Measures of central tendency

Question 1

what are measures of central tendency?

Answer 1

• single values describing a set of data by identifying central position within that set of data
• mode
• median
• mean

Question 2

What is the mode?

Answer 2

• the value that occurs most frequently
• most useful when working with nominal variables (only useful measure of central tendency for nominal variables)

Question 3

What is the median?

Answer 3

• the middlemost value in a distribution
• always the exact centre of a distribution
• half of the scores in a distribution are higher than the median and half are lower than median

Question 4

How do you calculate the median when there’s an odd number of cases?

Answer 4

1. all scores must be arranged in order from low to high
2. when there are an odd number of cases the median is the exact middle case
   eg. 10 15 25 40 60 > median is 25

Question 5

How do you calculate the median when there’s an even number of cases?

Answer 5

1. all scores must be arranged in order from low to high
2. Find case number by taking the number of scores, adding 1, then divide by 2 > (N+1) ÷2
3. median is the value between the 2 middlemost cases
4. Find the two middle cases, add them and divide by 2
   eg. 10 15 25 40 60 70 > (25+40) ÷ 2 = 32.5

Question 6

What are limitations of the median?

Answer 6

• cannot be calculated for nominal variables
• can be found in ordinal or interval-ration variables
• generally preferred measure of central tendency for ordinal variables because mean can be misleading

Question 7

How is the mean calculated?

Answer 7

X̄= ( Σ xi ) / N
where:
X̄ is the sample mean
Σ xi (sigma) is the summation of all the scores
N is the total number of cases

Question 8

What is the sum of each observation’s deviation from the mean?

Answer 8

Å (Xi - X̄)

Question 9

Why is the median a better measure of central distribution than the mean?

Answer 9

• Mean can be misleading if the distribution is skewed
• because it uses all the scores in its calculation, it can be affected by unusually high/low scores
• mean is pulled in the direction of these extreme values: when few unusually high values, the mean is pulled higher; when few unusually high values, the mean is pulled lower

Question 10

What is skew?

Answer 10

• skew refers to when an otherwise normal distribution has a few extremely high or a few extremely low scores
• positively skewed: few high scores (pulled up to the left)
• negatively skewed: few low scores (pulled up to the right)