5: Standard Deviation

Question 1

What is the mean value?

What symbol is given to the mean value of a sample?

What symbol is given to the mean value of the whole population?

Answer 1

The mean value is the ‘average’. It represents the central tendency in the data.

The mean value of a sample is ‘x’ with a squiggly line on top.

The mean value of a population is the greek letter ‘mu’

Question 2

What is standard deviation?

What symbol is given to the standard deviation of a sample?

What symbol is given to the standard deviation of a population?

Answer 2

A measure of how spread out the numbers are.

’s’

Sigma

Question 3

What is the formula for the sample mean?

Answer 3

Sum of Xi / n

Question 4

What is the formula for the uncorrected standard deviation of a sample?

Answer 4

s = Square Root ( sum of Xi^2/n - mean^2)

Question 5

What is the formula for the corrected standard deviation of a sample?

Answer 5

scor = Square root (n/n-1) x s

Question 6

How do you calculate sample mean and standard deviation with class intervals?

Answer 6

Table format:
- Columns for: mid point (Xi mid), ‘f’, f x Xi mid, f x Xi mid^2
- Summate frequency, sum of frequency x mid point, and sum of frequency x mid point^2
- Use the mean and standard deviation formulas for a sample

Question 7

How do you calculate values for the standard distribution table?

Answer 7

Use the formula:

z = x - mean / s

Where ‘x’ = the value specified in the question

Question 8

How do you read the values from the standard distribution table?

Answer 8

Use the calculated value of ‘z’, the rows dictate 0-3.4 and the columns dictate 0-0.09

Question 9

How do you convert the probabilities from the standard distribution table into percentages?

Answer 9

Multiply by 100

Question 10

If the calculated value of ‘z’ is < 0, how do you calculate the probability?

Answer 10

find the probability value from the standard distribution table as normal, but subtract this value from 1.00

Question 11

What is the total area under the curve equal to?

Answer 11

1.00

Question 12

How do you calculate the probability or percentage of a certain outcome between two values? (a range)

Answer 12

Calculate z1 using the first value (x1) and then z2 using the second value (x2), then subtract the lower probability value from the higher value

Question 13

How do you work out a number of a certain outcome when provided a new sample size?

Answer 13

Multiply the sample size by the calculated probability

Question 14

Why do we use confidence %?

Answer 14

Mean values of individual samples do not often coincide with the population mean. It has its own standard distribution.`

Question 15

What is a confidence interval?

Answer 15

A range of values between specific upper and lower limits within which the mean is expected to lie, within a level of confidence

Question 16

What are the most commonly adopted confidence levels?

Answer 16

95% and 99%

Question 17

What are the 4 steps to finding a P% confidence limit and confidence interval?

Answer 17

1: find sample mean and corrected standard deviation for the sample

2: calculate population mean and standard deviation

3: Use Z-table to convert confidence P% into the respective lower and upper z-values (z1 and z2)

4: Calculate confidence limits

Question 18

How do you calculate population mean given the sample mean?

Answer 18

Population mean, ‘mu’ = Sample mean, ‘x squiggly’

Question 19

How do you calculate the population standard deviation given the sample standard deviation?

Answer 19

sigma = sample corrected standard deviation / Square root (n)

Question 20

What is the formula for calculating confidence limits?

Answer 20

X1,2 = mu + sigma x Z1,2

Question 21

For a 90% confidence value, how do you use the z-table?

Answer 21

• You can’t find the middle 90%, so we go for 95% (missing the end 5%) and then use the same value as a negative to get rid of that additional 5%.
• In this instance, 0.90 +0.05 = 0.95, find the corresponding ‘z’ value to 0.95 (might be between two values in which case calculate)
• Lower confidence limit (x1) becomes the negative z-table value, upper confidence limit (x2) becomes the positive z-table value

Question 22

When you have calculated both the lower and upper confidence limits, what do you need to do to finish off?

Answer 22

Write a sentence describing the 90% confidence interval and then describe the interval width (difference between upper and lower limit)