Variance and standard deviation Flashcards","topicId":"90a1ef38-86ba-4425-b53e-fdabcef6005c","topicSlug":"variance-and-standard-deviation","cards":[{"id":"63cd7c06-0105-4a0d-990e-f733f6c568b2","cardType":"basic","front":"Why does adding deviations from the mean fail to measure spread?","back":"Positive and negative deviations cancel, so $\\sum(x-\\bar{x})=0$.","points":2,"mcqOptions":null},{"id":"721e59e6-841c-4049-ac18-f62ac977da21","cardType":"basic","front":"How does squaring deviations prevent cancellation?","back":"Squared deviations are non-negative.","points":2,"mcqOptions":null},{"id":"4ef0cf12-6b03-4fd5-b461-dafe2582ace5","cardType":"cloze","front":"The deviation of $x$ from the mean is $\\text{[...]}$.","back":"The deviation of $x$ from the mean is $\\boxed{x-\\bar{x}}$.","points":null,"mcqOptions":null},{"id":"1a9ccd69-865e-49ed-b054-d667c9593c22","cardType":"basic","front":"What does a large variance indicate?","back":"Values tend to lie far from the mean.","points":1,"mcqOptions":null},{"id":"fc1501ba-045a-439f-bb19-d78bf29c42b6","cardType":"basic","front":"Why can variance never be negative?","back":"It is a mean of squared deviations, which are non-negative.","points":2,"mcqOptions":null},{"id":"2506a745-580b-4cae-9594-ff953e323c62","cardType":"cloze","front":"Variance is $\\text{[...]}$.","back":"Variance is $\\boxed{\\displaystyle \\operatorname{Var}(X)=\\frac{\\sum(x-\\bar{x})^2}{n}}$.","points":null,"mcqOptions":null},{"id":"4588f28b-4c50-48ad-b12d-f075875f1288","cardType":"cloze","front":"The quicker raw-data variance formula is $\\text{[...]}$.","back":"The quicker raw-data variance formula is $\\boxed{\\displaystyle \\operatorname{Var}(X)=\\frac{\\sum x^2}{n}-\\bar{x}^2}$.","points":null,"mcqOptions":null},{"id":"0f397513-f14f-4f7a-ad60-02f238a7cc94","cardType":"basic","front":"What does a negative answer from the variance calculation usually indicate?","back":"The subtraction was reversed.","points":1,"mcqOptions":null},{"id":"83493be5-dc53-4569-8917-b029c8865d2f","cardType":"basic","front":"Why is standard deviation easier to interpret than variance?","back":"It has the same units as the original data.","points":2,"mcqOptions":null},{"id":"69b05f37-cab1-4fce-bf03-32f99f56ce0d","cardType":"cloze","front":"Standard deviation is the positive square root of variance: $\\text{[...]}$.","back":"Standard deviation is the positive square root of variance: $\\boxed{\\sigma=\\sqrt{\\operatorname{Var}(X)}}$.","points":null,"mcqOptions":null},{"id":"85644b49-42b3-47a2-9fa7-5a7759dcdc78","cardType":"basic","front":"What does a standard deviation of $4.3$ minutes suggest?","back":"Values typically differ from the mean by about $4.3$ minutes.","points":1,"mcqOptions":null},{"id":"e2238b23-2027-4812-9a16-c9934196173e","cardType":"basic","front":"Which of two comparable data sets is generally more consistent?","back":"The set with the smaller standard deviation.","points":1,"mcqOptions":null},{"id":"34e49b66-c45d-4c98-b04f-8b8ea4279039","cardType":"basic","front":"For 2, 3, 3, 5, 7, given $\\bar{x}=4$ and $\\sum x^2=96$, calculate the variance.","back":"$$\\displaystyle \\frac{96}{5}-4^2=\\strong{3.2}$","points":2,"mcqOptions":null},{"id":"735affcc-0b11-4b47-b0bc-5c6130d9cb86","cardType":"basic","front":"How is the total number of observations found from frequencies?","back":"$n=\\sum f$","points":1,"mcqOptions":null},{"id":"4dfd215b-39d8-40f5-9c60-caa909540f10","cardType":"cloze","front":"For a frequency distribution, the mean is $\\text{[...]}$.","back":"For a frequency distribution, the mean is $\\boxed{\\displaystyle \\bar{x}=\\frac{\\sum fx}{\\sum f}}$.","points":null,"mcqOptions":null},{"id":"bb889463-935a-4e2a-8c7e-9b960f86f9de","cardType":"basic","front":"In $fx^2$, which operation is performed first?","back":"Square $x$, then multiply by $f$.","points":1,"mcqOptions":null},{"id":"6f036e60-e231-48a2-8821-b5e9e0aa2ab1","cardType":"basic","

2.2.12 Variance and standard deviation Flashcards

2.2.12 Variance and standard deviation Flashcards