Data Description and their basic definitions

Basic Definitions of Data description:

Statistic: It is the feature or measure obtained from the sample.

Parameter: It is the feature or measure obtained from the population.

Mean: It is the sum of all values divided by the number of values. This can either be a population mean (symbolized by mu) or a sample mean (symbolized by x bar).

Median: The mid-point of data after being ranked (sorted in the ascending order). There are as much numbers beneath the median as above the median.

Mode: it is the most frequently occurred number.

Skewed Distribution: The majority of values lie altogether on one side with very little values (that is, the tail) to other side. In a positively skewed distribution, the tail is at the right and the mean is bigger than the median. In a negatively skewed distribution, the tail is at left and the mean is smaller than the median.

Symmetric Distribution: In a symmetric distribution, the mean is the median. In this, the data values are uniformly distributed on both sides of the mean.

Weighted Mean: Whenever each value is multiplied by its weight and summed up, then this is mean. This sum is then divided by the total of weights.

Midrange: It is the mean of highest and lowest values. (Max + Min)/2

Range: It is the difference between the maximum and minimum values. That is, Range = Max - Min

Population Variance: It is the average of the squares of distances from the population mean. This is the sum of squares of deviations from the mean divided by the population size. Units on variance are the units of the population squared.

Sample Variance: It is the population variance’s unbiased estimator. Rather than dividing by the population size, the sum of squares of the deviations from sample mean is divided by one less than the sample size. Variance units are the units of the population squared.

Standard Deviation: It is the square root of variance. The population standard deviation is computed by square root of the population variance and the sample standard deviation is computed by square root of sample variance. Sample standard deviation is not the unbiased estimator for population standard deviation. The units on standard deviation are similar as the units of population or sample.

Coefficient of Variation: The percentage can be expressed by the standard deviation divided by the mean.

Chebyshev's Theorem: The Chebyshev's theorem can be applied to any distribution despite of its shape. According to Chebyshev's theorem the proportion of values which fall in k standard deviations of the mean is at least 1 - 1/k^2where k > 1.

Empirical or Normal Rule: This rule is valid only whenever a distribution in the bell-shaped is normal. Around 68% lies in 1 standard deviation of mean; 95% in 2 standard deviations; and 99.7% within the 3 standard deviations of mean.

Standard Score or Z-Score: This score can be obtained by subtracting the mean and then dividing by the standard deviation. The latest mean for Z will be 0 and the standard deviation will be 1, if all the values are transformed to their standard scores.

Percentile: The data should be ranked to find out the percentiles. The percent of population always lies below that value.

Quartile: It is either 25th, 50th or the 75th percentiles. The 50th percentile is as well termed as the median.

Decile: It is either the 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, or the 90th percentiles.

Lower Hinge: It is the median of lower half of the numbers, up to and comprising the median. The lower hinge is the initial Quartile unless the remainder whenever dividing the sample size by four outcomes 3.

Upper Hinge: The median of upper half of numbers (comprising the median). The upper hinge is the 3rd Quartile except the remainder if dividing the sample size by four outcomes 3.

Box and Whiskers Plot (Box Plot): It is the graphical representation of the minimum value, upper hinge, lower hinge, median and maximum. To define five values some textbooks and TI-82 calculator, they use the minimum, median, first Quartile, third Quartile, and the maximum.

Five Number Summaries: It comprises the lower hinge, minimum value, median, upper hinge and the maximum.

InterQuartile Range (IQR): The InterQuartile Range or IQR can be defined by the difference of 3rd and 1st Quartiles.

Outlier: Whenever extremely high or low value is compared to the rest of values then it is termed as outlier.

Mild Outliers: The values that lie between 1.5 to 3.0 times the InterQuartile Range beneath the 1st Quartile or above the 3rd Quartile. It must be kept in mind that some texts utilize hinges rather than Quartiles.

Extreme Outliers: The values that lie more than 3.0 times the InterQuartile Range beneath the 1st Quartile or above the 3rd Quartile. It must be kept in mind that some texts utilize hinges rather than Quartiles.

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