How to Find Mean, Median, Mode, and Range of the Given Data

How to Find Mean, Median, Mode, and Range of the Given Data

 Read,7 minutes

The 3 clear-cut calculations linked with the Measure of Central Tendency are Mean, Median, and Mode. Each of the measurements is an effort to capture the fundamental nature of the way a standard number or entry in a data set might appear. The notion is to calculate one distinct value which could stand for the set’s elements.

Way to Determine the Mean

  • Add up every one of the data values to determine the sum.
  • Add the amount of values in the data set.
  • Divide your sum via the count.

Mean is equal to a data set’s average value.

Formula for Mean:

Mean \(= \ \frac{sum \ of \ the \ data}{total \ number \ of \ data \ entires}\)

Way to Determine the Median

Median \(x∼\) is the data value splitting the upper part of a data set from the lower half.

  • Assemble the data values beginning with the lowest to the highest value
  • Its median is the value of the data in the middle of your set
  • If there are two data values in the middle, then your median equals the mean of these two values.

Formula for Determining Median

  • If the data set \(n\)’s size is odd the median equals the value at your position \(p\) where:
    \(p \ = \ \frac{n \ + \ 1}{2} \ , \ x˜ \ = \ x_{p}\)
  • Should \(n\) be even the median is the values’ average at the positions \(p\) and \(p \ + \ 1\) where: 
    \(p \ = \ \frac{n}{2} \ , \ x˜ \ = \ \frac{x_{p} \ + \ x_{p \ + \ 1}}{2}\)

Way to Determine Mode

The mode is the value \(s\) in the data set which happens the most regularly.
With a data set \(1, \ 1, \ 2, \ 5, \ 6, \ 6, \ 9\) your mode is \(1\) as well as \(6\).

Way to Determine the Range

The range of the data set is the difference between the lowest and the highest value. To find the range, follow these steps:

  • Step 1: Arrange the data values from the lowest to the highest value.
  • Step 2: Find the difference between the highest and smallest value.
  • Step 3: Write down your answer.

Outliers

Possible Outliers are values which are above the Upper Fence or are under the Lower Fence of a sample set.

  • Upper Fence \(= \ Q_{3} \ + \ 1.5 \ \times\) Interquartile Range
  • Lower Fence \(= \ Q_{1} \ − \ 1.5 \ \times\) Interquartile Range

Free printable Worksheets

Exercises for Mean, Median, Mode, and Range of the Given Data

1) \(12, 21, 18, 1, 8, 32, 8 \)\(\ \Rightarrow \ \)

2) \(10, 24, 16, 1, 9, 47, 9 \)\(\ \Rightarrow \ \)

3) \(2, 54, 13, 24, 17, 6, 6 \)\(\ \Rightarrow \ \)

4) \(13, 21, 19, 3, 8, 62, 8 \)\(\ \Rightarrow \ \)

5) \(18, 8, 10, 8, 1, 55, 23 \)\(\ \Rightarrow \ \)

6) \(18, 5, 12, 5, 1, 40, 23 \)\(\ \Rightarrow \ \)

7)  \(4, 33, 10, 22, 15, 6, 6 \)\(\ \Rightarrow \ \)

8) \(10, 20, 16, 4, 5, 26, 5 \)\(\ \Rightarrow \ \)

9) \(4, 48, 12, 24, 16, 6, 6 \)\(\ \Rightarrow \ \)

10) \(14, 20, 19, 3, 9, 41, 9 \)\(\ \Rightarrow \ \)

 
1) \(12, 21, 18, 1, 8, 32, 8 \)\(\ \Rightarrow \ \) mean: \(\color{red}{14.29,}\) median: \(\color{red}{12,}\) mode: \(\color{red}{8,}\) range : \(\color{red}{31}\)
2) \(10, 24, 16, 1, 9, 47, 9 \)\(\ \Rightarrow \ \) mean: \(\color{red}{16.57,}\) median: \(\color{red}{10,}\) mode: \(\color{red}{9,}\) range : \(\color{red}{46}\)
3) \(2, 54, 13, 24, 17, 6, 6 \)\(\ \Rightarrow \ \) mean: \(\color{red}{17.43,}\) median: \(\color{red}{13,}\) mode: \(\color{red}{6,}\) range : \(\color{red}{52}\)
4) \(13, 21, 19, 3, 8, 62, 8 \)\(\ \Rightarrow \ \) mean: \(\color{red}{19.14,}\) median: \(\color{red}{13,}\) mode: \(\color{red}{8,}\) range : \(\color{red}{59}\)
5) \(18, 8, 10, 8, 1, 55, 23 \)\(\ \Rightarrow \ \) mean: \(\color{red}{17.57,}\) median: \(\color{red}{10,}\) mode: \(\color{red}{8,}\) range : \(\color{red}{54}\)
6) \(18, 5, 12, 5, 1, 40, 23 \)\(\ \Rightarrow \ \) mean: \(\color{red}{14.86,}\) median: \(\color{red}{12,}\) mode: \(\color{red}{5,}\) range : \(\color{red}{39}\)
7) \(4, 33, 10, 22, 15, 6, 6 \)\(\ \Rightarrow \ \) mean: \(\color{red}{13.71,}\) median: \(\color{red}{10,}\) mode: \(\color{red}{6,}\) range : \(\color{red}{29}\)
8) \(10, 20, 16, 4, 5, 26, 5 \)\(\ \Rightarrow \ \) mean: \(\color{red}{12.29,}\) median: \(\color{red}{10,}\) mode: \(\color{red}{5,}\) range : \(\color{red}{22}\)
9) \(4, 48, 12, 24, 16, 6, 6 \)\(\ \Rightarrow \ \) mean: \(\color{red}{16.57,}\) median: \(\color{red}{12,}\) mode: \(\color{red}{6,}\) range : \(\color{red}{44}\)
10) \(14, 20, 19, 3, 9, 41, 9 \)\(\ \Rightarrow \ \) mean: \(\color{red}{16.43,}\) median: \(\color{red}{14,}\) mode: \(\color{red}{9,}\) range : \(\color{red}{38}\)

Mean, Median, Mode, and Range of the Given Data Quiz