Statistics Calculator will help you to calculate and interpret important statistical values, including mean, median, mode, range, and standard deviation
Statistics Calculator
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How to use the Calculator
Statistic Calculator calculates the basic statistics values of the given data. The statistic calculator calculates the Minimum Data, Maximum Data, Count of input data, Sum, Mean, Median, Mode, Standard Deviation and Variance of the given input data.
To use the Calculator , enter the data in the input box available below the title “Enter the Data”. After entering the required data . Click in the Calculate Button.
Note : Enter each values separated by comma.
Mean
Mean is a measure of central tendency in statistics, also known as the average. It is calculated by adding up all the values in a data set and dividing the sum by the number of values. The mean is a useful tool for understanding the general value of a set of data.
How to Calculate Mean of given data ?
To calculate the mean of a set of data, follow these steps:
- Add up all the values in the data set.
- Count the number of values in the data set.
- Divide the sum of the values by the number of values.
The formula for calculating the mean is:
\( mean \ (\mu)\ = \frac{( \ sum \ of \ values \ )}{ ( \ number \ of \ values \ )}\ \)
\( mean \ (\mu)\ =\frac{x_1\ +\ x_2+\ x_3+\ x_4\ \ +\ …….\ +\ x_n}{n}\ \)
For example, to find the mean of the following data set: 5, 10, 15, 20
- Add up all the values: 5 + 10 + 15 + 20 = 50
- Count the number of values: There are 4 values in the data set.
- Divide the sum by the number of values: 50 / 4 = 12.5
Therefore, the mean of the data set is 12.5.
Example 1: Calculating the mean of a small set of data Suppose you have the following set of data: 3, 4, 5, 6
To find the mean, you would follow these steps:
- Add up all the numbers in the set: 3 + 4 + 5 + 6 = 18
- Divide the sum by the total number of values in the set: 18 ÷ 4 = 4.5 Therefore, the mean of the set is 4.5.
Example 2: Calculating the mean of a large set of data Suppose you have a larger set of data: 10, 12, 15, 17, 19, 20, 22, 23, 26, 28
To find the mean, you would follow these steps:
- Add up all the numbers in the set: 10 + 12 + 15 + 17 + 19 + 20 + 22 + 23 + 26 + 28 = 182
- Divide the sum by the total number of values in the set: 182 ÷ 10 = 18.2 Therefore, the mean of the set is 18.2.
Example 3: Calculating the mean of grouped data Suppose you have the following data, which is grouped into intervals:
0-10 | 5 |
10-20 | 12 |
20-30 | 8 |
30-40 | 3 |
To find the mean, you would follow these steps:
- Multiply each interval midpoint by its corresponding frequency (number of observations): (5 × 5) + (15 × 12) + (25 × 8) + (35 × 3) = 455
- Divide the sum by the total number of observations: 455 ÷ 28 = 16.25 Therefore, the mean of the data is 16.25.
Example 4: Calculating the weighted mean Suppose you have the following set of data, where each value has a corresponding weight:
Value: | 10 | 20 | 30 | 40 | 50 |
Weight: | 1 | 2 | 3 | 2 | 1 |
To find the weighted mean, you would follow these steps:
- Multiply each value by its corresponding weight: (10 × 1) + (20 × 2) + (30 × 3) + (40 × 2) + (50 × 1) = 200
- Add up all the weights: 1 + 2 + 3 + 2 + 1 = 9
- Divide the sum from step 1 by the sum from step 2: 200 ÷ 9 = 22.22 (rounded to two decimal places) Therefore, the weighted mean of the data is 22.22.
Median
In statistics, the median is a measure of central tendency that represents the middle value of a set of data when it is arranged in order of magnitude. Specifically, it is the value that separates the lower half of the data from the upper half.
How to find Median of given data ?
Steps to find the median of a data set:
Step 1: Arrange the data in order from lowest to highest (or highest to lowest).
Step 2: Determine if the data set has an odd or even number of values.
Step 3: If the data set has an odd number of values, the median is the middle value.
Step 4: If the data set has an even number of values, the median is the average of the two middle values.
Let’s use the following data sets as examples:
Example 1: Find Median of given data {5, 10, 15, 20, 25}
- Arrange the data in order: {5, 10, 15, 20, 25}
- Since there are an odd number of values (5), we know that the median will be a single value.
- The middle value is 15, so the median is 15.
Example 2: Find Median of given data {3, 6, 9, 12, 15, 18}
- Arrange the data in order: {3, 6, 9, 12, 15, 18}
- Since there are an even number of values (6), we know that the median will be the average of two values.
- The two middle values are 9 and 12, so the median is (9 + 12)/2 = 10.5.
Example 3: Find Median of given data {10, 15, 20, 25}
- Arrange the data in order: {10, 15, 20, 25}
- Since there are an even number of values (4), we know that the median will be the average of two values.
- The two middle values are 15 and 20, so the median is (15 + 20)/2 = 17.5.
Example 4: Find Median of given data {4, 8, 12, 16, 20, 24}
- Arrange the data in order: {4, 8, 12, 16, 20, 24}
- Since there are an even number of values (6), we know that the median will be the average of two values.
- The two middle values are 12 and 16, so the median is (12 + 16)/2 = 14.
To find the median of a data set, you need to arrange the data in order, determine if the data set has an odd or even number of values, and then calculate the median based on whether there is a single middle value or two middle values. The median is a useful measure of central tendency that is less sensitive to outliers than the mean.
Mode
In statistics, the mode is the value or values that occur most frequently in a given dataset. It is one of the most common measures of central tendency, along with mean and median.
The mode is often used in cases where the data is not normally distributed, or where there are extreme values that would skew the mean. For example, if we have a set of test scores where most of the scores are around 70, but there are a few scores in the 90s, the mode would be 70, while the mean might be closer to 80.
How to Calculate Mode ?
To calculate the mode of a dataset, you can follow these steps:
Step 1: Arrange the data in ascending or descending order.
Step 2: Count the frequency of each value in the dataset.
Step 3: Identify the value(s) that occur most frequently. These value(s) represent the mode(s) of the dataset.
If there is no value that occurs more than once in the dataset, then the dataset has no mode.
Here are some examples to illustrate the calculation of mode:
Example 1: Find the mode of the following dataset: 2, 5, 6, 5, 8, 9, 5, 2, 1
Step 1: Arrange the data in ascending order: 1, 2, 2, 5, 5, 5, 6, 8, 9
Step 2: Count the frequency of each value: 1 occurs once, 2 occurs twice, 5 occurs three times, 6 occurs once, 8 occurs once, and 9 occurs once.
Step 3: Identify the value(s) that occur most frequently: 5 occurs three times, so the mode of the dataset is 5.
Example 2: Find the mode of the following dataset: 10, 12, 15, 17, 19
Step 1: Arrange the data in ascending order: 10, 12, 15, 17, 19
Step 2: Count the frequency of each value: each value occurs once.
Step 3: There is no value that occurs more than once, so this dataset has no mode.
Example 3: Find the mode of the following dataset: 5, 7, 9, 7, 5, 3, 1, 2, 5
Step 1: Arrange the data in ascending order: 1, 2, 3, 5, 5, 5, 7, 7, 9
Step 2: Count the frequency of each value: 1 occurs once, 2 occurs once, 3 occurs once, 5 occurs three times, 7 occurs twice, and 9 occurs once.
Step 3: Identify the value(s) that occur most frequently: 5 occurs three times, so the mode of the dataset is 5.
Example 4: Find the mode of the following dataset: 1, 2, 3, 4, 5, 6, 7, 8, 9
Step 1: Arrange the data in ascending order: 1, 2, 3, 4, 5, 6, 7, 8, 9
Step 2: Count the frequency of each value: each value occurs once.
Step 3: There is no value that occurs more than once, so this dataset has no mode.
Variance
In statistics, variance is a measure of how spread out a set of data is around its mean. It is a measure of the variability or dispersion of a dataset. The variance measures how far the data points are from the mean.
The formula for variance is as follows:
Variance = (1/n) * Σ(xi – x̄)^2
where n is the number of data points, xi is each individual data point, x̄ is the mean of the data, and Σ represents the sum of all the values in the parentheses.
The variance is always non-negative, meaning it cannot be less than zero. A small variance indicates that the data points are clustered closely around the mean, while a large variance indicates that the data points are spread out over a wider range of values.
Variance is often used in conjunction with the standard deviation, which is the square root of the variance. The standard deviation provides a more intuitive measure of the spread of the data, as it is expressed in the same units as the original data.
Example 1: Suppose we have the following data set of 5 numbers: {4, 7, 11, 13, 16}. To calculate the variance, we can follow these steps:
Step 1: Find the mean (average) of the data set:
Mean \( ( \mu )= \ \frac{(4 + 7 + 11 + 13 + 16)}{ 5} \ = \ 10.2 \)
Step 2: For each data point, subtract the mean and square the result:
(4 – 10.2)^{2} = 38.44
(7 – 10.2)^{2} = 10.24
(11 – 10.2)^{2} = 0.64
(13 – 10.2)^{2} = 7.84
(16 – 10.2)^{2} = 33.64
Step 3: Calculate the average of the squared differences (also known as the mean squared deviation): (38.44 + 10.24 + 0.64 + 7.84 + 33.64) / 5 = 18.56
Therefore, the variance of the data set is 18.56.
Example 2: Suppose we have the following data set of 8 numbers: {1, 3, 5, 7, 9, 11, 13, 15}. To calculate the variance, we can follow these steps:
Step 1: Find the mean (average) of the data set: Mean = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15) / 8 = 8
Step 2: For each data point, subtract the mean and square the result:
(1 – 8)^{2} = 49
(3 – 8)^{2} = 25
(5 – 8)^{2} = 9
(7 – 8)^{2} = 1
(9 – 8)^{2} = 1
(11 – 8)^{2} = 9
(13 – 8)^{2} = 25
(15 – 8)^{2} = 49
Step 3: Calculate the average of the squared differences (also known as the mean squared deviation):
\( \frac{(49 + 25 + 9 + 1 + 1 + 9 + 25 + 49)}{8 } \ = \ 18 \)
Therefore, the variance of the data set is 18.
Standard Deviation
Standard deviation is a measure of the amount of variation or dispersion in a set of data. It tells us how spread out the data is from the mean.
The standard deviation is calculated as the square root of the variance. A small standard deviation indicates that the data is clustered around the mean, while a large standard deviation indicates that the data is spread out over a wider range of values.