Formula Sheet On Statistics Notes
Statistical Measured are employed in situations where we have a large group of data to analyse. In order to make sense of the data, we use these measures to help generalize a group of data, make inferences about it, and compare it with other groups of data.
Measures of Central Tendency: Statistical measures mainly include mean, Median, mode. They are also known as Measures of Central Tendency.
1. Mean: The mean is synonymous with the average of the group of It is basically the sum of all the data items divided by the number of data items.
The population mean is represented by the Greek letter mu (μ).
2. Median: The median is the middle value in a sample of data that is ordered from least to greatest.
If there is an odd number of terms in the sample, the middle number will be the median of the sample. If there is an even number of terms, the average of two middle numbers will be the median of the sample.
Steps to Find Median -
STEP 1. Arrange the observations in increasing order.
STEP 2. If there is an odd number of terms, find the middle term of the ordered sample. It is the median.
STEP 3. If there is an even number of terms, find the average of the middle two terms. This average is the median.
3. Mode: The mode is the number that occurs most In other words, the most frequent number in a sample of data is called a mode of the sample.
Measures of Variability: Measures of central tendency yield information about particular points of a data set. However, researchers can use another group of analytic tools to describe a set of data. These tools are measures or variability, which describe the spread or the dispersion of a set of data.
4. Range: The range is the difference between the largest value of a data set and the smallest value. Although, it is usually a single numeric value, some researchers define the range as the ordered pair of smallest and largest numbers (smallest, largest).
Range = Highest – Lowest
5. Mean Absolute Deviation: The mean absolute deviation (MAD) is the average of the absolute values of the deviations around the mean for a set of
6. Variance: The variance is the average of the squared deviations about the arithmetic mean for a set of numbers. The population variance is denoted by σ2.
7. Standard Deviation: The standard deviation is the square root of the population standard deviation is denoted by σ.
Ex. 1] A manager at a small movie theatre was analysing the number of people who came to the movies during the week. Over nine days, he found the following data: 81, 88, 93, 85, 93, 62, 86, 100, and 95. Find the mean, median, mode, range, Mean Absolute Deviation, Variance and Standard Deviation of the data.
On arranging the numbers in ascending order - 62,81,85,86,88,93,93,95,100
Now the middle number = 88, will be the median.
Mode = We can observe from given data that 93 occurs two times and all of the other numbers only once.
So, the mode is 93.
Range = 100−62 = 38
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