## Median calculator

For median calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). For example: 706.2 -962.6 454.4 206.1 966.5 678.2 733.3 234.4 444.3 184.1 655.5 354.5 824.9

### Median

The median separates the higher half of the ordered data sample (or data file) from the lower half.
The median is the 2nd quartile (Q2), 5th decile, and 50th percentile.

### How to calculate the median?

Sort data set with n elements and select n/2-th element. If the index n/2 is not an integer, then use interpolation between the surrounding elements (in this case median does not belong to the input data set).

For example, for n=10 elements, the median is equal to the 5th element. For n=50 elements, the median is equal to the 25th of the ordered data, etc.

### How to enter data as a frequency table?

Simple. First-type data elements (separated by spaces or commas, etc.), then type f: and further write the frequency of each data item. Each element must have a defined frequency that count of numbers before and after symbol f: must be equal. For example:

1.1 2.5 3.99
f: 5 10 15

### How to enter grouped data?

Grouped data are formed by aggregating individual data into groups so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

 group frequency 10-20 5 20-30 10 30-40 15

This grouped data you can enter:
10-20 20-30 30-40
f: 5 10 15

### How to enter data as a cumulative frequency table?

Similar to a frequency table, but instead f: type cf: in the second line. For example:

Read:   What is 12x3 9x2 4x 3 in Factored Form

10 20 30 40 50 60 70 80
cf: 5 13 20 32 60 80 90 100

The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always be equal to the total for all observations since all frequencies will already have been added to the previous total.

## Practice problems from statistics:

• The data

The data set represents the number of cars in a town given a speeding ticket each day for ten days. 2 4 5 5 7 7 8 8 8 12 What is the IQR?
• Median and modus

Radka made 50 throws with a dice. The table saw fit individual dice’s wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell.
• The size 2

The size of pants sold during one business day in a department store are 32, 38, 34, 42, 36, 34, 40, 44, 32, and 34. Find the average size of the pants sold.
• Harmonic HM example

Find the harmonic mean of 4 and 8.
• 75th percentile (quartille Q3)

Find 75th percentile for 30,42,42,46,46,46,50,50,54
• Increase the mean

To which number should the number 4 be changed between the numbers 4,5,7, 1,0,9,7,8, -3,5 to increase these numbers’ arithmetic mean by 1.25?
• 45 percentile

Given the following data 11 15 24 33 10 35 23 25 40 What is P45?
• Centimeters 66264

The average height of the basketball team’s primary five players is 196 cm. The underscore player is 216 cm tall. What is the average height of the remaining four players in centimeters?
• Harmonic and arithmetic means

The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff: Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20 Calculate: a
• Five number summary

Find the five-number summary for these data and make a boxplot. 14,5,12,19,2,35,5,4,3,7,5,8
• A student 2

A student randomly selected 225 college students and asked them whether they ate breakfast that morning before coming to campus. There were 57 students that were at least 25 years old, of which 30 had breakfast that morning. Of the 168 students that were