Standard deviation quiz

The standard deviation is a typical distance from the mean: the square root of the average squared deviation. The most common value is the mode, and the largest minus the smallest is the range. What is standard deviation?.

The standard deviation is in the same unit as the data. The variance is in squared units (cm²), which is why the square root is taken. A unitless measure of spread is the coefficient of variation. Standard deviation vs variance.

The sample mean is, by construction, the point that minimises the sum of squared deviations for that sample. Squared deviations from it are therefore slightly too small on average. Dividing by n − 1 (Bessel’s correction) removes that bias from the variance. Sample vs population standard deviation.

The 28 scores are the whole group of interest, so it is a population and the divisor is n. If the class were being used to generalise about all students who take the test, it would be a sample. Population standard deviation calculator.

The standard deviation is the square root of the variance: √25 = 5. Squaring it (625) goes the wrong way. Variance calculator.

SE = s ÷ √n = 12 ÷ √36 = 12 ÷ 6 = 2. The standard deviation describes individual values; the standard error describes how precisely the mean is known. Standard error calculator.

70 and 130 are two standard deviations either side of the mean (100 ± 2 × 15). By the empirical rule about 95% of a normal distribution lies within ±2 SD. The exact figure is 95.45%. Empirical rule calculator.

z = (x − mean) ÷ SD = (82 − 70) ÷ 8 = 1.5. The score is one and a half standard deviations above the mean, around the 93rd percentile if the scores are normal. Z-score calculator.

Adding a constant moves every value and the mean by the same amount, so every deviation from the mean is unchanged. The mean rises by 10; the spread does not. The standard deviation formula.

Every deviation triples, so the standard deviation triples. The variance is built from squared deviations, so it grows by 3² = 9. Converting units works the same way: metres to centimetres multiplies the SD by 100. Standard deviation vs variance.

The IQR is the width of the middle half of the data, so one value at the extreme can shift it only slightly. The range moves by the full distance of the outlier, and the SD and variance square its deviation. Outlier and IQR calculator.

CV = SD ÷ mean = 5 ÷ 50 = 0.10, or 10%. It has no unit, which is what lets you compare spreads measured on different scales. Coefficient of variation calculator.

A standard deviation of 0 means no value deviates from the mean, so every value is identical. The mean can be anything. A standard deviation can never be negative. What is standard deviation?.

The mean is 40 ÷ 8 = 5. The squared deviations are 9, 1, 1, 1, 0, 0, 4, 16, which sum to 32. Divided by n = 8 that gives a variance of 4, so σ = 2. The sample SD (dividing by 7) would be 2.14. How to calculate standard deviation.

The mean is 3. The squared deviations are 4, 0 and 4, summing to 8. Divided by n − 1 = 2 that gives a variance of 4, so s = 2. Dividing by n = 3 instead gives the population figure, 1.63. Sample standard deviation calculator.