Measures of spread and dispersion
Measures of central tendency are not the only statistics used to summarise a distribution . We also have to identify the spread of the distribution of the data set. Spread defines how widely the observations are spread out around the measure of central tendency. Note that the words, spread, dispersion and variation denote the same meaning. The most commonly used measures of spread are range, variance and standard deviation. The scales of measurement appropriate for the use of variance and standard deviation are ratio and interval scales.
Measures of spread increase on greater variation on the variable. Measures of spread equal zero when there is no variation. Maximum spread for numeric and ordinal variables
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Chebyshev theorem applies to all kinds of distribution regardless of their shape. It can be used in scenarios where the shape of the distribution is not known or not normal.
Chebyshev Theorem states at least 1-(1/k2) values will fall within (+/- )k standard deviations of the mean regardless of the shape of the distribution.
Within k standard deviations of the mean μ (+/- )kσ lie at-least 1-(1/k2) Proportion of values.
Assumption : k>1
Coefficient of variation
The Coefficient of variation is a statistic that is the ratio of the standard deviation to the mean expressed in percentage and denoted by CV.
CV = (σ / μ ) * 100
The coefficient of variation is essentially a comparison of standard deviation to its mean. The coefficient of variation can be useful in computing standard deviation that have been computed from data with different means.
For example, Five weeks of average prices of a stock of Apple Inc. is 103.6, 107, 110, 92, 111 . To compute the coefficient of variation for these stock prices, first determine the mean and standard deviation . (σ = 7.67 μ = 104.72)
CV = (σ / μ ) * 100
CV = (7.67/104.72) * 100 = 7.32 %
The standard deviation is 7.32 % of the
With more genetic variation, there are more “options” to be selected for. A lot of variation makes it so a species can become best adapted for an environment.
Collected data were subjected to analysis of variance using the SAS (9.1, SAS institute, 2004) statistical software package. Statistical assessments of differences between mean values were performed by the LSD test at P = 0.05.
Investigating the Effect of Concentration on the Rate of Diffusion Aim: To find out if concentration affects the rate of diffusion. Prediction: I predict that the higher the concentration of acid the faster the reaction will be. Hypothesis: Diffusion is the spreading out of a gas or liquid from an area of low concentration to another area where it has a lower concentration until the overall concentrations are balanced. The Hydrochloric acid (HCl) diffuses into the gelatine cube of which contains Sodium Hydroxide (NaOH), which is an alkali. When the Hydrochloric acid combines with the Sodium Hydroxide they form salt and water, which is neutral therefore turning the pink cube to clear.
The extent to which a distribution of values deviates from symmetry around the mean is the skewness. A value of zero means the distribution is symmetric, while a positive skewness indicates a greater number of smaller values, and a negative value indicates a greater number of larger values (Grad pad, 2013). Values for acceptability for psychometric purposes (+/-1 to +/-2) are the same as with kurtosis.
This method is used since it is the most appropriate for calculating the mean and the standard deviation of a grouped data.
The first thing that was decided upon was to find the Mean, Median, and Mode. Using a calculator they were able to obtain the exact numbers.
2 + 0.75(100) = 77. However, in any particular year when sales X = 100, the actual cost of goods sold can deviate randomly around 77. This deviation from the average is called the “disturbance” or the “error” and is represented by “e”.
When comparing groups, the use of frequency polygons helps us decide which measure of central tendency is the most appropriate to calculate. How so?
...will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the mean. The Empirical Rule is used in statistics for showing final outcomes. After a standard deviation is found, and before exact data can be collected, this rule can be used as an estimate to the outcome of the new data. This probability can be used for gathering data that may be time consuming, or even impossible to found. When the mean equals the median and the values cluster around the mean and median, producing a bell-shaped distribution, then we can use the empirical rule to examine the variability. In this bell-shaped data set, we can calculate the mean and the standard deviation. The mean means the average value of the set of data. The standard deviation means the average scatter around the mean.
Variance (2) Standard Deviation () Reaction 1 7.6 x 10-4. 2.76 x 10-2.
Standard Deviation is a measure about how spreads the numbers are. It describes the dispersion of a data set from its mean. If the dispersion of the data set is higher from the mean value, then the deviation is also higher. It is expressed as the Greek letter Sigma (σ).
Descriptive statistics can be defined as statistics that summarizes data that is collected from a research. One way of summarizing research data is by calculating the measure of central tendency. Examples of measure of central tendency includes mode, mean and Midian. Data can also be summarized in respect to variance. When the scores are more spread out of the mean, there is a greater variance.
The two columns in the graph represent the mean values and the error lines represent the standard deviations of the tested grasshopper and human subject. The jumping distance of the grasshoppers was more than the jumping distance of humans and the TTEST value was less than 0.05.
It is also known as the coefficient of determination, or the coefficient of multiple determinations for multiple regression. It is the percentage of the response variable variation that is explained by a linear model.
In this experiment, I would run a simple T test. I would collect the data for both groups. I would record the data for each group and then calculate the mean for each group. After calculating the mean, I would calculate the variance within each group. Then I would calculate the variance of the difference between both groups, which would yield square root. I would get a T value by comparing the means of both groups. 3b. I would calculate variation within groups by using standard deviation. In the end of my calculations, I would have two numbers because there are two groups. Standard deviation starts with the calculation of the average between the two groups. Next, I would find the deviation from the mean and square it. Then, I take all the squared sums and divide them by 60, the number of participants in each group. Lastly, by taking the square root of that final number, I would have my standard variation. 3c. Statistical significance is the probability a specific outcome was not due to chance, rather due to an effect. For the difference between groups to be statistically significant, the difference between groups has to be 1.96 times as large as the variation within group. If the difference between groups is less than 1.96, it is possible that the specific outcome was due to