Data Descriptions

Measures of Central Tendency There are 4 measures of central tendency (also called measures of average): Mean Median Mode Midrange 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 for a specific population.

Mean Mean: The sum of the values divided by the total number of values. Mean formula:

Mean Examples Determine the mean of the following sets of data. Round to the tenths if necessary. #1: 3,8,5,12,14,12 #2: 6.5,6.5,9.5,8,14,8.5,3,7.5,16.5,7,8 #3: In set #1 can the mean 15.7? Explain why or why not.

Mean for Ungrouped Data So what might we have to do if the data is given to us in an ungrouped freq. distribution like the one below? Need to multiply the class column by the frequency column giving is the f ● X column. f = frequency and X = points

Mean for Grouped Data f = frequency and Xm = class midpoint So what might we have to do if the data is given to us in a grouped freq. distribution like the one below? Need to find the midpoint of each class and multiply that by the frequency column giving us the f ● Xm column. f = frequency and Xm = class midpoint

Median Median: The midpoint of the data array. Breaks the data into 2 equal pieces with the same amount below and above the median. Symbol for median is MD. How do we find it? Is there a difference if there is an odd or even amount of data?

Median Examples Use the data sets to determine the median of the set. #1: 180, 201, 220, 191, 219, 209, 186. #2: 18, 24, 20, 35, 19, 23, 26, 23, 19, 20

Median for Ungrouped Data So what might we do to find the median of a freq. distribution like the one below? Need to create a cf column for the data. Using the cf we will simply divide the total number by 2. After dividing we determine in which class the data will fall, therefore getting us our median.

Ungrouped Median Example Use the data set to determine the median.

Median for Grouped Data Step 1: Using the freq. distribution divide the total frequency by 2. Determines which piece of data we are looking for. Step 2: Find the class that contains that piece of data by using the cf column. This class is known as the median class.

Median Grouped Data Continued Step 3: Use the following formula to find the median.

Median Grouped Example Use the data below to find the median of the group.

Mode Mode: The value that occurs the most often in a data set. Data sets can have one mode, more than one mode (multi-modal), or no mode at all. Examples: #1: 8,9,9,14,8,8,10,7,6,9,7,8,10,14,11,8,14,11 #2: 2,5,7,8,9 #3: 26,18,15,18,22,24,18,24,26,24

Modes for Ungrouped Data Find the mode for the following data set.

Modes for Grouped Data Modal class: The class with the largest frequency. Example:

Midrange Midrange: The sum of the lowest and highest values in the data set divided by 2. The symbol for midrange is MR. Find the midrange of the following sets. #1: 8,9,9,14,8,8,10,7,6,9,7,8,10,14,11,8,14,11 #2: 2,5,7,8,9 #3: 26,18,15,18,22,24,18,24,26,24