Mean Median Mode Calculator

Not only the median, mean and mode of the data set, you can also check other details like minimum, maximum values, range, quartiles, others using this tool. Here we are giving the step by step procedure to get the mean, median, mode values accurately. You should use these easy steps to find the values manually.

Take any data set having various numbers separated by commas.

Mean Calculation:

• Add all the values in the data set to get the total.
• Count the total number of values in the data set.
• Divide the total by the count to find mean.

Median Calculation:

• Arrange the values of the data set in ascending order from the lowest value to the highest value.
• Median is the middle value in the arranged data.
• If you have more than one value at the middle place them median is the average of those two values.

Mode Calculation:

Mode is the value that occurs most frequently or repetedly.

Mean:

Mean is similar to the average value of the data set. It is obtained by adding all the elements and dividing the result by the number of elements in the data set. The formula to calculate mean is as follows:

Mean = x_mean = (∑_{i = 1}ⁿx_i) / n

Median:

Median is the value that separates the ordered data set into two equal parts. The formula to compute the median value is given as:

If the size of the data set is odd, then

position p = (n + 1) / 2

x_median = x_p

If data set size is even, then

position p = n/2

x_median = (x_p + x_p+1) / 2

Mode:

Mode is the value or values that occurs more times.

Minimum:

Which is the lowest value in the data set. Arrange the data set in the ascending order.

x_min = min(x_i)_i=1ⁿ

Maximum:

It is the highest value available in the data set. Arrange the data set from the lowest to highest values.

x_max = max(x_i)_i=1ⁿ

Range:

It is the difference between maximum and minimum value.

Range = x_max - x_min

Count:

It defines the size of the data set.

Count = count(x_i)_{i = 1}ⁿ

Sum:

It gives the sum of values in the data set.

sum = ∑_{i = 1}ⁿx_i

Quartiles:

Q1 is lower half of median, Q2 is the median, Q3 is the higher half of median.

Interquartile Range IQR:

Range from Q1 to Q3 is the IQR.

IQR = Q3 - Q1

Example

Question: Calculate mean, median, mode of the data set {2, 5, 8, 1, 12, 8, 2, 15}

Solution:

Given data set is {2, 5, 8, 1, 12, 8, 2, 15}

Mean = x_mean = (∑_{i = 1}ⁿx_i) / n

= (2 + 5 + 8 + 1 + 12 + 8 + 2 + 15) / 8

= 53/8

= 6.625

Median = x_median = (x_p + x_p+1) / 2

Arrange given data set in ascending order.

= {1, 2, 2, 5, 8, 8, 12, 15}

p = n/2 = 8/2 = 4

x_median = (5 + 8) / 2

= 13/2

= 6.5

Mode = {2, 8}

Minimum = 2

Maximum = 15

count = 8

Range = x_max - x_min

= 15 - 2

= 13

Sum = ∑_{i = 1}ⁿx_i

= 2 + 5 + 8 + 1 + 12 + 8 + 2 + 15

= 53

Q2 → 6.5

Q1 → 2

Q3 → 10

Interquartile Range IQR = Q3 - Q1

= 10 - 2

= 8

∴ Mean = 6.625, median = 6.5, mode = {2, 8}, minimum - 2, maximum = 15, count = 8, range = 13, sum = 53, IQR = 8

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1. What is meant by mean median mode?

Mean, median, and mode are three measures which are used to find the central value of the data set values. these are considered as the measures of central tendencies. Mean is defined as the average value. Median value when the given data set is arranged in ascending order. Mode is the repeated value.

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2. What is mean, median, mode formula?

Mean = Sum of data items / n

If n is odd, position is p = (n + 1) / 2

Median = x_p

if n is even, position is p = n/2

Median= (x_p + x_p+1) / 2

Mode is the repeatedly occurred value in the data set.

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3. How to use Mean Median Mode Calculator?

At first, enter data set values in the input segment. Hit on the calculate button which is in blue color to get the output as mean, mode, and median of the data set values.

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4. Can a data set has more than one mode?

Yes, it is possible to have more than one mode value for a data set. It is just the numbers which are frequently occurs in the data set.

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