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

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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

### 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) **\(14, 20, 19, 3, 9, 41, 9 \)\(\ \Rightarrow \ \)