4 Commonly Used Measures of Dispersion | Statistics

Feb 15, · 1) Which of the following is not a measure of dispersion? a) mean, B) range, C) variance, d) standard deviation 2) Which of the following can have more than one value? a) Median, b) variance, c) mode, d) mean 3) Which of the following summary measures is/are influenced by extreme values a. Mean b. Range c. none d. Median e. A measure of dispersion gives an idea about the skewness of a distribution from the mean value of the distribution, that is, how much of the data is different from the mean of the distribution.

There are four commonly used measures to indicate the variability or dispersion within a set of measures. They are: 1. Range 2. Quartile Deviation 3. Average Deviation 4. Standard Deviation. Range is the interval between the highest and the lowest score. Range is a measure of variability or scatteredness of the variates or observations among themselves and does not give an idea about the spread of the observations around some central value.

Here we find that the scores of boys are widely scattered. Thus the scores of boys vary much But the scores of girls do not vary much of course they vary less. Thus the variability of the scores of boys is more than the variability of the scores of girls.

Find the range of data in following distribution:. Range is an index of variability. When the range is more the group is more variable. The smaller the range the more homogeneous is the group. When we wish to make a rough comparison of variability of two or more groups we may compute the range. Range as compared above is in a crude form or is an absolute measure of dispersion and is unfit for the purposes of comparison, especially when the series are in two different units.

For the purpose of comparison, coefficient of range is calculated by dividing the range by the sum of the largest how to do an iv the smallest- items. Range is not based on all the observations of the series. It takes into account only the most extreme cases. Thus when N is small or when there are large gaps in the frequency distribution, range as a measure of variability is quite unreliable.

Just compare the series of scores in group A and group B. In group A if a single score 33 the last score is changed to 93, the range is widely changed. Thus a single high score may increase the range from low to high. This is why range is not a reliable measure of variability.

It is affected very greatly by fluctuations in sampling. Its value is never stable. In a class where normally the height of students ranges from cm to cm, if a dwarf, whose height is 90 cm is admitted, the range would shoot up from 90 cm to cm. Range does not present the series and dispersion truly. Asymmetrical and symmetrical distribution can have the same range but not the same dispersion. It is of limited accuracy and should be used with caution. However, we should not overlook the fact that range is a crude measure of dispersion and is entirely unsuitable for precise and accurate studies.

Range is the interval or distance on the scale of measurement which includes percent cases. The limitations of the range are due to its dependence on the two extreme values only. There are some measures of dispersion which are independent of these two extreme values. Most common of these is the quartile deviation which is based upon the interval containing the middle 50 percent of cases in a given distribution.

Quartile deviation is one-half the scale distance between the third quartile and the first quartile. It is the Semi-interquartile range of a distribution:. For example a test results 20 scores and these scores are arranged in a descending order.

Let us divide the distribution of scores into four equal parts. With a view to having a better study of the composition of a series, it may be necessary to divide it in three, four, six, seven, eight, nine, ten or hundred parts. Usually, a series is divided in four, ten or hundred parts. One item divides the series in two parts, three items in four parts quartilesnine items in ten parts decilesand ninety-nine items in hundred parts percentiles.

There are, thus, three quartiles, nine deciles and ninety-nine percentiles in a series. The second quartile, or 5th decile or the 50th percentile is the median see Figure. The value of the item which divides the first half of a series with values less than the value of the median into two equal parts is called the First Quartile Q 1 or the Lower Quartile. Q 1 is the 25th percentile. A median is the 50th percentile. The value of the item which divides the latter half of the series with values more than the value of the median into two equal parts is called the Third Quartile Q 3 or the Upper Quartile.

Q 3 is the 75th percentile. A student must clearly distinguish between a quarter and a quartile. Quarter is a range; but quartile is a point on the scale. Quarters are numbered from top to bottom or from highest score what is the branches of government lowest scorebut quartiles are numbered from the bottom to the top.

The range between the third quartile and the first quartile is known as the inter-quartile range. If we will compare the formula of Q 3 and Q 1 with the formula of median the following observations will be clear:. In case of median we use fm to denote the frequency of c. In order to calculate Q we are required to calculate Q 3 and Q 1 first. Q 1 and Q 3 are calculated in the same manner as we were computing the median.

Find out Q of the following scores 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, In this example, Q 1 is a point below which 5 cases lie. From the mere inspection of ordered data it is found that below In a symmetrical distribution, the median lies halfway on the scale from Q 1 and Q 3. The scores obtained by 36 students in a test are shown in the table. Find the quartile deviation of the scores. In column 1, we have taken class Interval, in column 2, we have taken the frequency, and in column 3, cumulative frequencies starting from the bottom have been written.

Q1 would lie in the interval So Q 3 would lie in the interval What paint to use on plastic flower pots interpreting the value of quartile deviation it is better to have the values of Median, Q 1 and Q 3along with Q. If the value of Q is more, then the dispersion will be more, but again the value depends on the scale how to play craps come bet measurement.

What do lice eggs look like dead values of Q are to be compared only if scale used is the same. Q measured for scores out of 20 cannot be compared directly with Q for scores out of Sometimes, the extreme cases or values are not known, in which case the how is oil used to create energy alternative available to us is to compute median and quartile deviation as the measure of central, tendency and dispersion.

Through median and quartiles we can infer about the symmetry or skewness of the distribution. Let us, therefore, get some idea of symmetrical and skewed distributions. A distribution is said to be symmetrical when the frequencies are symmetrically distributed around the measure of central tendency. In other words, we can say that the distribution is symmetrical if the values at equal distance on the two sides of the measure of central tendency have equal frequencies. Here the measure of central tendency, mean as well as median, is 5.

If we start comparing the frequencies of the values on the two sides of 5, we find that the values 4 and 6, 3 and 7, how much calories to burn to lose weight calculator and 8, 1 and 9, 0 and 10 have the same number of frequencies.

So the distribution is perfectly symmetrical. In a symmetrical distribution, mean and median are equal and median lies at an equal distance from the two quartiles i. If a distribution is not symmetric, then the departure from the symmetry refers to its skewness. Skewness indicates that the curve is turned more towards one side than the other.

So the curve will have a longer tail on one side. The skewness is said to be positive if the longer tail is on the right side and it is said to the negative if the longer tail is on the left side. The following figures show the appearance of a positively skewed and negatively skewed curve:. Wherever median is preferred as a measure of central tendency, quartile deviation is preferred as measure of dispersion. However, like median, quartile deviation is not amenable to algebraic treatment, as how to create a file format does not take into consideration all the values of the distribution.

It only calculates the third and the first quartile and speaks us about the range. It ignores the scores above the third quartile and the scores below the first quartile. Coefficient is calculated by dividing the quartile deviation by the average of quartiles. The range of two series may be the same or the quartile deviation of two series may be same, yet the two series may be dissimilar. These two measures do not take into consideration the individual scores.

The average deviation is also called the first moment of dispersion and is based on all the items in a series. Average deviation is the arithmetic mean of the deviations of a series computed from some measure of central tendency mean, median or modeall the deviations being considered positive. In other words the average of the deviations of all the values from the arithmetic mean is known as mean deviation or average deviation.

Usually, the deviation is taken from the mean of the distribution. Find mean deviation for the following set of variates:. Find the mean deviation for the scores given below:. Here, in column 1, we write the c.

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Explanation: In statistics, Quartile is not a measure of dispersion because it is the measure of central tendency. 2nd quartile is equal to rutlib6.com range, mean deviation, standard deviation are the measure of dispersion. Which Of The Following Is Not A Measure Of Dispersion? Question: Which Of The Following Is Not A Measure Of Dispersion? This problem has been solved! See the answer. Which of the following is not a measure of dispersion? Expert Answer % (3 ratings) Previous question Next question. Oct 26, · The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is ____ (1) 3 (2) 15 (3) 5 (4)

Quantitative data can be described by measures of central tendency, dispersion, and "shape". Central tendency is described by median, mode, and the means there are different means- geometric and arithmetic. Dispersion is the degree to which data is distributed around this central tendency, and is represented by range, deviation, variance, standard deviation and standard error. This chapter answers parts from Section A e of the Primary Syllabus, "Describe frequency distributions and measures of central tendency and dispersion".

This topic was examined in Question 23 from the first paper of Lecture on types of data; by Keith G. Richards, Derek. Previous chapter: Different types of data Next chapter: Parametric and non-parametric tests.

All SAQs related to this topic. All vivas related to this topic. This sort of data is: Expressed numerically, and ordered on a scale Interval data: increase at constant intervals, but do not start at zero, eg. Examples: Median is the middle number in a data set that is ordered from least to greatest Mode is the number that occurs most often in a data set Arithmetic mean is the average of a set of numerical values, Geometric mean is the n th root of the product of n numbers Degree of dispersion These describe the dispersion of data around some sort of mean.

Because the difference can be positive or negative and this is cumbersome, usually the absolute deviation is used which ignores the plus or minus sign. Variance : deviation squared Standard deviation : square root of variance Measure of the average spread of individual samples from the mean Reporting the SD along with the mean gives one the impression of how valid that mean value actually is i.

Standard error This is an estimate of spread of samples around the population mean. You don't known the population mean- you only know the sample mean and the standard deviation for your sample, but if the standard deviation is large, the sample mean may be rather far from the population mean.

How far is it? The SE can estimate this. Mean absolute deviation is the average of the absolute deviations from a central point for all data. As such, it is a summary of the net statistical variability in the data set. On average, it says, the data is this different from this central point. Coefficient of variation, also known as "relative standard deviation", is the SD divided by the mean.

As a dimensionless number, it allows comparisons between different data sets i. Shape of the data This vaguely refers to the shape of the probability distribution bell curve. Skewness is a measure of the assymetry of the probability distribution - the tendency of the bell curve to be assymmetrical. Kurtosis or "peakedness" describes the width and height of the peak of the bell curve, i.

A normal distribution is a perfectly symmetrical bell curve, and is not skewed. Point estimate According to the college, point estimate is "a single value estimate of a population parameter. It represents a descriptive statistic for a summary measure, or a measure of central tendency from a given population sample. Confidence interval The range of values within which the "actual" result is found. The CI gives an indication of the precision of the sample mean as an estimate of the "true" population mean A wide CI can be caused by small samples or by a large variance within a sample.

References Lecture on types of data; by Keith G. Calkins Richards, Derek. Email Address. Send Message.

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