{"id":693,"date":"2024-04-17T10:49:58","date_gmt":"2024-04-17T14:49:58","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&p=693"},"modified":"2024-06-11T15:58:18","modified_gmt":"2024-06-11T19:58:18","slug":"cumulative-frequency-distributions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/cumulative-frequency-distributions\/","title":{"raw":"Histograms, Boxplots and Ogives","rendered":"Histograms, Boxplots and Ogives"},"content":{"raw":"
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\u00a0Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nCreate and interpret Histograms, Boxplots and Ogives\r\n\r\n<\/div>\r\n<\/div>\r\n

Histograms:<\/h2>\r\n\r\n\r\n\r\n
\r\n
    \r\n \t
  • A type of 'bar chart' organized by classes\/categories created for the data (bins)<\/li>\r\n \t
  • Where the heights of the bars equal to the frequencies of those classes<\/li>\r\n \t
  • Useful for determining the 'shape' of the distribution of the data<\/li>\r\n<\/ul>\r\n<\/td>\r\n
\"\"<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Box Plots:<\/h2>\r\n\r\n\r\n\r\n
\r\n
    \r\n \t
  • The 'box' spans from quarter 1 to quarter 3<\/li>\r\n \t
  • The middle line of the box indicates the median<\/li>\r\n \t
  • If there are outliers (extremely large\/small values), they are indicated by dots or asterisks (*)<\/li>\r\n \t
  • The lower and upper lines (fences) indicate the highest and lowest non-outlier values in the data<\/li>\r\n \t
  • Is a great visual tool to help understand the dispersion\/spread of the data<\/li>\r\n<\/ul>\r\n<\/td>\r\n
\"\"<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Ogives:<\/h2>\r\n\r\n\r\n\r\n
\r\n
    \r\n \t
  • A line chart where the heights are the cumulative frequency values<\/li>\r\n \t
  • Useful for estimating the percent of data that lie below or above particular variables or values[footnote]https:\/\/byjus.com\/maths\/ogive\/#:~:text=The%20word%20Ogive%20is%20a,calculated%20using%20a%20frequency%20table.[\/footnote]<\/li>\r\n \t
  • Can be made by inserting in a line chart where the y-axis values are the cumulative percent frequencies and the x-axis is the class limits column from the cumulative frequency table<\/span><\/li>\r\n \t
  • Useful for determining the 'spread' of the data<\/li>\r\n<\/ul>\r\n<\/td>\r\n
\"\"<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Creating a Histogram in Excel (video)<\/h1>\r\n

Example 12.1.1<\/h2>\r\nProblem Setup: <\/strong><\/span>Again, we are working with the 30 students' heights from BCIT (click here to download as Excel sheet<\/a>) and see the table of values below.\r\n\r\n\r\n\r\n\r\n\r\n
173<\/td>\r\n153<\/td>\r\n172<\/td>\r\n191<\/td>\r\n173<\/td>\r\n167<\/td>\r\n156<\/td>\r\n169<\/td>\r\n175<\/td>\r\n169<\/td>\r\n<\/tr>\r\n
159<\/td>\r\n163<\/td>\r\n177<\/td>\r\n155<\/td>\r\n152<\/td>\r\n178<\/td>\r\n172<\/td>\r\n188<\/td>\r\n152<\/td>\r\n171<\/td>\r\n<\/tr>\r\n
174<\/td>\r\n183<\/td>\r\n192<\/td>\r\n151<\/td>\r\n159<\/td>\r\n184<\/td>\r\n170<\/td>\r\n186<\/td>\r\n155<\/td>\r\n156<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nQuestion: <\/strong><\/span>Can you create a histogram of these heights?\r\n\r\n[embed]https:\/\/youtu.be\/6V_m7HFofKA[\/embed]\r\n\r\nSolution: Click here<\/a><\/strong><\/span> to view the Excel solutions shown in the above video.\r\n

Creating a BOXPLOT in Excel (video)<\/h1>\r\n

Example 12.1.2<\/h2>\r\nProblem Setup: <\/strong><\/span>Again, we are working with the 30 students' heights from BCIT (click here to download as Excel sheet<\/a>) and see the table of values below.\r\n\r\n\r\n\r\n\r\n\r\n
173<\/td>\r\n153<\/td>\r\n172<\/td>\r\n191<\/td>\r\n173<\/td>\r\n167<\/td>\r\n156<\/td>\r\n169<\/td>\r\n175<\/td>\r\n169<\/td>\r\n<\/tr>\r\n
159<\/td>\r\n163<\/td>\r\n177<\/td>\r\n155<\/td>\r\n152<\/td>\r\n178<\/td>\r\n172<\/td>\r\n188<\/td>\r\n152<\/td>\r\n171<\/td>\r\n<\/tr>\r\n
174<\/td>\r\n183<\/td>\r\n192<\/td>\r\n151<\/td>\r\n159<\/td>\r\n184<\/td>\r\n170<\/td>\r\n186<\/td>\r\n155<\/td>\r\n156<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nQuestion: <\/strong><\/span>Can you create a boxplot of these heights?\r\n\r\n[embed]https:\/\/youtu.be\/G2ZbSE4uR9c[\/embed]\r\n\r\nSolution: Click here<\/a><\/strong><\/span>\u00a0to view the Excel solutions shown in the above video.\r\n

Understanding Outliers in Boxplots and Histograms (video)<\/h1>\r\n

Example 12.2.1<\/h2>\r\nProblem Setup: <\/strong><\/span>We will now revisit the student survey data inputted by students in 2019 (Click here to download<\/a>).\r\n\r\nQuestion: <\/strong><\/span>Can you create an explain the values in the boxplot created for the students' heights?\r\n\r\n[embed]https:\/\/youtu.be\/ZfIyExSlwp0[\/embed]\r\n\r\nSolution: Click here<\/a><\/strong><\/span>\u00a0to view the Excel solutions shown in the above video.\r\n

Creating Ogives in Excel (video)<\/h1>\r\n

Example 12.1.3<\/h2>\r\nProblem Setup: <\/strong><\/span>Again, we are working with the 30 students' heights from BCIT (click here to download as Excel sheet<\/a>).\r\n\r\n\r\n\r\n\r\n\r\n
173<\/td>\r\n153<\/td>\r\n172<\/td>\r\n191<\/td>\r\n173<\/td>\r\n167<\/td>\r\n156<\/td>\r\n169<\/td>\r\n175<\/td>\r\n169<\/td>\r\n<\/tr>\r\n
159<\/td>\r\n163<\/td>\r\n177<\/td>\r\n155<\/td>\r\n152<\/td>\r\n178<\/td>\r\n172<\/td>\r\n188<\/td>\r\n152<\/td>\r\n171<\/td>\r\n<\/tr>\r\n
174<\/td>\r\n183<\/td>\r\n192<\/td>\r\n151<\/td>\r\n159<\/td>\r\n184<\/td>\r\n170<\/td>\r\n186<\/td>\r\n155<\/td>\r\n156<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nQuestion: <\/strong><\/span>Can you create an ogive of these heights?\r\n\r\n[embed]https:\/\/youtu.be\/0QBCxmyymXw[\/embed]\r\n\r\nSolution: Click here<\/a><\/strong><\/span> to view the Excel solutions shown in the above video.\r\n

Key Takeaways (EXERCISE)<\/h1>\r\n
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Key Takeaways: Histograms, Boxplots and Ogives<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\n[h5p id=\"27\"]\r\n\r\n[h5p id=\"28\"]\r\n\r\n<\/div>\r\n<\/div>\r\n

Your Own Notes (EXERCISE)<\/h1>\r\n