12 Slide 1- All the values are included in computing the mean. 2- A set of data has a unique mean. 3- The mean is affected by unusually large or small data values. 4- It is a measure of central tendency not a measure of variation Properties of the Arithmetic Mean
22 Slide Average A measure of average is a number that is typical for a set of figures. Finding the average helps you to draw conclusions from data. The main types are mean, median and mode. 3 Different types
23 Slide A call centre claims to answer the calls on an average of 3 rings or less. Do you believe them ? Mode 7101080
24 Slide Median The median of a data set is the value in the middle when the data items are arranged in ascending order Whenever a data set has extreme values, the median is the preferred measure of central location. A few extremely large incomes or property values can inflate the mean. The median is the measure of location most often. reported for annual income and property value data. Just a note if you have an even amount of numbers a,b,c,d the median is b+c/2.
28 Slide Mode - The mode of a data set is the value that occurs with greatest frequency The greatest frequency can occur at two or more different values. If the data have exactly two modes, the data are bimodal. If the data have more than two modes, the data are multimodal.
34 Slide ~ What does Average really tell us? 10 50 90 40 50 60
35 Slide Measures of Variability (Dispersion) It is often desirable to consider measures of variability (dispersion), as well as measures of location. For example, in choosing supplier A or supplier B we might consider not only the average delivery time for each, but also the variability in delivery time for each.
36 Slide Measures of Variability (Dispersion) Range Interquartile Range or Midspread Variance Standard Deviation Coefficient of Variation
37 Slide Range - The range of a data set is the difference between the largest and smallest data values. It is the simplest measure of variability. It is very sensitive to the smallest and largest data values.
41 Slide Interquartile Range or Midspread - The interquartile range of a data set is the difference between the third (upper) quartile and the first (lower) quartile. It is the range for the middle 50% of the data. It overcomes the sensitivity to extreme data values—it is not effected by the extreme values.
42 Slide The Five-Number Summary The five-number summary is a set of five descriptive statistics that divide the data set into four equal sections. The five numbers in a five number summary are: 1. The minimum (smallest) number in the data set. 2. The 25th percentile, aka the first quartile, or Q1. 3. The median (or 50th percentile). 4. The 75th percentile, aka the third quartile, or Q3. 5. The maximum (largest) number in the data set.
43 Slide Where are the quartiles of 3, 4, 4, 6, 8, 8,10, 10, 11, 12, 31 Lower quartile is the (n + 1) ÷ 4 th value.
48 Slide Variance The variance is computed as follows: The variance is computed as follows: The variance is the average of the squared The variance is the average of the squared differences between each data value and the mean. differences between each data value and the mean. Note: from now on I will just give out one formula, I will use sample (inferred) formula's and not population. Saves confusion
49 Slide Don’t worry We will return to the data, to calculate who was the closest at guessing ages.