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Class | xi | fi | Average | Total |
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Arithmetic Mean | Weighted Average | Median | Mode | Average Deviation |
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Variance | Standard Deviation |
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Variance | Standard Deviation |
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A statistical calculator is a device or program that is used to perform statistical calculations, such as mean, median, standard deviation, and regression analysis. Some statistical calculators are handheld devices, while others are software programs that run on a computer or mobile device. They are commonly used in fields such as business, finance, and science to analyze data sets and make informed decisions based on the results.

The arithmetic mean, also known as the "average," is a statistical measure that is used to find the central tendency of a data set. To find the arithmetic mean of a set of numbers, you add all the numbers together and then divide the sum by the number of numbers in the set.

For example, if a data set contains the numbers 2, 4, and 6, the sum of the numbers is 2 + 4 + 6 = 12, and the average of the numbers is 12 / 3 = 4. It is considered as one of the measure of central tendency.

Average x̄ = Sum of all observations / Number of observations

A weighted average is a type of average in which each value in a data set is assigned a weight, or coefficient, that reflects its relative importance or contribution. The weighted average is calculated by multiplying each value in the data set by its corresponding weight, summing the products, and dividing the sum by the total weight.

For example, if a data set contains the numbers 2, 4, and 6, with corresponding weights of 0.1, 0.2, and 0.7 respectively, the weighted average can be calculated as follows:

(20*0.1) + (40*0.2) + (6*0.7) = 0.2 + 0.8 + 4.2 = 5.2 / (0.1+0.2+0.7) = 5.2 / 1 = 5.2

Weighted averages are used in many different contexts, such as calculating grades in a class where some assignments are worth more than others, or determining the overall value of a portfolio of investments where some assets are more important than others.

The median is a statistical measure that is used to find the middle value in a data set. To find the median of a set of numbers, you first need to arrange the numbers in numerical order, and then identify the middle value. For example, in a data set of {3,5,7,9,11}, the median is 7.

If the data set contains an even number of values, then the median is the average of the two middle values. For example, in a data set of {3,5,7,9,11,13}, the median is (7+9)/2 = 8.

The median is considered as one measure of central tendency and one of the advantage of median is that it is not affected by outliers, or extremely high or low values that can skew the mean. It also gives a good representation of the center of the dataset in case of skewed or non-normal distributed data.

The formula for finding the median of a data set depends on whether the data set has an odd or even number of values.

For a data set with an odd number of values:

The median is the middle value in the list.

For a data set with an even number of values:

Arrange the data set in numerical order The median is the average of the two middle values. For example, if you have a data set {a1,a2,a3....an} and n is odd then median is (a(n+1)/2). If the n is even then median is (a(n/2) + a(n/2 +1))/2.

Median = a((n+1)/2) if n is odd

Median = (a(n/2) + a(n/2 +1))/2 if n is even

Where a is the value of nth number in the dataset and n is the total number of value in the dataset.

The mode is a statistical measure that is used to find the most frequently occurring value in a data set. In other words, it is the value that appears most often in a set of data. A set of data can have one mode, more than one mode, or no mode at all.

For example, in a data set {1, 2, 2, 3, 4}, the mode is 2, because it is the value that occurs most often. In a data set {1, 2, 3, 4, 5} there is no mode, because all the values occur with the same frequency. When a dataset have multiple values which have the same maximum frequency, dataset is said to have multiple modes.

Mode is also a measure of central tendency and is useful in cases where the dataset is discrete in nature like in case of Nominal or Ordinal data. It is less robust to outliers as compared to mean and median, and is often not defined for datasets with continuous variables.

Example: 1, 5, **7**, **7**, **7**, 8, 9, 11, 12, 15, **19**, **19**, **19**, 25, 27

In the example above, both the number 7 and number 19 are modes, as they each occur three times and no other number occurs more often.

Variance is a statistical measure of the spread between numbers in a data set. It is a measure of how far each number in the set is from the mean (average), and thus from every other number in the set. Variance gives a sense of how dispersed the individual data points are from the mean of the distribution.

The formula for calculating variance of a sample is:

Sample Variance = (1/(n-1)) * Σ(x(i) - mean(x))^2

Where n is the number of observations in the sample, x(i) is the ith observation, and mean(x) is the mean of the sample.

The formula for calculating variance of a population is similar:

Population Variance = (1/N) * Σ(x(i) - mean(x))^2

Where N is the number of observations in the population and x(i), mean(x) have the same meaning as before.

The square root of the variance is called the standard deviation, it's also a measure of spread. The standard deviation is in the same unit as the variable itself, while the variance is squared, making it difficult to interpret. Variance and standard deviation are used to quantify the degree of dispersion of a set of data.

The variance and standard deviation can be very useful in understanding the spread and distribution of data, but it's important to keep in mind that it can be sensitive to outliers or extreme values.

The standard deviation is a statistical measure that quantifies the spread of a data set. It is the square root of the variance, which is a measure of the average distance of each data point from the mean. The standard deviation is used to describe the variability of a set of observations.

The formula for calculating the sample standard deviation is:

Sample Standard deviation = sqrt((1/(n-1)) * Σ(x(i) - mean(x))^2)

Where n is the number of observations in the sample, x(i) is the ith observation, and mean(x) is the mean of the sample.

The formula for calculating the population standard deviation is:

Population Standard deviation = sqrt((1/N) * Σ(x(i) - mean(x))^2)

Where N is the number of observations in the population and x(i), mean(x) have the same meaning as before.

The standard deviation can be used to compare data sets by providing a normalized measure of variability. A smaller standard deviation indicates that the data points tend to be close to the mean (average), while a larger standard deviation indicates that the data points are more spread out from the mean. The standard deviation is also commonly used to find outliers or to establish whether a data set is homoscedastic (or consistent) or heteroscedastic (or inconsistent).

It is important to note that, like the variance, the standard deviation is sensitive to outliers or extreme values, so it should be used with caution when analyzing data sets that may contain such values.

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