Unit 2 Section 2.3

What we will be able to do throughout this part of the chapter…  Use statistical methods to summarize data  The most familiar method is using “averages”. Also known as measures of central tendencies.  Mean, Median, Mode, and Midrange  Measures of variation or measures of dispersion  Range, Variance, and Standard Deviation  Measures of position  Percentiles and Quartiles Section 2.3

2.3: Measures of Central Tendency  Statistic – a characteristic or measure obtained by using the data values from a sample.  Parameter – a characteristic or measure obtained by using all the data values from a specific population.  NOTE: General Rounding Rule  In statistics, rounding takes place when all computations are completed.

 Mean – the sum of the data entries, divided by the total number of entries.  Also known as the arithmetic average.  Sample mean: (read as “x bar”)  Population mean: (pronounced mu)  Rules for a Rounding a Mean:  If the original data is given in whole numbers, we would round the mean to 1 decimal place.  If the original data is given to one decimal place, we would round the mean to 2 decimal places. Section 2.3

Finding the Mean Section 2.3  Determine the mean of the following data representing the number of days off for individuals from a sample of nine different countries. 20, 26, 40, 36, 23, 42, 35, 24, 30

 Median – the midpoint of the data array.  Think of it as the middle number.  Divides the data into two equal parts  Notation: MD  Steps for finding the median:  Place the numbers in order.  Select the middle point. If there are two numbers that fall in the middle, add the two values together and divide by two Section 2.3

Finding the Median Section 2.3  Find the median for each data set: 1, 3, 4, 2, 3, 5, 1 684, 764, 656, 702, 856, 1133, 1132, 1303

 Mode – the value that occurs most often in a data set (greatest frequency).  Unimodal – a data set that has only one value that occurs the most.  Bimodal – a data set that has two values that occur with the same greatest frequency.  Multimodal – a data set that has more than two values that occur with the same greatest frequency.  No Mode – a data set where no values occur more than once. Section 2.3

Finding the Mode Section 2.3  The following data represents the duration (in days) of U.S. Space Shuttle voyages for the years Find the mode 8, 9, 9, 14, 8, 8, 10, 7, 6, 9, 7, 8, 10, 14, 11, 8, 14, 11

Homework Section 2.3  Pg. 75 (17 – 23)  Read and Take Notes on Section 2.3 (Pgs. 67 – 70)