12 Properties of the Arithmetic Mean 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
22 AverageA 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 A call centre claims to answer the calls on an average of 3 rings or less. Do you believe them ? 7101080Mode
24 Median The median of a data set is the value in the middle when the data items are arranged in ascending orderJust a note if you have an even amount of numbers a,b,c,d the median is b+c/2.Whenever a data set has extreme values, the medianis the preferred measure of central location.The median is the measure of location most oftenreported for annual income and property value data.A few extremely large incomes or property valuescan inflate the mean.
28 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.
35 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 wemight consider not only the average delivery time foreach, but also the variability in delivery time for each.
36 Measures of Variability (Dispersion) RangeInterquartile Range or MidspreadVarianceCoefficient of VariationStandard Deviation
37 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 andlargest data values.
41 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 datavalues—it is not effected by the extreme values.
42 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 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 Variance The variance is the average of the squared differences between each data value and the mean.The variance is computed as follows:Note: from now on I will just give out one formula , I will use sample (inferred) formula's and not population. Saves confusion
49 Don’t worryWe will return to the data , to calculate who was the closest at guessing ages.