Module 2: Measures of Location – Ungrouped Data The information in this module is contained in Chapter 3 in the text. This focus of this module is finding measures of location in ungrouped data. Specifically, we’ll learn how to find and interpret the following: 1. The Range (already covered in Module 1) 2. Mode 3. Mean 4. Median 5. Percentiles 6. Quartiles 7. The Interquartile Range 8. The 5 Number Summary We’ll first learn how to calculate these measures mathematically, then learn how to use Excel to find them. When answering homework or test questions, you can use which ever method you want.
Module 2: Measures of Location – Ungrouped Data 1. The Range (See Module 1) 2. The Mode – The mode is the most frequently occurring value in a data set. It’s easiest to find by placing the data in ascending order and looking for the most frequently occurring value. It’s possible for there to be no mode. It’s also possible for there to be more than one mode: If there are two modes, the data is bi-modal. If there are three modes, the data is tri-modal. If there are four or more, the data is multi-modal. 3. The Mean – The Average Let’s use the following data to find the mode and the mean. First, we’ll put the data into ascending order (next slide) 150 149 145 144 89 116 139 128 112 118 143 116 156 175 122 167 139 120 110 171 118 134 178 102
Module 2: Measures of Location – Ungrouped Data Mode – In looking at the ordered array, it’s clear this data set is tri-modal. There are two “116s”, two”118s”, and two “139s”. Had there, for example, been 3 “139s”, and everything else the same, 139 would have been the one and only mode. Mean– The mean is calculated using the following formula: is found by adding up all the numbers in the column. This sums to 3241. n is the sample size. In this case, there are 24 values in the column Therefore, the mean is = 135.0417 Using Excel to calculate the mode and mean. Mode: Excel is not a good tool for finding the mode unless there is only one mode. If there is more than one mode, Excel will only list one of them when using the mode command. Mean: Excel is an excellent tool for finding the mean. 89 102 110 112 116 116 118 118 120 122 128 134 139 139 143 144 145 149 150 156
Module 2: Measures of Location – Ungrouped Data At the bottom of the column on the left, you’ll see the Excel formulas for calculating the mode and median. Again note that Excel only lists the first mode in the ordered array, making Excel a poor tool for finding the mode if there is more than one. Note: The “(A1:A24)” part of the Excel command indicates the data is in the first 24 rows of column A in Excel. 89 102 110 112 116 116 118 118 120 122 128 134 139 139 143 144 145 149 150 156
Module 2: Measures of Location – Ungrouped Data 4. The Median – The middle value of an ordered array of numbers (ascending order, although with a median it technically could be descending order, too. But all other measures of location require ascending order). The median divides the data into two equal parts. 50% of the data lies above the median, 50% lies below.
- Spring '14