5 Number Summary Calculator

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**Step 1 :**

**Step 2 :**

The 5 number summary is a easy way to have the statistical idea. It consists of following 5 statistical percentiles:

- Maximum = Largest number
- Minimum = smallest number
- Median = It is the value that is in between the largest and the smallest data
- First quartile = It is the value that separates the 75% percent of the largest data from the 25% smallest data
- Third quartile = It is the value that separates the 25% percent of the largest data from the 75% smallest data.

Set the given data in ascending order, note down the number of elements in the given data n and find the maximum and minimum value.

The mean is calculated using the formula

Median = $\frac{n+1}{2}$ term

The Upper quartile is given by

Q_{1} = $\frac{n+1}{4}$ term

The lower quartile is given by

Q_{3} = $\frac{3(n+1)}{4}$ term

Substitute the values in above formula and get the answer.

Find the max, min, median and other percentiles for the following set of data: {34,35,46,57,8,67}.

**Step 1 :**The given set of data is {34,35,46,57,8,67} and the order is {8,34,35,46,57,67 }

No of elements n = 6

Minimum value = 8

Maximum value = 67**Step 2 :**The mean is calculated using the formula

Median = $\frac{n+1}{2}$ = $\frac{6+1}{2}$ = 3rd and 4th term

$\therefore$ Median = $\frac{35+46}{2}$ = 40.5

The Upper quartile is given by

Q_{1}= $\frac{n+1}{4}$

= $\frac{6+1}{4}$

= $\frac{7}{4}$

= 1.75

First quartile is the average of 1st and 2nd term, i.e. $\frac{8+34}{2}$ = $\frac{42}{2}$ = 21

The lower quartile is given by

Q_{3}= $\frac{3(n+1)}{4}$

= 3 $\times$ 1.75

= 5.25

Third quartile is the average of 5th and 6th term, i.e. $\frac{57+67}{2}$ = $\frac{124}{2}$ = 62

**Answer :**Hence No of elements n = 6, minimum value = 8, maximum value = 67, median = 40.5, first quartile, Q

_{1}= 21, third quartile, Q_{3}= 62.Calculate the max, min, median and upper quartile for the following set of data: {4,6,7,5,3,4}.

**Step 1 :**The given set of data is {4,6,7,5,3,4} and the order is {3,4,4,5,6,7}

No of elements n = 6

Minimum value = 3

Maximum value = 7**Step 2 :**The mean is calculated using the formula

Median = $\frac{n+1}{2}$ = $\frac{6+1}{2}$ = 3rd and 4th term

$\therefore$ Median = $\frac{4+5}{2}$ = 4.5

The Upper quartile is given by

Q_{1}= $\frac{n+1}{4}$

= $\frac{6+1}{4}$

= $\frac{7}{4}$

= 1.75

First quartile is the average of 1st and 2nd term, i.e. $\frac{3+4}{2}$ = $\frac{7}{2}$ = 3.5

The lower quartile is given by

Q_{3}= $\frac{3(n+1)}{4}$

= 3 $\times$ 1.75

= 5.25.

Third quartile is the average of 5th and 6th term, i.e. $\frac{6+7}{2}$ = $\frac{13}{2}$ = 6.5

**Answer :**Hence No of elements n = 6, minimum value = 3, maximum value = 7, median = 4.5, first quartile Q

_{1}= 3.5, third quartile Q_{3}= 6.5.