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href="https://economictimes.indiatimes.com">Business News<meta content="Business News" itemprop="name"></a></span>&rsaquo;<span itemtype="https://schema.org/ListItem" itemscope="" itemprop="itemListElement"><a title="News" alt="News" itemprop="item" href="https://economictimes.indiatimes.com/news"><meta content="2" itemprop="position">News<meta content="News" itemprop="name"></a></span>&rsaquo;<span>Standard Deviation Calculator</span> </div></div><div id="breakingNews"><div class="contentwrapper prel"><ul class="bnews flt"></ul><div class="nextPrev"><span class="flt prev"></span><span class="flr next"></span></div></div></div><div class="clr"></div><section class="clearfix main_container"><div class="calc_wrapper ageCalc sd_calc"><h1 class="font_mon calc_title">STANDARD DEVIATION CALCULATOR</h1><p class="calc_sys font_faus">Use standard deviation and variance calculator to find the mean, sum, variance and standard deviation for the defined set of numbers.</p><div class="faq-template"><div class="panel jsTwoDate font_mon" data-panel="daysBetween"><div class="panelBodyContainer"><div class="jsResultStartEnd hidden"><div class="topParent"><div class="sd_result_head"><h4>RESULT</h4><div class="final_r_block">Standard Deviation <span>(<span class="sd_sign">σ</span>) = </span><span class="final_val">4.6733285782192</span></div></div><div class="sd_step_wrap"><div class="sd_step sd_step1"><p class="sd_step_hd"><b>Step 1 :</b> Average or Arithmetic Mean of the Numbers</p><div class="sd_r_inbutbox"><span class="sdri_title">Count (N) :</span><input disabled="true" type="text" class="sdr_input count_input"><span class="sdri_sys">How many numbers</span></div><div class="sd_r_inbutbox"><span class="sdri_title">Sum (∑x) :</span><input disabled="true" type="text" class="sdr_input sum_input"><span class="sdri_sys">All the numbers added up</span></div><div class="sd_r_inbutbox"><span class="sdri_title">Mean (<span class="mean_sign">µ</span>) :</span><input disabled="true" type="text" class="sdr_input mean_input"><span class="sdri_sys">Arithmetic Mean = Sum / Count</span></div></div><div class="sd_step sd_step2"><p class="sd_step_hd"><b>Step 2 :</b> Subtract the mean and square the result</p><div class="sd_r_inbutbox"><span class="sdri_title">Differences :</span><input disabled="true" type="text" class="sdr_input diff_input"><span class="sdri_sys">Every number minus Mean</span></div><div class="sd_r_inbutbox"><span class="sdri_title">Differences<sup>2</sup> :</span><input disabled="true" type="text" class="sdr_input diff_sq_input"><span class="sdri_sys">Square of each difference</span></div></div><div class="sd_step sd_step3"><p class="sd_step_hd"><b>Step 3 :</b> Calculate Variance</p><div class="sd_r_inbutbox"><span class="sdri_title">Sum of Differences<sup>2</sup> :</span><input disabled="true" type="text" class="sdr_input sum_diff"><span class="sdri_sys">Add up the squared differences</span></div><div class="sd_r_inbutbox"><span class="sdri_title">Variance (<span class="sd_sign">σ</span><sup>2</sup>) :</span><input disabled="true" type="text" class="sdr_input var_input"><span class="sdri_sys">Sum of Difference<sup>2</sup> / <span class="var_count_text">Count</span></span></div></div><div class="sd_step sd_step4"><p class="sd_step_hd"><b>Step 4 :</b> Square root of the Variance</p><div class="sd_r_inbutbox"><span class="sdri_title">Standard Deviation (<span class="sd_sign">σ</span>) :</span><input disabled="true" type="text" class="sdr_input final_val_input"><span class="sdri_sys">The square root of the Variance</span></div></div><div class="sd_step sd_quation"><p class="sd_step_hd"><b>Equation : </b>Standard Deviation</p><div class="sd_q_s sd_f_s"><span class="sd_q_equal sd_sign">σ</span><span class="sd_equl_sign"> = </span><div class="dib vam"><span class="sq_icon flt">√</span><div class="dt sq_table"><div class="dtc f_sq tac vam"><span>1</span><br><span class="i">N</span></div><div class="dtc s_sq i tac"><span>N</span><span class="s_sq_m">∑</span><span>i=1</span></div><div class="dtc vam"><span>(x<sub>i</sub> - <span class="mean_sign">µ</span>)<sup>2</sup></span></div></div></div></div><div class="sd_q_s sd_s_s"><span class="sd_q_equal"><span class="sd_sign">σ</span><sup>2</sup></span><span class="sd_equl_sign"> = </span><div class=" dib vam tac"><div class="sd_s_s_q">∑(x<sub>i</sub> - <span class="mean_sign">µ</span>)<sup>2</sup></div><div>N</div></div></div><div class="sd_q_s sd_t_s"><span class="sd_q_equal"></span><span class="sd_equl_sign"> = </span><div class=" dib vam tac"><div>(<span class="f_diff">-5 - 2.6</span>)<sup>2</sup>+...+(<span class="l_diff">-5 - 2.6</span>)<sup>2</sup></div><div class="bt count_text">5</div></div></div><div class="sd_q_s sd_ft_s"><span class="sd_q_equal"></span><span class="sd_equl_sign"> = </span><div class=" dib vam tac"><div class="sum_sq_diff_text">109.2</div><div class="bt count_text">5</div></div></div><div class="sd_q_s sd_fv_s"><span class="sd_q_equal"></span><span class="sd_equl_sign"> = </span><div class=" dib vam tac var_text">21.84</div></div><div class="sd_q_s sd_sx_s"><span class="sd_q_equal sd_sign">σ</span><span class="sd_equl_sign"> = </span><div class=" dib vam tac"><span class="sd_s_sq flt">√</span><div class="dib sd_s_val var_text">21.84</div></div></div><div class="sd_q_s sd_sv_s"><span class="sd_q_equal"></span><span class="sd_equl_sign"> = </span><div class=" dib vam tac final_val">4.5678</div></div></div></div></div><span class="errorMsg"></span></div><div class="panelBody"><div class="inputContainer"><div class="sd_input "><input id="xVal" autocomplete="off" type="text"><div class="sd-info dib prel"><span class="ques_sign">?</span><div class="sd_tooltip"><ul class="sd_tt_list"><li>A <b>population</b> is an entire group that you want to draw conclusions about.</li><li>A <b>sample</b> is a specific group that you will collect data from. The size of the sample is always less than the total size of the population.</li><li class="prel"><span>Please input values with comma separation example: 2,3,4,5,6</span><img src="https://img.etimg.com/photo/msid-86467154/et-star.jpg" width="369" class="data_table"></li></ul></div></div></div><div class="sd_des tac"><span>Is it a</span><label for="population"><input value="Population" checked="true" name="method_type" id="population" type="radio"><span>Population</span></label><label for="sample"><input value="Sample" name="method_type" id="sample" type="radio"><span>Sample</span></label><span>?</span></div></div><div class="cta tac"><input value="Calculate" class="sdcalc_btn" type="button"><span class="clear clearBtn">Clear</span></div></div></div></div></div><div class="contentContainer"><div class="lftSide"><div class="relatedCalc"><h2>Related Calculators</h2><div class="calculators"><ul><li itemprop="itemListElement" itemscope="" itemtype="https://schema.org/ListItem"><meta itemprop="position" content="1"><a href="/news/date-calculator" itemprop="item">Date Calculator</a></li></ul></div></div><div class="calcContent"><div class="article_wrap"><style xmlns:java="java"> .calc-article .article-heading{border-left: 3px solid #00789D;color: #747B81;font-size: 20px;padding: 3px 0 3px 12px;} .calc-article .article-heading span{font-size: 11px;} .article_block .articleImg.midImg{float: left;margin-right: 20px;margin-bottom: 20px;} .calcContent .artText a {font-weight: 600;border-bottom: 1px solid;} </style><script> console.log('content msid - ', '86548913'); </script><div class="article_block" data-article_id="86548913" data-agency="" data-budget-keyword="0" data-authors=""><section class="pageContent"><article><div class="artText"><div class="section1"><div class="Normal">Enter the data set, with each individual value separated by commas, to determine the <a href="/topic/standard-deviation" target="_blank">standard deviation</a> and <a href="/topic/variance" target="_blank">variance</a>.<br><br><strong>What is Standard Deviation & Variance?</strong><br>Standard deviation and variance are both statistical functions used to measure the dispersion or variation of the values in a data set from its mean. In simpler terms, standard deviation and variation indicate how close or how far the values comprising a data set are from each other and thus, indicating their deviation from the mean or average value. The larger the standard deviation and variance, the larger is the disparity in the data set and vice versa.<br><br>While calculating, standard deviation is the square root of the variance. <br><br><strong><a href="/topic/Standard-Deviation-Formula" target="_blank">Standard Deviation Formula</a>:</strong><br><br>When calculating for a population,<br><br><img src="https://lh3.googleusercontent.com/NdE-ttBwmuywl2ZMs36dJgKLoZa-JUR-pI1gWBq_wIO__853bRHfY9Wl02loJX6VNWT9vFVLY0JWvdhjP8Ki5EVyha67NGi9iS3_1sjZaOxvJ8-7z27ofqbiKjX16t_l7WEJAJeB=s0"><br><br>Here, <br>σ = Population standard deviation<br>N = Total number of values in the data set<br>x<sub>i</sub> = Individual value in the data set<br>µ = Mean<br><br>When calculating for a sample,<br><br><img src="https://lh3.googleusercontent.com/9z9MoNJXphi9K7CcRYLvjObBRfEsa7e8Sbh1qb1wbD-Q8LWHEK39xd2qKRvqAZ7mzZ99MeVN4l80IWwliBODYbI55Fse71e8Tusxmd46iJCySlYwkwyXNv3yXlUT2KQrvpfAQQQZ=s0"><br><br>Here,<br>s = Sample standard deviation<br>N = Total number of values in the data set<br>x<sub>i</sub> = Individual value in the data set<br>x¯ = Mean of the sample<br><br><strong><a href="/topic/Variance-Formula" target="_blank">Variance Formula</a>:</strong><br><br>When calculating for a population,<br> <br>σ2 = ∑(xi - μ)2 / N<br><br>Here, <br>σ<sup>2</sup> = Population variance<br>N = Total number of values in the data set<br>x<sub>i</sub> = Individual value in the data set<br>µ = Mean<br><br><br>When Calculating for a sample,<br><br>s<sup>2</sup> = ∑(xi - x̄)<sup>2</sup> / (N - 1)<br><br>Here,<br>s<sup>2</sup> = Sample variance<br>N = Total number of values in the data set<br>x<sub>i</sub> = Individual value in the data set<br>x¯ = Mean of the sample<br><br><strong>What is a standard deviation & variance <a href="/topic/calculator" target="_blank">calculator</a>?</strong><br>The calculator given above is a digital tool that calculates the standard deviation, variance, and some other statistical functions such as the mean of the given data set. Users need to enter the collection of data, where each individual value is separated by a comma, to determine the value of the above mentioned statistical functions. <br><br><strong>How does this calculator work?</strong><br>This calculator is an online tool that can be accessed for a smartphone or computer with an active internet connection. Here’s a step-by-step guide to use this standard deviation & variance calculator:<br><ul><li>The input box is for entering the data set. Here, all the individual values of the data set should be separated by a comma. The values entered can either be a positive or a negative number</li><li>Select the ‘Population’ tab if the data set accounts for the entire population of the group being considered</li><li>Select the ‘Sample’ tab if the data set only represents a fraction of the concerned population or group</li><li>After entering all the required details, click on the ‘Calculate’ button to view the result</li><li>Click on the ‘Clear’ button to provide new input</li></ul><br><strong>What does the result page show?</strong><br>In the result section, the ‘standard deviation’ is displayed at the top, followed by the ‘count’ of the individual values, the ‘sum’ of the values, the ‘mean’ of the data set and lastly, the ‘variance’ of the data provided. <br><br>The section below it shows the steps involved in the calculation, followed by the margin of error or confidence interval of the calculation. 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