{"id":6502,"date":"2014-02-06T17:19:43","date_gmt":"2014-02-06T17:19:43","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6502"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"representing-data-frequency-distributions-and-stem-and-leaf-plots","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/02\/06\/representing-data-frequency-distributions-and-stem-and-leaf-plots\/","title":{"rendered":"Representing Data: Frequency Distributions and Stem and Leaf Plots"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

In order to use raw data effectively, it must usually be organized in some way.\u00a0 A group of test scores would not be useful unless there was some way to tell how many scores there were, and if any score occurred more frequently than others.\u00a0 One of the shorthand ways to show values is to organize the data in a frequency distribution and then construct a stem-and-leaf-plot from the frequency distribution.<\/p>\n

What Is a Frequency Distribution?<\/strong><\/p>\n

A frequency distribution is an arrangement of raw data in such a way to show how many\u00a0 are in each group or within a range.\u00a0 Suppose an experimenter has measured the heights of 20 12 year olds and gets the following values in inches:\u00a0 64 48 55 68 72 59 57 61 63 60 60 43 67 70 65 55 56 64 61 60.\u00a0 It’s a small group of data, so it is easy to arrange from smallest to largest, and notice that there are some heights that occur more than once: 43\u00a048 55 55 56 57 59 60 60 60 61 61 63 64 64 65 67 68 70 72.<\/p>\n

How Can Data Be Grouped?<\/strong><\/p>\n

One of the simplest ways to group this data set is to divide it into four ranges, from 41-49, 50-59, 60-69, and 70-79.\u00a0 In the 41-49 group, there are two scores, 43 48.\u00a0 In the 50-59 group there are five scores, 55 55 56 57 59.\u00a0 In the 60-69 group there are 11 scores, 60 60 60 61 61 63 64 64 65 67 68.\u00a0 In the 70-79 group, there are two scores, 70 72.<\/p>\n

How Can Data Be Represented?<\/strong><\/p>\n

The data can be represented in several different ways, in a table, a bar graph, a line graph, or a circle graph.\u00a0 However, a bar graph\u00a0may lose the exact values.\u00a0 It does show that most 12 year olds in this particular group have heights in the 60-69 inch range.<\/p>\n

<\/p>\n

<\/p>\n

<\/p>\n

What Is a Stem and Leaf Plot?<\/strong><\/p>\n

A stem and leaf plot is another way to represent the same data, but without losing any of the raw data.\u00a0 That way, one can see the exact values of the data.\u00a0 The ranges are represented, but so are the exact values.\u00a0 In the stem and leaf plot, the tens place of the raw scores forms the stem and the ones place of the raw scores forms the leaves.\u00a0 A chart can be made with the data as follows:<\/p>\n

Stem\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Leaf<\/p>\n

4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3 8<\/p>\n

5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5 5 6 7 9<\/p>\n

6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 0\u00a00 1 1 3 4 4 5 7 8<\/p>\n

7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 0 2<\/p>\n

The chart could be then read easily, as the lowest scores are 43 and 48, followed by 55 55 56 57 59, then 60 60 60 61 61 63 64 64 65 67 68, then 70 and 72.<\/p>\n

Interested in statistics tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Augusta, ME visit: Tutoring in Augusta, ME<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"Overview: In order to use raw data effectively, it must usually be organized in some way.\u00a0 A group of test scores would not be useful unless there was some way to tell how many scores there were, and if any score occurred more frequently than others.\u00a0 One of the shorthand ways to show values is [...]","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,17],"tags":[699,1730],"class_list":["post-6502","post","type-post","status-publish","format-standard","hentry","category-algebra","category-statistics-2","tag-frequency-distributions","tag-stem-and-leaf-plots"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6502","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6502"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6502\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6502"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6502"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6502"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}