what is central tendency explain its main types
Answers
Its main types are mean median and mode
Mean:
We commonly used mean method for measuring Central tendency.
Average usually refers to mean.
We find mean by sum of the values divided by the total number of items.
The Result is referred as the Arithmetic mean.
Mean= sum of the values/ total no.of items
2. Median:
We find median by arranging the data for lowest to highest means in ascending order & taking the data point in the middle of the sequence.
Above and below the median there is an equal number of points.
If total number of observation is n. If n is Odd then median is the value o
( (n+1)/2)th observation.
If n is even then median is the Arithmetic mean of the values of(n/2)th &( (n/2)+1))th observations
3. Mode:
Mode is the most frequently occurring frequency in the data.
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Relationship among mean median and mode
1. Mode= 3 median - 2 mean
2. Median = mode +2/3 (mean - mode)
3. Mean= mode +3/2 (median- mode)
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Hope this will help you...
Explanation:
Central tendency is a descriptive summary of a dataset through a single value that reflects the center of the data distribution. Along with the variability (dispersion) of a dataset, central tendency is a branch of descriptive statistics.
The central tendency is one of the most quintessential concepts in statistics. Although it does not provide information regarding the individual values in the dataset, it delivers a comprehensive summary of the whole dataset.
Measures of Central Tendency
Generally, the central tendency of a dataset can be described using the following measures:
Mean (Average): Represents the sum of all values in a dataset divided by the total number of the values.
Median: The middle value in a dataset that is arranged in ascending order (from the smallest value to the largest value). If a dataset contains an even number of values, the median of the dataset is the mean of the two middle values.
Mode: Defines the most frequently occurring value in a dataset. In some cases, a dataset may contain multiple modes while some datasets may not have any mode at all.
Even though the measures above are the most commonly used to define central tendency, there are some other central tendency measures, including, but not limited to, geometric mean, harmonic mean, midrange, and geometric median.
The selection of central tendency as a measure depends on the properties of a dataset. For instance, mode is the only central tendency measure of categorical data while a median works best with ordinal data.
Although mean is regarded as the best measure of central tendency for quantitative data, it is not always the case. For example, mean may not work well with quantitative datasets that contain extremely large or extremely small values. The extreme values may distort the mean. Thus, you may consider other options of central tendency.
The measures of central tendency can be found using a formula or definition. Also, they can be identified using a frequency distribution graph. Note that for the datasets that follow a normal distribution, the mean, median, and mode are located on the same spot on the graph.
