**Median**

Median is the middle value of the data when the observations are sorted (ascending or descending order)

- When sorted (ascending or descending), the median splits the data into two halves equally (upper and lower halves).
- The percentile rank of median = 50%
- Median is not calculated based on all the values in data and is therefore not impacted by outliers.
- When sorted,
- If the number of observations (n) is odd, then the median is the value of the middle observation at position (n + 1) / 2.
- Else If the number of observations (n) is even, then the median is the mean of the two middle-most values at position ( n/2, (n+1)/2 ) .

**Example**

There are 15 tiny tots in a preschool and their age in months is given below. Calculate median:

- To find the median, first we sort the values in ascending order (or descending)
- As
**n = 15 (n is odd),**the median will be 8th position value [(15 + 1)/2 = 8].

**The value at 8th position is 38, therefore Median = 38**

**Interpretation**

50% of the tiny tots in preschool are below the age of 38 months and the remaining 50% are above 38 months.

**Median vs. Mean**

There are three preschools in a city and their summary details are given below. Calculate the mean and median for all the three preschools taken together.

Preschool Name |
# Children |
Median Age(in months) |
Mean Age(in months) |

Fun School |
40 | 40 | 41 |

Play School |
20 | 36 | 35 |

Enjoy School |
30 | 37 | 37 |

Median represents the value of the central observation in a given sample. From the above table, **we cannot compute the median of all three preschools together**. To be able to compute the median we will require the age at individual children level.

Mean is computed as the arithmetic average of the values in a sample data. From the above table, We can compute the mean of all three preschools together using Weight Mean calculation but not Median. Dear blog reader, I leave the calculation as a practice for you.

**Practice Exercise 1**

Compute median from the below histogram.

**Practice Exercise 2**

A small startup has 10 employees including the founders. The monthly salaries of all the employees is given in the table below. Find the median salary.

Emp. No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Monthly Salary (k) | 90 | 80 | 18 | 18 | 17 | 16 | 16 | 16 | 15 | 14 |

**Next Blog**

In the next blog, we will discuss Mode.

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