Measures of Central Tendency

Question 1

What formula do you use to calculate the mean?

Answer 1

x̄ = ∑X
______
N

N= number of scores
x̄= mean
∑= summation
∑X= add up all of the scores

Question 2

How do you find outliers?

Answer 2

Need to calculate the interquartile range by finding the smallest and largest 25% of scores. In the middle 50% take away the lowest score from the highest score. Multiple this by 1.5. Whatever this new score is, take that away from the lowest and highest score in the 50%. If any scores fall outside of these new scores, they’re outliers.

To find extreme outliers, multiply by 3 rather than 1.5.

Question 3

What are variables?

Answer 3

Things we measure, they vary

Question 4

What types can data be classified into?

Answer 4

Nominal: more qualitative, things we can’t express as meaningful numbers
Numerical: things can be expressed in meaningful numbers

Question 5

What is nominal data?

Answer 5

Categorical data
Things we can name e.g. gender, countries
Can’t be ranked

Question 6

What is interval data?

Answer 6

Equal intervals between each number on our scale
No true 0
e.g. temperature

Question 7

What is ratio data?

Answer 7

Equal intervals between each number on our scale
0 indicates the absence of the thing we are measuring
The 0 is true
Other measurements might have a label of 0 but that doesn’t mean the absence e.g. temperature whereas a ruler with 0cm means an absence of zero
Can measure the ratio of things

Question 8

What is ordinal data?

Answer 8

Numerically measured and ranked
Each difference in position doesn’t mean they have the same meaning
e.g. language ability, rank people as beginner, intermediate and fluent
e.g. likert questions most to least satisfied

Question 9

What are frequency tables, what are the symbols?

Answer 9

A count of how many times a certain response occurs in a data set
X: variable name
F: frequency of each value
∑= summation
∑F= sum of all frequencies
N: sample size

We don’t have to just use numerical data for frequency tables, we can use nominal data too.

Question 10

What do we do for larger data sets?

Answer 10

For larger data sets we group our data in the frequency tables

Question 11

Why do we use histograms?

Answer 11

Distribution of our data
Group our data, usually 10 or fewer so data is easy to understand
Helps us see if we have issues with our data, one issue could be that data is skewed (positive or negative.)

Question 12

What are positive/negative skews and bell curves?

Answer 12

positive skew= skew is on the right end
negative skew= skew is on the left end
Normal distributions usually have a bell curve, symmetrical, this is ideal

Question 13

What is the mean?

Answer 13

The average
Add all values, divide by how many values there are

Question 14

What is the mode?

Answer 14

Most frequent
Number that appears most which can be assessed in frequency tables
2 modes= bimodal distribution

Question 15

What is the median?

Answer 15

halfway between lowest and highest value (middle value)
Order data lowest to highest and find the data in the middle
If there are 2 mediums, we add them together and divide by 2

Question 16

What are the advantages/disadvantages of the mean?

Answer 16

+ find the value to represent the whole data set
- affected by outliers

Question 17

What are the advantages/disadvantages of the mode?

Answer 17

+ can be found for nominal data as well
- can be more than one mode, or none at all

Question 18

What are the advantages/disadvantages of the median?

Answer 18

+ not affected by outliers
- when we have 2 middle items, we need to add them up and divide by 2, the number we get after may not actually be a part of our data set

Question 19

When to use mode, median and mean?

Answer 19

Mean: most preferred
Median: used when there are outliers or distribution is heavily skewed. Also better for ordinal data
Mode: best for nominal data or when we can’t use the median or mean