{"id":24975,"date":"2022-11-02T10:40:52","date_gmt":"2022-11-02T10:40:52","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=24975"},"modified":"2025-12-09T14:43:22","modified_gmt":"2025-12-09T14:43:22","slug":"data-visualization","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/quantitative-methods\/data-visualization\/","title":{"rendered":"Data Visualization"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"VideoObject\",\n  \"name\": \"Organizing, Visualizing, and Describing Data \u2013 Part I: Data Visualization (2025 CFA\u00ae Level I \u2013 M2)\",\n  \"description\": \"This video covers data visualization, including identifying and comparing data types, organizing data for quantitative analysis, interpreting frequency distributions and contingency tables, and evaluating visualization methods. It also explains how to select appropriate visualization types to effectively analyze and present data insights.\",\n  \"uploadDate\": \"2018-04-04T00:00:00+00:00\",\n  \"thumbnailUrl\": \"https:\/\/img.youtube.com\/vi\/XCKuqfoNqOo\/maxresdefault.jpg\",\n  \"contentUrl\": \"https:\/\/youtu.be\/XCKuqfoNqOo\",\n  \"embedUrl\": \"https:\/\/www.youtube.com\/embed\/XCKuqfoNqOo\",\n  \"duration\": \"PT32M43S\"\n}\n<\/script>\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-43.jpg\",\n  \"caption\": \"Image of a Histogram\",\n  \"width\": 1463,\n  \"height\": 1206,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  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\"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_13-1024x896.png\",\n  \"caption\": \"A scatter plot graph\",\n  \"width\": 1024,\n  \"height\": 896,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14-768x1061.png\",\n  \"caption\": \"A scatter plot matrix\",\n  \"width\": 768,\n  \"height\": 1061,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"ImageObject\",\n  \"url\": \"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_15-1024x762.png\",\n  \"caption\": \"A heat map\",\n  \"width\": 1024,\n  \"height\": 762,\n  \"copyrightNotice\": \"\u00a9 2024 AnalystPrep\",\n  \"acquireLicensePage\": \"https:\/\/analystprep.com\/license-info\",\n  \"creditText\": \"AnalystPrep Design Team\",\n  \"creator\": {\n    \"@type\": \"Organization\",\n    \"name\": \"AnalystPrep\"\n  }\n}\n<\/script>\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Which of the following most likely represents the graph drawn by connecting successive mid-points in a histogram by straight lines?\",\n    \"text\": \"Which of the following most likely represents the graph drawn by connecting successive mid-points in a histogram by straight lines? A. Histogram. B. Frequency curve. C. Frequency polygon.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is C. When straight lines connect successive midpoints in a histogram, the resulting graph is called a frequency polygon. A histogram uses bars over intervals, not midpoints, and a frequency curve is a smoothed version of a frequency polygon.\"\n    }\n  }\n}\n<\/script>\n\n\n\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/XCKuqfoNqOo\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Data visualization refers to the presentation of data in a pictorial or graphical format using different graphs such as histograms, polygons, line charts, bar charts, etc.<\/p>\n<h2>Histogram<\/h2>\n<p>A histogram is a graphical representation of the data contained in a frequency distribution. It is a bar chart of data that groups data into intervals. The intervals should capture all the data points, and, in addition, the intervals should not overlap. A histogram is constructed by plotting intervals on the horizontal axis and the absolute frequencies on the vertical axis.<\/p>\n<p>If a histogram has equal size intervals, a rectangle should be erected over it, with its <strong>height <\/strong>being proportional to the absolute frequency. If intervals are of unequal sizes, then the erected rectangle has an <strong>area <\/strong>proportional to the absolute frequency of that particular interval. In such a case, we would have the vertical axis labeled as &#8216;density&#8217; instead of frequency. There should be no space between bars to indicate that the intervals are <strong>continuous<\/strong>.<\/p>\n<h4><strong>Example: Histogram<\/strong><strong>\u00a0<\/strong><\/h4>\n<p>Consider the previous example of the returns offered by a stock. To bring you up to speed, these were the intervals and the corresponding frequencies:<\/p>\n<p>$$<br \/>\\begin{array}{c|c|c}<br \/>\\text { Interval } &amp; \\text { Tally } &amp; \\text { Frequency } \\\\<br \/>\\hline-30 \\% \\leq \\mathrm{R}_{\\mathrm{t}} \\leq-20 \\% &amp; \\text { II } &amp; 2\u00a0 \\\\<br \/>-20 \\% \\leq \\mathrm{R}_{\\mathrm{t}} \\leq-10 \\% &amp; \\text { I } &amp; 1\u00a0 \\\\<br \/>-10 \\% \\leq \\mathrm{R}_{t} \\leq 0 \\% &amp; \\text { III } &amp; 3 \\\\<br \/>0 \\% \\leq \\mathrm{R}_{t} \\leq 10 \\% &amp; \\text { IIIII } &amp; 6\u00a0 \\\\<br \/>10 \\% \\leq \\mathrm{R}_{t} \\leq 20 \\% &amp; \\text { IIIIII } &amp; 7\u00a0 \\\\<br \/>20 \\% \\leq \\mathrm{R}_{t} \\leq 30 \\% &amp; \\text { IIII } &amp; 5\\\\<br \/>30 \\% \\leq \\mathrm{R}_{t} \\leq 40 \\% &amp; \\text { I } &amp; 1\u00a0 \\\\ \\hline<br \/>\\text { Total } &amp; &amp; 25 &amp; =25 \/ 25=100 \\%<br \/>\\end{array}<br \/>$$<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16302 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-43.jpg\" alt=\"Image of a Histogram\" width=\"1463\" height=\"1206\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-43.jpg 1463w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-43-300x247.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-43-768x633.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-43-1024x844.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-43-400x330.jpg 400w\" sizes=\"auto, (max-width: 1463px) 100vw, 1463px\" \/><\/p>\n<p>As mentioned earlier, histograms can also be created with relative frequencies\u2014the choice of using either absolute or relative frequency depends on the question being answered. An absolute frequency histogram best answers the question of how many items are in each bin. In contrast, a relative frequency histogram gives the proportion or percentage of the total observations in each bin.<\/p>\n<h2>Frequency Polygon<\/h2>\n<p>A frequency polygon is used to represent the distribution of data graphically. However, there is a major difference between a frequency polygon and a histogram. Instead of having the class intervals on the horizontal axis clearly showing their upper and lower limits, a frequency polygon uses the <strong>midpoints of the class intervals\u00a0<\/strong>where:<\/p>\n<p>$$\\text{Midpoint of a class interval}= \\text{Lower limit}+\\frac{\\text{Upper limit-Lower limit}}{2}$$<\/p>\n<p>The vertical axis features the absolute frequencies, which are then joined using straight lines and markers.<\/p>\n<h4>Example: Frequency Polygon<\/h4>\n<p>Going back to the stock return data, we could come up with a frequency polygon. To come up with the midpoints, we use the formula above. As an example, the midpoint of the interval -30% \u2264 R<sub>t<\/sub> \u2264 -20% is:<\/p>\n<p>$$ \\text{Midpoint} = -30 + \\cfrac {(-20 &#8211; &#8211; 30)}{2} = -25 $$<\/p>\n<p>We can calculate the midpoints for the other intervals in a similar manner. The final frequency polygon should look like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-16306 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-441.jpg\" alt=\"Image of a Frequency Polygon\" width=\"1463\" height=\"972\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-441.jpg 1463w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-441-300x199.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-441-768x510.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-441-1024x680.jpg 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2019\/08\/page-441-400x266.jpg 400w\" sizes=\"auto, (max-width: 1463px) 100vw, 1463px\" \/><\/p>\n<p>The frequency polygon is important because it shows the shape of a distribution of data. It can also be very useful when comparing two sets of data side-by-side. Note that the endpoints touch the X-axis. The vertical scale can also be positioned at the left margin.<\/p>\n<p>A cumulative frequency distribution graph can plot the cumulative frequency or relative frequency against the upper interval limit. The cumulative frequency distribution allows us to see how many or what percentage of the observations lie below a certain value. The figure below is an example of a cumulative frequency distribution.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31046 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_3.png\" alt=\"Image showing Cumulative Frequency Distribution\" width=\"1590\" height=\"1147\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_3.png 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_3-300x216.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_3-1024x739.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_3-768x554.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_3-1536x1108.png 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_3-400x289.png 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/p>\n<p>As we move from one interval to the next, The change in the cumulative relative frequency represents the interval&#8217;s relative frequency. A steep slope of the cumulative frequency distribution indicates that the frequencies are large. It is pertinent to note that the slope of the cumulative absolute distribution at any particular interval is proportional to the number of observations in that interval.<\/p>\n<h2>Bar Chart<\/h2>\n<p>A bar chart is used to plot the frequency distribution of category-based data. In a bar chart, each bar represents a distinct category, while the height of a bar is proportional to the frequency of the corresponding category. Bar charts can be vertical or horizontal.<\/p>\n<ul>\n<li>In a vertical (horizontal) bar chart, the y-axis (x-axis) represents the absolute or relative frequency.<\/li>\n<li>In contrast, the x-axis (y-axis) represents the mutually exclusive categories to be <em>compared <\/em>rather than bins that group numerical data (unlike histogram).<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-37265 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-bar-charts.png\" alt=\"cfa level 1 bar charts\" width=\"782\" height=\"526\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-bar-charts.png 782w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-bar-charts-300x202.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-bar-charts-768x517.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-bar-charts-400x269.png 400w\" sizes=\"auto, (max-width: 782px) 100vw, 782px\" \/><\/p>\n<h3>Pareto Chart<\/h3>\n<p>A bar chart in which categories are ordered by frequency in descending order and has a line displaying cumulative relative frequency is known as a Pareto Chart. This chart is used to highlight dominant categories or the most important groups.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-31052 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_5.png\" alt=\"Image of a Pareto Chart\" width=\"1794\" height=\"1251\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_5.png 1794w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_5-300x209.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_5-1024x714.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_5-768x536.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_5-1536x1071.png 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_5-400x279.png 400w\" sizes=\"auto, (max-width: 1794px) 100vw, 1794px\" \/><\/p>\n<h2>Grouped Bar Chart<\/h2>\n<p>A grouped bar chart (also known as a clustered bar chart) plots two category-based variables to represent their joint frequencies.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-37270 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-grouped-bar-chart-1.png\" alt=\"cfa level 1 grouped bar chart\" width=\"726\" height=\"528\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-grouped-bar-chart-1.png 726w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-grouped-bar-chart-1-300x218.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-grouped-bar-chart-1-400x291.png 400w\" sizes=\"auto, (max-width: 726px) 100vw, 726px\" \/><\/p>\n<h3>\u00a0<\/h3>\n<h2>Stacked Bar Chart<\/h2>\n<p>A stacked bar chart also presents the joint frequency distribution of two cat\u00adegory-based variables. In a vertically stacked bar chart, the bars representing the sub-groups are placed on top of each other to form a single bar. Each sub-section of the bar is shown in a different color to represent the contribution of each sub-group. Further, the stacked bar&#8217;s overall height represents the category&#8217;s marginal frequency.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-37271 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-stacked-bar-chart.png\" alt=\"cfa level 1 stacked bar chart\" width=\"738\" height=\"505\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-stacked-bar-chart.png 738w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-stacked-bar-chart-300x205.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/cfa-level-1-stacked-bar-chart-400x274.png 400w\" sizes=\"auto, (max-width: 738px) 100vw, 738px\" \/><\/p>\n<h2>Tree-map<\/h2>\n<p>A tree-map chart displays hierarchical data. A rectangular shape represents each item on a tree-map. It is critical to note that smaller rectangles represent the sub-groups. Further, there is a correlation between the color and size of rectangles and the tree structure. Equally worth noting is the fact that the area of each rectangle is proportional to the value of the corresponding group.<\/p>\n<p>The tree-map below depicts the revenues of different companies in the food sector. We can observe that ABC Company has the highest revenue in the sector, represented by the rectangle with the largest area.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31055 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_8.png\" alt=\"A tree-map chart\" width=\"1590\" height=\"1090\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_8.png 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_8-300x206.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_8-1024x702.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_8-768x526.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_8-1536x1053.png 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_8-400x274.png 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/p>\n<h2>Word Cloud<\/h2>\n<p>A word cloud (also known as a tag cloud) is a visual representation of textual data. The size of each specific word is proportional to the frequency of words within a given body of text. We can use a different colors to convey different sentiments. For example, we can use green color to display profit. On the other hand, we can use red color to symbolize loss. A word cloud is generally used to display unstructured data.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-39047 size-full\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Word-Cloud.jpg\" alt=\"Word Cloud\" width=\"800\" height=\"510\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Word-Cloud.jpg 800w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Word-Cloud-300x191.jpg 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Word-Cloud-768x490.jpg 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Word-Cloud-400x255.jpg 400w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>Line Chart<\/h2>\n<p>A line chart is used to display the change in data series over time. It&#8217;s important to note that both the frequency polygons and the cumulative frequency distribution charts are line charts, representing data frequency distributions. However, they do not display the change in data over time.<\/p>\n<p>In a line chart, the x-axis represents the period (say years), while the y-axis represents the data we want to plot (say, the real GDP growth rate).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31057 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_10.png\" alt=\"A line chart\" width=\"1590\" height=\"1187\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_10.png 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_10-300x224.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_10-1024x764.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_10-768x573.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_10-1536x1147.png 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_10-400x299.png 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/p>\n<p>A line chart can be drawn using more than one set of data points, which can be used for comparisons.<\/p>\n<h2>Bubble Line Chart<\/h2>\n<p>In a bubble line chart, data points are represented by bubbles of various sizes. The bubbles represent the third dimension of data. These bubbles can be of different colors to represent additional information, i.e., red bubbles for negative values and green bubbles for positive values.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31058 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_12.png\" alt=\"Bubble Line Chart\" width=\"1590\" height=\"1350\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_12.png 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_12-300x255.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_12-1024x869.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_12-768x652.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_12-1536x1304.png 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_12-400x340.png 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/p>\n<h2>Scatter Plot<\/h2>\n<p>A scatter plot is a graph that shows the relationship between two numerical variables. It helps in displaying and understanding potential relationships between two variables. In a scatter plot, one variable is plotted on the x-axis and another, on the y-axis.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31059 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_13.png\" alt=\"A scatter plot graph\" width=\"1590\" height=\"1391\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_13.png 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_13-300x262.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_13-1024x896.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_13-768x672.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_13-1536x1344.png 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_13-400x350.png 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/p>\n<p>As shown above, a positive slope for a line of data points indicates a positive relationship between two variables, and vice-versa. The strength of the relationship between variables can be determined based on how closely the data points are clustered around the line. Tight clustering indicates a potentially stronger relationship. Further, data points located toward the ends of each axis represent the maximum or minimum values (i.e., outliers).<\/p>\n<h2>Scatter Plot Matrix<\/h2>\n<p>A scatter plot matrix is a grid of scatter plots used to visualize bivariate relationships between combinations of variables.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31060 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14.png\" alt=\"A scatter plot matrix \" width=\"1590\" height=\"2197\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14.png 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14-217x300.png 217w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14-741x1024.png 741w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14-768x1061.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14-1112x1536.png 1112w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14-1482x2048.png 1482w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_14-400x553.png 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/p>\n<h2>Heat Map<\/h2>\n<p>A heat map is a graphical representation of data that uses a system of color-coding to represent different values. More intense color is displayed as the marks \u201cheat up\u201d due to their higher values or density of records. Heat maps can display frequency distributions and visualize the degree of correlation among different variables.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-31061 size-full\" style=\"max-width: 100%;\" src=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_15.png\" alt=\"A heat map\" width=\"1590\" height=\"1183\" srcset=\"https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_15.png 1590w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_15-300x223.png 300w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_15-1024x762.png 1024w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_15-768x571.png 768w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_15-1536x1143.png 1536w, https:\/\/analystprep.com\/cfa-level-1-exam\/wp-content\/uploads\/2021\/08\/Img_15-400x298.png 400w\" sizes=\"auto, (max-width: 1590px) 100vw, 1590px\" \/><\/p>\n<blockquote>\n<h2>Question<\/h2>\n<p>Which of the following <em>most likely <\/em>represents the graph drawn by connecting successive mid-points in a histogram by straight lines?<\/p>\n<ol style=\"list-style-type: upper-alpha;\">\n<li>Histogram.<\/li>\n<li>Frequency curve.<\/li>\n<li>Frequency polygon.<\/li>\n<\/ol>\n<p><strong>Solution<\/strong><\/p>\n<p>The correct answer is\u00a0<strong>C<\/strong>.<\/p>\n<p>When straight lines connect successive midpoints in a histogram, the graph is called a frequency polygon.<\/p>\n<p><strong>A is incorrect<\/strong>. A histogram is a graphical representation of the data contained in the frequency distribution but not using mid-points. Instead, a rectangle should be erected over the whole interval.<\/p>\n<p><strong>B is incorrect<\/strong>. When a frequency polygon is smoothed, a frequency curve is obtained.<\/p>\n<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>Data visualization refers to the presentation of data in a pictorial or graphical format using different graphs such as histograms, polygons, line charts, bar charts, etc. Histogram A histogram is a graphical representation of the data contained in a frequency&#8230;<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-24975","post","type-post","status-publish","format-standard","hentry","category-quantitative-methods","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Data Visualization Tools Explained | CFA Level 1<\/title>\n<meta name=\"description\" content=\"Understand how data visualization uses scatter plots, histograms, and bubble plots to represent variables. 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