Mean/SD

Question 1

What is the mean?

Answer 1

The mean is the most common measure of central tendency.

Question 2

How to calculate the mean?

Answer 2

Add up all the scores in a sample and divide by the total number of scores you added up.

X = sample mean
Sum of = a symbol directing you to add up a set of scores
x = a score in the sample
n = total number of scores in the sample

Question 3

When to use the mean?

Answer 3

Only calculated for numerical scales - not nominal

Question 4

What’s SD?

Answer 4

Standard deviation is based on the fact that (usually) all scores in a distribution will be different (i.e. deviate) from the mean value.

The larger the squared deviations from the mean of a set of scores, the larger the value of standard deviation obtained.

Question 5

SD calculation

Answer 5

Σ(x-x^)/n -1 (square root)
where:

x = any score in our sample.
̄x = the mean value of the set of scores (i.e. the mean of all the x values).
Σ = a symbol directing you to add up a set of scores (also pronounced ‘sigma’). n = the total number of scores in our sample.
n = total number of scores in sample

Question 6

Steps to calculate SD?

Answer 6

Step 1: Calculate the mean task completion time value for the sample as shown
in column 1.

Step 2: Subtract the mean value from the task completion time of each participant and write this value in column 2.

Step 3: Square each value in column 2. Write this value in column 3.

Step 4: Add up the values in column 3. This gives the value, Σ ( x - ̄x )2

Step 5: The value, Σ ( x - x ̄ )2 and the total number of people in our sample (n=10) may then be substituted into the equation for standard deviation shown above.

Question 7

SD for normal distribution?

Answer 7

For many types of numerical data that psychologists can measure, we may usually expect about one third of participants (34.13%) in a sample will achieve a score between the mean and one standard deviation above the mean.

For example, we would expect 34.14% of participants using the multi-press text method to have a task completion time between the mean value (28.19) and one standard deviation above the mean (28.19 + 6.44 = 34.63). This arises since many forms of numerical measurement will correspond to a particular type of distribution, called a normal distribution.

Figure 3 shows a normal distribution curve. The normal distribution curve is a special type of frequency distribution which underpins many of the tests you will be learning in this text. Normal distributions are important since many natural phenomena (e.g. weight) and psychological attributes (e.g. intelligence) may be expected to be normally distributed in a general population of individuals.

Since the normal distribution is symmetrical, we can also say that just over two thirds of our sample (34.13 + 34.13 = 68.26 %) should have a task completion time somewhere between 1 s.d. below and 1 s.d. above the mean (i.e. between a value of 21.75 and 34.63)