88}

3; one less than the 4 in the whole group (n-1)

400

What number is the divisor if asked to calculate the sample standard deviation:

{24, 37, 52, 68, 91}

4; one less than the whole group of data (n-1)

500

What's the divisor if asked to calculate both population standard deviation and sample standard deviation:

{5, 10, 15, 20, 25, 30}

Population divisor: 6, the whole group or n, the number of data inputs

Sample: one less than the count of data responses (n-1), so 5

Standard Deviation

100

Find the population standard deviation for the data set: [12, 15, 18, 20, 25]

Population SD = 4.4272

200

Find the sample standard deviation for the data set: [68, 72, 70, 69, 75, 73, 71]

Sample SD = 2.4103

300

Find the population standard deviation for the data set: [62, 59, 61, 63, 60]

Population SD = 1.4142

400

Find the sample standard deviation for the data set: [30, 28, 35, 40, 25]

Sample SD = 5.9414

500

Find the population standard deviation for the data set: [10, 12, 9, 15, 11, 13]

Population SD = 1.9720