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

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.

### 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

### 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

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