It’s better to use the interquartile range. Confidence intervals are often based on the standard normal distribution. It’s a very useful probability distribution and relatively easy to use. When a variable follows a normal distribution, the histogram is bell-shaped and symmetric, and the best measures of central tendency and dispersion are the mean and the standard deviation. The reason why standard deviation is so popular as a measure of dispersion is its relation with the normal distribution which describes many natural phenomena and whose mathematical properties are interesting in the case of large data sets. Standard deviation is equal to 0 if all values are equal (because all values are then equal to the mean).For two data sets with the same mean, the one with the larger standard deviation is the one in which the data is more spread out from the center.A single very extreme value can increase the standard deviation and misrepresent the dispersion. Standard deviation is sensitive to extreme values.Remember the following properties when you are using the standard deviation: This is why, in most situations, it is helpful to assess the size of the standard deviation relative to its mean. For example, a measure of two large companies with a difference of $10,000 in annual revenues is considered pretty close, while the measure of two individuals with a weight difference of 30 kilograms is considered far apart. When you are measuring something that is in the scale of millions, having measures that are close to the mean value doesn’t have the same meaning as when you are measuring something that is in the scale of hundreds. It was originally defined as 550 foot-pounds per second (ft-lb/s). The magnitude of the mean value of the dataset affects the interpretation of its standard deviation. horsepower (hp): The horsepower (hp) is a unit in the foot-pound-second ( fps ) or English system, sometimes used to express the rate at which mechanical energy is expended. Standard deviation might be difficult to interpret in terms of how large it has to be when considering the data to be widely dispersed. A single extreme value can have a big impact on the standard deviation. However, standard deviation is affected by extreme values. An item selected at random from a data set whose standard deviation is low has a better chance of being close to the mean than an item from a data set whose standard deviation is higher. The data set with the smaller standard deviation has a narrower spread of measurements around the mean and therefore usually has comparatively fewer high or low values. Calculate the power of the elevator.Standard deviation is useful when comparing the spread of two separate data sets that have approximately the same mean. It may also by defined in comparison to distributive equality, power structures between individuals, or justice and political egalitarianism. These include equality of power, rights, goods, opportunities, capabilities, or some combination of these things. Hence, power delivered by pump is 3271 W.Įxample 3: An elevator is designed to lift a load of 500 kg through 5 floors of a building averaging 3 m per floor in 5 seconds. Social equality is variously defined and measured by different schools of thought. Hence, power delivered to the box is 100 J/s.Įxample 2: A pump is required to lift 500 kg of water per minute from an 8 m deep well and eject it with a speed of 25 m/s. Work done by the boy, W = F d = 200 N ×5 J = 1000 J Weight of the box, F = mg = 20 ×10 N = 200 N Role of Mahatma Gandhi in Freedom Struggle.
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