Range: The first method of measuring "spread" of a data set that you learned was finding the range. Range is the differene between the largest data value and the smallest data value in the set. While the range is simple to compute, it is often unreliable as a measure of variability. The range is based on only two values within the set, which may tell very little about "how" the remaining values are distributed in the set. For this reason, range is used as a supplement to other measures of spread, instead of being the only measure of spread.
This range of 43 tells us very little about how the data in this set is scattered. The range alone cannot tell us, for example, if the data is clustered to one end of the set, or if there is an outlier in the data set. For calculator help with range click here. For calculator help with IQR from 5 number summary click here. For the following methods, you need to understand "population" vs "sample" data. Unlike range and interquartile range, these methods utilize all of the values in a data set to produce a measure of spread.
For calculator help with MAD click here. Variance: Read more about Variance The variance is the average of the squared differences from the mean. A small variance indicates that the data points tend to be very close to the mean and to each other A high variance indicates that the data points are very spread out from the mean and from each other. One problem with the variance is that it does not have the same unit of measure as the original data. For example, original data containing lengths measured in feet has a variance measured in square feet.
The process is very similar to finding the MAD. The only difference is the squaring of the distances. As discussed in the Measures of Central Tendency page, the mode, median, and mean summarise the data into a single value that is typical or representative of all the values in the dataset, but this is only part of the 'picture' that summarises a dataset. Measures of spread summarise the data in a way that shows how scattered the values are and how much they differ from the mean value.
For example: Dataset A. Calculating the Range Dataset A. Calculating Quartiles Dataset A. The standard deviation describes variability in a set of data. The standard error of the mean refers to variability we might expect in the arithmetic means of repeated samples taken from the same population. The standard error assumes that the data you have is actually a sample from a larger population.
According to the assumption, your sample is just one of an infinite number of possible samples that could be taken from the source population.
Thus, the mean for your sample is just one of an infinite number of other sample means. The standard error quantifies the variation in those sample means. Find the standard error of the mean for the length-of-stay data in Table 2. Often, epidemiologists conduct studies not only to measure characteristics in the subjects studied, but also to make generalizations about the larger population from which these subjects came.
This process is called inference. For example, political pollsters use samples of perhaps 1, or so people from across the country to make inferences about which presidential candidate is likely to win on Election Day. Usually, the inference includes some consideration about the precision of the measurement. The results of a political poll may be reported to have a margin of error of, say, plus or minus three points.
A narrow confidence interval indicates high precision; a wide confidence interval indicates low precision. Confidence intervals are calculated for some but not all epidemiologic measures. The two measures covered in this lesson for which confidence intervals are often presented are the mean and the geometric mean.
Confidence intervals can also be calculated for some of the epidemiologic measures covered in Lesson 3, such as a proportion, risk ratio, and odds ratio. The confidence interval for a mean is based on the mean itself and some multiple of the standard error of the mean. Recall that the standard error of the mean refers to the variability of means that might be calculated from repeated samples from the same population.
Fortunately, regardless of how the data are distributed, means particularly from large samples tend to be normally distributed. This is from an argument known as the Central Limit Theorem. So we can use Figure 2. Consider a population-based sample survey in which the mean total cholesterol level of adult females was , with a standard error of the mean of 3.
If this survey were repeated many times, One might say that the investigators are Thus, the confidence interval indicates how precise the estimate is. This confidence interval is narrow, indicating that the sample mean of is fairly precise. It also indicates how confident the researchers should be in drawing inferences from the sample to the entire population. Imagine you are going to Las Vegas to bet on the true mean total cholesterol level among adult women in the United States.
When the serum cholesterol levels of 4, men were measured, the mean cholesterol level was , with a standard deviation of Calculate the standard error of the mean for the serum cholesterol level of the men studied.
Description: Bell-shaped curve. The central tendency, the middle is the median, 50th percentile. The largest value is the th percentile. Return to text. Description: An Interquartile Range is depicted along a horizontal axis.
The minimum is on the left followed by Q1, the median, Q3 and the maximum on the far right. Description: Bell-shaped curve with the standard deviations equally distributed on the x-axis. Section Navigation. Facebook Twitter LinkedIn Syndicate.
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