{"id":1520,"date":"2020-04-01T07:00:51","date_gmt":"2020-04-01T07:00:51","guid":{"rendered":"http:\/\/ibalmaths.com\/?post_type=knowledgebase&#038;p=1520"},"modified":"2020-04-01T10:16:01","modified_gmt":"2020-04-01T10:16:01","slug":"practice-questions-bivariate-statistics","status":"publish","type":"knowledgebase","link":"https:\/\/ibalmaths.com\/index.php\/ibdp-math-hl-2\/bivariate-statistics\/practice-questions-bivariate-statistics\/","title":{"rendered":"Practice Questions &#8211; Bivariate Statistics"},"content":{"rendered":"<p><strong>1.<\/strong><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1521\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/i.jpg\" alt=\"\" width=\"922\" height=\"601\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/i.jpg 922w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/i-300x196.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/i-768x501.jpg 768w\" sizes=\"auto, (max-width: 922px) 100vw, 922px\" \/><\/p>\r\n<p>The diagram represents the sales of Superclene toothpaste over the last few years. Give a reason why it is misleading. [1]<br \/>\r\n(ii) The following data represent the daily ticket sales at a small theatre during three weeks.<\/p>\r\n<p>52, 73, 34, 85, 62, 79, 89, 50, 45, 83, 84, 91, 85, 84, 87, 44, 86, 41, 35, 73, 86<\/p>\r\n<p><br \/>\r\n(a) Construct a stem-and-leaf diagram to illustrate the data. [3]<br \/>\r\n(b) Use your diagram to find the median of the data. [1]<\/p>\r\n<div id=\"link1-link-1520\" class=\"sh-link link1-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link1', 1520, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link1-toggle-1520\">Solution<\/span><\/a><\/div><div id=\"link1-content-1520\" class=\"sh-content link1-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>(i) False zero (or any other sensible statement)<\/p>\r\n<p>(ii)<br \/>\r\n<img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1526 size-full\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/i-1.jpg\" alt=\"\" width=\"251\" height=\"284\" \/><\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>(b) 79<\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>2.<\/strong> A random sample of 97 people who own mobile phones was used to collect data on the amount of time they spent per day on their phones. The results are displayed in the table below.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1528\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1.jpg\" alt=\"\" width=\"1150\" height=\"163\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1.jpg 1150w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-300x43.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-1024x145.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-768x109.jpg 768w\" sizes=\"auto, (max-width: 1150px) 100vw, 1150px\" \/>(i) Calculate estimates of the mean and standard deviation of the time spent per day on these mobile phones. [5]<br \/>\r\n(ii) On graph paper, draw a fully labelled histogram to represent the data. [4]<\/p>\r\n<div id=\"link2-link-1520\" class=\"sh-link link2-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link2', 1520, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link2-toggle-1520\">Solution<\/span><\/a><\/div><div id=\"link2-content-1520\" class=\"sh-content link2-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p>(i) Mean =(2.5 x 11 + 7.5 x 20 +15 x 32 + 25 x 18 + 35 x 10 +55 x 6)\/97 = 18.4<\/p>\r\n<p>sd = \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msqrt><\/msqrt><\/math>\r\n (2.52x 11 + 7.52x 20 +152x 32 + 252x 18 +352x 10 + 552x 6)\/97-mean<sup>2<\/sup>) = 13.3<\/p>\r\n<p>(ii)<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1529\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-1.jpg\" alt=\"\" width=\"322\" height=\"329\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-1.jpg 322w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-1-294x300.jpg 294w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>3.<\/strong> An experiment was conducted to investigate how the mass of a drug in a human body varies with time, measured from when the drug is given. The results are summarised in the following table.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1533\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-3.jpg\" alt=\"\" width=\"943\" height=\"114\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-3.jpg 943w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-3-300x36.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-3-768x93.jpg 768w\" sizes=\"auto, (max-width: 943px) 100vw, 943px\" \/><\/p>\r\n<p>(i) Draw a scatter diagram for the data. [2]<br \/>\r\n(ii) It is desirable to predict the mass of the drug in the long run. Explain why, in this context, neither a linear nor a quadratic model is likely to be appropriate. [2]<br \/>\r\n(iii) It is decided that a model of the form\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>t<\/mi><mfenced><mrow><mi>x<\/mi><mo>&#8211;<\/mo><mi>a<\/mi><\/mrow><\/mfenced><mo>=<\/mo><mi>b<\/mi><\/math>\r\n will be used. Calculate the least squares estimates of a and b and estimate the mass of the drug after two hours. [3]<br \/>\r\n(iv) Give an interpretation, in context, of the value of a. [1]<\/p>\r\n<div id=\"link3-link-1520\" class=\"sh-link link3-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link3', 1520, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link3-toggle-1520\">Solution<\/span><\/a><\/div><div id=\"link3-content-1520\" class=\"sh-content link3-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1534\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-4.jpg\" alt=\"\" width=\"1075\" height=\"909\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-4.jpg 1075w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-4-300x254.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-4-1024x866.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-4-768x649.jpg 768w\" sizes=\"auto, (max-width: 1075px) 100vw, 1075px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>4.<\/strong> Eight randomly selected students were asked to indicate the number of hours they spent studying Mathematics per week during the June holiday. The corresponding Mathematics Mid-year examination scores marked out of 100 marks of the eight students were recorded. The eight pairs of data are given in the table below.<\/p>\r\n<p>(i) Given that the regression line of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><\/math>\r\n on\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n is \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mn>1<\/mn><mo>.<\/mo><mn>9263<\/mn><mo>+<\/mo><mn>9<\/mn><mo>.<\/mo><mn>6223<\/mn><mi>x<\/mi><\/math>\r\n , find the value of p. [3]<br \/>\r\nDraw a scatter diagram to illustrate the data. Calculate the product moment correlation coefficient between\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n and \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><\/math>\r\n . [2]<br \/>\r\n(ii) Calculate the least squares estimates of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>a<\/mi><\/math>\r\n and\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><\/math>\r\n for the model\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mi>ln<\/mi><mo>&#160;<\/mo><mi>x<\/mi><\/math>\r\n . Find the product moment correlation coefficient between\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>ln<\/mi><mo>&#160;<\/mo><mi>x<\/mi><\/math>\r\n and \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><\/math>\r\n . [2]<br \/>\r\n(iii) Using your answers to parts (i) and (ii), explain which of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mn>1<\/mn><mo>.<\/mo><mn>9263<\/mn><mo>+<\/mo><mn>9<\/mn><mo>.<\/mo><mn>6223<\/mn><mi>x<\/mi><\/math>\r\n or \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mi>ln<\/mi><mo>&#160;<\/mo><mi>x<\/mi><\/math>\r\n \u00a0is the better model. [2]<br \/>\r\n(iv) Using the appropriate regression line, estimate the Mathematics Mid-year examination score of a student who spent 5.0 hours studying Mathematics during the June holiday. Comment on the reliability of your estimate. [2]<br \/>\r\n<br \/>\r\n<\/p>\r\n<div id=\"link4-link-1520\" class=\"sh-link link4-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link4', 1520, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link4-toggle-1520\">Solution<\/span><\/a><\/div><div id=\"link4-content-1520\" class=\"sh-content link4-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1536\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-5.jpg\" alt=\"\" width=\"1061\" height=\"1742\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-5.jpg 1061w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-5-183x300.jpg 183w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-5-624x1024.jpg 624w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-5-768x1261.jpg 768w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-5-936x1536.jpg 936w\" sizes=\"auto, (max-width: 1061px) 100vw, 1061px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p><strong>5. <\/strong>A particular hospital in Town A observed that the number of patients seeking medical treatment for respiratory problems has changed due to changes in air quality. The hospital decided to monitor the situation and the table below shows the results:<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1539\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-6.jpg\" alt=\"\" width=\"1077\" height=\"78\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-6.jpg 1077w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-6-300x22.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-6-1024x74.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-6-768x56.jpg 768w\" sizes=\"auto, (max-width: 1077px) 100vw, 1077px\" \/><\/p>\r\n<p>The least square regression line of\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><\/math>\r\n on\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n has equation \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mo>&#8211;<\/mo><mn>14<\/mn><mo>.<\/mo><mn>894<\/mn><mo>+<\/mo><mn>0<\/mn><mo>.<\/mo><mn>89875<\/mn><mi>x<\/mi><\/math>\r\n correct to 5significant figures.<br \/>\r\nThe line passes through \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mover><mi>x<\/mi><mo>&#175;<\/mo><\/mover><mo>&#160;<\/mo><mo>,<\/mo><mo>&#160;<\/mo><mover><mi>y<\/mi><mo>&#175;<\/mo><\/mover><\/mrow><\/mfenced><\/math>\r\n and the mean pollutants index,\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mover><mi>x<\/mi><mo>&#175;<\/mo><\/mover><\/math>\r\n , is 104.75.<br \/>\r\n(i) Show that \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><mo>=<\/mo><mn>67<\/mn><\/math>\r\n . [2]<br \/>\r\n(ii) Draw a scatter diagram to illustrate the data. [2]<br \/>\r\n(iii) Explain, giving your reasons, why a model of the form\u00a0 \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><mo>=<\/mo><mi>a<\/mi><mi>ln<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><\/math>\r\n fits the data better. [1]<br \/>\r\n(iv) Using the model in part (iii), calculate the equation of the least square regression line and the value of \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>r<\/mi><\/math>\r\n . [3]<br \/>\r\n(v) The hospital decided that they will need to purchase new equipment if the number of patients reaches 120. Explain, with reason, whether it is advisable for the hospital to purchase new equipment if the pollutant index is 150. [1]<\/p>\r\n<div id=\"link5-link-1520\" class=\"sh-link link5-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link5', 1520, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link5-toggle-1520\">Solution<\/span><\/a><\/div><div id=\"link5-content-1520\" class=\"sh-content link5-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1540\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-7.jpg\" alt=\"\" width=\"1075\" height=\"925\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-7.jpg 1075w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-7-300x258.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-7-1024x881.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-7-768x661.jpg 768w\" sizes=\"auto, (max-width: 1075px) 100vw, 1075px\" \/><\/p>\r\n<p><\/div>\r\n<p><strong>6.<\/strong> May travels regularly from home to the hospital for treatment. She leaves home at \r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n minutes after 8 am and takes\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><\/math>\r\n minutes to arrive at the hospital. Ten pairs of data are recorded in the table below.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1542\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-8.jpg\" alt=\"\" width=\"894\" height=\"102\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-8.jpg 894w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-8-300x34.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-8-768x88.jpg 768w\" sizes=\"auto, (max-width: 894px) 100vw, 894px\" \/><\/p>\r\n<p>(i) Draw a scatter diagram to illustrate the data, labelling the axes clearly. [1]<\/p>\r\n<p>(ii) Calculate the equation of the least squares regression line of\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><\/math>\r\n on\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n and the value the linear product moment correlation coefficient for the data. [3]<\/p>\r\n<p>(iii) Interpret the regression coefficient in the context of the question.[1]<\/p>\r\n<p>(iv) Draw the regression line of\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>y<\/mi><\/math>\r\n on\u00a0\r\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><\/math>\r\n on the scatter diagram. [1]<\/p>\r\n<p>(v) May has a hospital treatment appointment at 8.45 am on a particular day. If she leaves home at 8.10 am, explain whether she is likely to be on time for her hospital treatment. Comment on the reliability of your answer. [3]<\/p>\r\n<div id=\"link6-link-1520\" class=\"sh-link link6-link sh-hide\"><a href=\"#\" onclick=\"showhide_toggle('link6', 1520, 'Solution', 'Hide Solution'); return false;\" aria-expanded=\"false\"><span id=\"link6-toggle-1520\">Solution<\/span><\/a><\/div><div id=\"link6-content-1520\" class=\"sh-content link6-content sh-hide\" style=\"display: none;\"><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1543\" src=\"http:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-9.jpg\" alt=\"\" width=\"1071\" height=\"1031\" srcset=\"https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-9.jpg 1071w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-9-300x289.jpg 300w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-9-1024x986.jpg 1024w, https:\/\/ibalmaths.com\/wp-content\/uploads\/2020\/04\/1-9-768x739.jpg 768w\" sizes=\"auto, (max-width: 1071px) 100vw, 1071px\" \/><\/p>\r\n<p>\u00a0<\/div>\r\n<p>&nbsp;<\/p><!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"1. The diagram represents the sales of Superclene toothpaste over the last few years. Give a reason why it is misleading. [1] (ii) The following data represent the daily ticket sales at a small theatre during three weeks. 52, 73, 34, 85, 62, 79, 89, 50, 45, 83, 84, 91, 85, 84, 87, 44, 86, [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt -->","protected":false},"author":4,"featured_media":0,"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1520","knowledgebase","type-knowledgebase","status-publish","hentry","knowledgebase_cat-bivariate-statistics","no-wpautop"],"_links":{"self":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1520","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase"}],"about":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/types\/knowledgebase"}],"author":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/comments?post=1520"}],"version-history":[{"count":12,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1520\/revisions"}],"predecessor-version":[{"id":1544,"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/knowledgebase\/1520\/revisions\/1544"}],"wp:attachment":[{"href":"https:\/\/ibalmaths.com\/index.php\/wp-json\/wp\/v2\/media?parent=1520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}