(a)
\nThere are 6 datapoints so the mean is
\n$\\frac{\\var{a2}+\\var{a3}+\\var{a4}+ \\var{a5}+ \\var{a6}+\\var{a7}}{6}=\\var{precround((a2+a3+a4+a5+a6+a7)/6,3)}$
\n\n(b)
\nTo find the median, we first put our values in order:
\n$\\var{a3},\\var{a4},\\var{a7},\\var{a5},\\var{a6},\\var{a2}$
\nThere are two middle values, $\\var{a7}$ and $\\var{a5}$.
\nSince there are two middle values, the median is equal to the mean of these:
\nSo the median is $\\frac{\\var{a7}+\\var{a5}}{2}$ =$\\var{(a7+a5)/2}$
\n\n(c)
\nThe mode is $\\var{a4}$ as it is the only value which appears twice.
\n\n(d)
\nThe range is the largest value minus the smallest value.
\nIn our example the largest value is $\\var{a2}$ and the smallest value is $\\var{a3}$
\nSo:
\nrange = $\\var{a2}-\\var{a3}=\\var{a2-a3}$
", "statement": "Seven students were asked how they rated the online maths assessment tool numbas on a scale of 0-10, with 0 representing terrible and 10 representing excellent. The results are below. Calculate the mean, median, mode and range for the set of data.
\n$ \\var{a2}, \\var{a3}, \\var{a4}, \\var{a5}, \\var{a6}, \\var{a7}$ .
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\n ", "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "scripts": {}, "type": "gapfill", "sortAnswers": false, "marks": 0, "variableReplacements": [], "gaps": [{"showPrecisionHint": true, "extendBaseMarkingAlgorithm": true, "marks": 1, "allowFractions": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "mustBeReducedPC": 0, "variableReplacements": [], "precisionType": "dp", "minValue": "1/6*{(a2+a3+a4+a5+a6+a7)}", "precision": "3", "showFeedbackIcon": true, "correctAnswerFraction": false, "maxValue": "1/6*{(a2+a3+a4+a5+a6+a7)}", "precisionPartialCredit": 0, "mustBeReduced": false, "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true}], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "steps": [{"variableReplacements": [], "prompt": "To find the mean:
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\n2. Divide by the number of numbers.
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", "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "scripts": {}, "type": "gapfill", "sortAnswers": false, "marks": 0, "variableReplacements": [], "gaps": [{"showPrecisionHint": true, "extendBaseMarkingAlgorithm": true, "marks": 1, "allowFractions": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "mustBeReducedPC": 0, "variableReplacements": [], "precisionType": "dp", "minValue": "(a7+a5)/2", "precision": "1", "showFeedbackIcon": true, "correctAnswerFraction": false, "maxValue": "(a7+a5)/2", "precisionPartialCredit": 0, "mustBeReduced": false, "showCorrectAnswer": true, "scripts": {}, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true}], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "steps": [{"variableReplacements": [], "prompt": "To find the median:
\nList the numbers in order of increasing size. The median is then the middle number. If there are two middle numbers we take the mean of the two middle numbers.
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", "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "scripts": {}, "type": "gapfill", "sortAnswers": false, "marks": 0, "variableReplacements": [], "gaps": [{"extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "allowFractions": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{a4}", "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "mustBeReduced": false, "marks": 1, "correctAnswerStyle": "plain", "variableReplacements": [], "mustBeReducedPC": 0, "minValue": "{a4}", "customMarkingAlgorithm": "", "showFeedbackIcon": true}], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "steps": [{"variableReplacements": [], "prompt": "The mode is the number that occurs most often.
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\nTopics covered are calculating the mean, median, mode and standard deviation.
\nrebelmaths
\n