{"id":2322,"date":"2025-02-19T03:40:26","date_gmt":"2025-02-19T03:40:26","guid":{"rendered":"https:\/\/donhit.com\/en\/?p=2322"},"modified":"2025-02-19T03:40:26","modified_gmt":"2025-02-19T03:40:26","slug":"central-limit-theorem","status":"publish","type":"post","link":"https:\/\/donhit.com\/en\/calculator\/central-limit-theorem\/","title":{"rendered":"Central Limit Theorem Calculator"},"content":{"rendered":"<p><center><div class=\"container123\">\r\n        <div class=\"header123\">\r\n            <h2>Central Limit Theorem Calculator<\/h2>\r\n            <p>Explore the magic of probability distributions and sampling<\/p>\r\n        <\/div>\r\n\r\n        <div class=\"calculator\">\r\n            <div class=\"input-group\">\r\n                <div class=\"input-field\">\r\n                    <label for=\"population-mean\">Population Mean (\u03bc)<\/label>\r\n                    <input type=\"number\" id=\"population-mean\" value=\"50\" step=\"any\">\r\n                <\/div>\r\n                <div class=\"input-field\">\r\n                    <label for=\"population-sd\">Population Standard Deviation (\u03c3)<\/label>\r\n                    <input type=\"number\" id=\"population-sd\" value=\"10\" min=\"0\" step=\"any\">\r\n                <\/div>\r\n                <div class=\"input-field\">\r\n                    <label for=\"sample-size\">Sample Size (n)<\/label>\r\n                    <input type=\"number\" id=\"sample-size\" value=\"30\" min=\"1\">\r\n                <\/div>\r\n                <div class=\"input-field\">\r\n                    <label for=\"num-samples\">Number of Samples<\/label>\r\n                    <input type=\"number\" id=\"num-samples\" value=\"1000\" min=\"1\">\r\n                <\/div>\r\n            <\/div>\r\n\r\n            <button onclick=\"calculate()\">Calculate<\/button>\r\n\r\n            <div class=\"results\" id=\"results\">\r\n                <h3>Results<\/h3>\r\n                <p><strong>Sample Mean (x\u0304):<\/strong> <span id=\"sample-mean\"><\/span><\/p>\r\n                <p><strong>Standard Error (SE):<\/strong> <span id=\"standard-error\"><\/span><\/p>\r\n                <p><strong>95% Confidence Interval:<\/strong> <span id=\"confidence-interval\"><\/span><\/p>\r\n                \r\n                <div class=\"chart-container\">\r\n                    <canvas id=\"distributionChart\"><\/canvas>\r\n                <\/div>\r\n            <\/div>\r\n        <\/div>\r\n    <\/div>\r\n\r\n    <script>\r\n        let chart = null;\r\n\r\n        function calculate() {\r\n            const populationMean = parseFloat(document.getElementById('population-mean').value);\r\n            const populationSD = parseFloat(document.getElementById('population-sd').value);\r\n            const sampleSize = parseInt(document.getElementById('sample-size').value);\r\n            const numSamples = parseInt(document.getElementById('num-samples').value);\r\n\r\n            \/\/ Validate inputs\r\n            if (isNaN(populationMean) || isNaN(populationSD) || isNaN(sampleSize) || isNaN(numSamples)) {\r\n                alert('Please enter valid numbers for all fields');\r\n                return;\r\n            }\r\n\r\n            if (populationSD <= 0 || sampleSize <= 0 || numSamples <= 0) {\r\n                alert('Standard deviation, sample size, and number of samples must be positive');\r\n                return;\r\n            }\r\n\r\n            \/\/ Generate sample means\r\n            const sampleMeans = [];\r\n            for (let i = 0; i < numSamples; i++) {\r\n                const sample = generateSample(populationMean, populationSD, sampleSize);\r\n                const mean = sample.reduce((a, b) => a + b) \/ sampleSize;\r\n                sampleMeans.push(mean);\r\n            }\r\n\r\n            \/\/ Calculate statistics\r\n            const meanOfMeans = sampleMeans.reduce((a, b) => a + b) \/ numSamples;\r\n            const standardError = populationSD \/ Math.sqrt(sampleSize);\r\n            const confidenceInterval = [\r\n                meanOfMeans - 1.96 * standardError,\r\n                meanOfMeans + 1.96 * standardError\r\n            ];\r\n\r\n            \/\/ Update results\r\n            document.getElementById('sample-mean').textContent = meanOfMeans.toFixed(2);\r\n            document.getElementById('standard-error').textContent = standardError.toFixed(2);\r\n            document.getElementById('confidence-interval').textContent = \r\n                `(${confidenceInterval[0].toFixed(2)}, ${confidenceInterval[1].toFixed(2)})`;\r\n\r\n            \/\/ Show results\r\n            document.getElementById('results').style.display = 'block';\r\n\r\n            \/\/ Create histogram\r\n            createHistogram(sampleMeans, meanOfMeans, standardError);\r\n        }\r\n\r\n        function generateSample(mean, sd, size) {\r\n            const sample = [];\r\n            for (let i = 0; i < size; i++) {\r\n                \/\/ Box-Muller transform\r\n                let u1 = Math.random();\r\n                let u2 = Math.random();\r\n                let z = Math.sqrt(-2 * Math.log(u1)) * Math.cos(2 * Math.PI * u2);\r\n                sample.push(mean + sd * z);\r\n            }\r\n            return sample;\r\n        }\r\n\r\n        function createHistogram(data, mean, se) {\r\n            \/\/ Create bins\r\n            const min = Math.min(...data);\r\n            const max = Math.max(...data);\r\n            const binWidth = (max - min) \/ 30;\r\n            const bins = new Array(30).fill(0);\r\n            \r\n            data.forEach(value => {\r\n                const binIndex = Math.min(Math.floor((value - min) \/ binWidth), 29);\r\n                bins[binIndex]++;\r\n            });\r\n\r\n            \/\/ Create labels\r\n            const labels = bins.map((_, i) => (min + (i + 0.5) * binWidth).toFixed(1));\r\n\r\n            \/\/ Destroy previous chart if it exists\r\n            if (chart) {\r\n                chart.destroy();\r\n            }\r\n\r\n            \/\/ Create new chart\r\n            const ctx = document.getElementById('distributionChart').getContext('2d');\r\n            chart = new Chart(ctx, {\r\n                type: 'bar',\r\n                data: {\r\n                    labels: labels,\r\n                    datasets: [{\r\n                        label: 'Frequency',\r\n                        data: bins,\r\n                        backgroundColor: 'rgba(52, 152, 219, 0.5)',\r\n                        borderColor: 'rgba(52, 152, 219, 1)',\r\n                        borderWidth: 1\r\n                    }]\r\n                },\r\n                options: {\r\n                    responsive: true,\r\n                    maintainAspectRatio: false,\r\n                    scales: {\r\n                        y: {\r\n                            beginAtZero: true,\r\n                            title: {\r\n                                display: true,\r\n                                text: 'Frequency'\r\n                            }\r\n                        },\r\n                        x: {\r\n                            title: {\r\n                                display: true,\r\n                                text: 'Sample Mean'\r\n                            }\r\n                        }\r\n                    },\r\n                    plugins: {\r\n                        title: {\r\n                            display: true,\r\n                            text: 'Distribution of Sample Means'\r\n                        },\r\n                        legend: {\r\n                            display: false\r\n                        }\r\n                    }\r\n                }\r\n            });\r\n        }\r\n    <\/script><\/center><br \/>\nEasily compute sample means with our Central Limit Theorem Calculator. Get accurate probabilities and insights for any population distribution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Easily compute sample means with our Central Limit Theorem Calculator. Get accurate probabilities and insights for any population distribution.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[184],"tags":[],"class_list":["post-2322","post","type-post","status-publish","format-standard","hentry","category-calculator"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Central Limit Theorem Calculator - DonHit<\/title>\n<meta name=\"description\" content=\"Easily compute sample means with our Central Limit Theorem Calculator. 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