STATS Lec-1 Descriptive stats

Question 1

Types of statistics

Answer 1

• Descriptive- describing data sets- this allows us to take a lot of data and summarise it so that it can be understood by many people
• Inferential- Making inferences (Looking for similarities or differences in a data set)- from data about the general population from samples of data i.e. was this pattern due to chance or real effect

Question 2

Types of descriptive statistics

Answer 2

• Measures of central tendency- Where is the middle of the data set, or the most common trend
• The measure of the dispersion-How variable is the data?- can be very broad or narrow, this helps to describe and define a data set we have collected
• Measures of Kurtosis and Skewness (These are a measure of non-symmetrical data)- Is the data set symmetrical around the central tendency?
• Graphical representations
• Raw data

Question 3

3 measures of central tendency- Mean

Answer 3

• What we normally think of as the average
• The arithmetic average
• Add up all of the scores and divide by the number of scores

+ Takes into account the value of all scores

• BUT is affected by anomalies or extremes of value

Question 4

3 measures of central tendency- Median

Answer 4

• The middle score if all the scores are put in rank order of size

+ Less affected by outliers (anomalies)

• Provides less detail than the mean
• NB in a data set {1,2,2,3,3,4} median = (2+3) / 2 = 2.5

Question 5

3 measures of central tendency- Mode

Answer 5

• The most common score

+Not at all affected by outliners

• Very crude- doesn’t give a lot of detail about the data set
• Often mode is used for non-numerical data
  • Qualitative data

Question 6

Nominal data

Answer 6

• Data in which the data are neither measure no ordered by subjects are merely allocated to distinct categories
• We can only use the mode

Question 7

Ordinal data

Answer 7

• This is when the data have a natural variable, ordered categories and distances between the categories are not known
• e.g. Number of students that got a certain result
• You can use the median or the mode

Question 8

Categorical data: Uniform distribution

Answer 8

• Uniform distribution is when for each category selected there is roughly the same frequency
• Measurements of central tendency are often useless due to the fact that there is no central tendency as the value are all similar

Question 9

Appropriate measures of different distribution: central tendency

Answer 9

• The mean is sensitive to outliers so not always good if outliers or extreme scores are present - The median may be a better measure
• Neither mean nor medians are useful for categorical data- the mode would be more appropriate
• The mode can be misleading if its frequency is only just greater than that of other scores or categories

Question 10

The appropriate measure for different distribution: Spread of data

Answer 10

• Range: Maximum score minus minimum score
  
  • Suitable for ordinal or interval data
  • Limited in its descriptive powers
• Interquartile range: Split into quartiles and calculate the difference between 3^rd and 1^st quartile
  
  • Useful when the median is used as a measure of central tendency
  • If looked at carefully can give you clues as for the shape of the distribution
• The most powerful use is the variance or Standard Deviation (Measure of deviation from the mean)
  
  • Mathematical: for normal distribution only