2.4 Mean and Standard Deviation

Question 1

Range

Answer 1

Maximum - minimum

Question 2

Deviation from the Mean

Answer 2

Distance from the mean
Find it for each point
Deviation of x = x - μ

Question 3

Population Mean

Answer 3

μ

Question 4

Sample Mean

Answer 4

x ̅

Question 5

Sum of the Squares

Answer 5

SSx

Question 6

Population Standard Deviation

Answer 6

σ

Question 7

Population Variance

Answer 7

σ^2

Question 8

Sample Standard Deviation

Answer 8

s

Question 9

Sample Variance

Answer 9

s^2

Question 10

What is the relationship between Standard Deviation and Variance?

Answer 10

The Square root of Variance is Standard Deviation

Question 11

Why is Standard Deviation used instead of Variance?

Answer 11

Variance is the average of squared values and prove not meaning to us where standard deviation is the average distance away from the mean each value is.

Question 12

How to find Standard deviation

Answer 12

1. list x values
2. find the mean
3. subtract the mean from each x value
4. square each of those values (always positive)
5. Find the sum of the squares from adding up everything from step 4.
6. Divide SSx by either n or n-1 depending on sample or population (this is the variance)
7. Take the square root of the variance to get SD

Question 13

When finding a sample Standard deviation divide by…

Answer 13

n - 1

Question 14

When finding a population Standard deviation divide by…

Answer 14

n

Question 15

The smaller the standard deviation…

Answer 15

The closer the values are to the mean, more consistent.

Question 16

The larger the standard deviation…

Answer 16

The more spread out the data is, less consistent.

Question 17

When all the data values are equal…

Answer 17

The standard deviation is 0

Question 18

The standard deviation and variance are always positive because…

Answer 18

The deviations have all been squared.

Question 19

Using the Empirical Rule, 68% of data lies within…

Answer 19

1 Standard Deviation

Question 20

Using the Empirical Rule, 95% of data lies within…

Answer 20

2 Standard Deviations

Question 21

Using the Empirical Rule, 99.7% of data lies within…

Answer 21

3 Standard Deviations

Question 22

Chebychev’s Theorem

Answer 22

The portion of an data set lying within k standard deviations of the mean is 1 - 1/(k^2)

Question 23

Using Chebychev’s Theorem, when k = 2

Answer 23

k = 2,

1 - 1/4 = 3/4 = 75%

Question 24

Using Chebychev’s Theorem, when k = 3

Answer 24

k = 3

1 - 1/9 = 8/9 = 89%

Question 25

Finding the mean of grouped data

Answer 25

∑xf/∑f

Question 26

Grouped is not 100% accurate…

Answer 26

When using grouped data frequency distributions to find the SD, it is an approximation!