STATS 1

JCU Summer session 1 with Dr.Robert

Define Statistics

the art and science of collecting, presenting, analyzing and interpreting data

data→____→____

data→statistics→information

Define Data

facts and figures

• ex) can be numbers, can also be words

Define Data Set

all data collected in a study

Define Elements

entities on which data are collected

• also called unit/subject

• ex) person, country, car, day

Define Variable

characteristics of interest for the elements

• ex) ppl are elements. Hair color is the variables

Define Observation

set of measurements obtained for each element

• N^o observations always= N^o elements

  • this means there is a 1-1 relationship between elements and observations

What are the 4 scales of elements

1. Nominal Scale

2. Ordinal Scale

3. Interval Scale

4. Ratio Scale

Define Nominal Scale

objects, adjectives, numbers

Define Ordinal Scale

nominal data with meaningful order or rank

• ex) excellent, good, poor; 1st, 2nd, 3rd

Define Interval Scale

ordinal data; fixed interval between values

• always numeric

• differences between scores are meaningful

• no meaning zero

• ex) 10^o, 20^o, 30^o. 25/05, 27/05, 29/05.v

  • it’s not twice as hot, or twice as many days. It’s just 10 degrees hotter, or 2 days later

Define Ratio Scale

interval data with meaningful ratios

• Time, distance→ ex) speed

• Height, weight→ BMI

• *Must have a ZERO value*→ nothing exists for variable at zero

• ex) 10 years, 20 years, 30 years, 0 years

  • you can double values, and have a zero value

Which one has a zero value? Interval Scale or Ratio Scale

Ratio Scale

Pick whether it is categorical or quantitative for the following scales of measurements

1. Nominal Scale

2. Ordinal Scale

3. Interval Scale

4. Ratio Scale

1. Nominal Scale is categorical

2. Ordinal Scale is categorical

3. Interval Scale is quantitative

4. Ratio Scale is quantitative

Mean

• (average)

• sum of all results divided by number of results

• The mean had information from all of your data set

Median

• the result in the middle

• (n+1)/2 if it’s a even data set

Mode

• the result that occurs most frequently (can be less than or equal to 1)

• the tallest bar in a frequency distribution

• can have more than 1 answer

Percentiles equation

i=(p/100)n

• if i is not an integer: round UP

• if i is an integer: average of the values in positions i and i+1

  • and then divided it all by 2 like you would when finding median in an even data set

Quartiles

• divided into 4 equal parts

• division points are referred to as quartiles

  • Q1 first quartile (25th percentile)

  • Q2 second quartile (50th percentile)

  • Q3 third quartile (75th percentile)

What are the measures of variability?

1. range

2. interquartile range

Range is

the largest value-smallest value

• influenced by extreme values

Interquartile Range (IQR)

• overcomes extreme values

• difference between Q3 and Q1

• range for the middle 50% of data

• IQR=Q3-Q1

What are measures of spread?

1. Variance

2. Standard deviation

Variance equation

Sum of deviations are always equal to ___

zero

the Deviation from mean is

the distance from the a specific data point to the mean

Standard Deviation

the square root of the variance

Coefficient of variation (%) equation=

standard deviation/mean times 100