Utilize the Five Number Summary Calculator and find the set of observations of a data ie., 180,191,314,243, and displays the outcome as the min value is 180, the max value is 314, the median is 4, Q1 is 185.5, and Q3 is 278.5 in a fraction of seconds along with detailed solution steps.
Ex: 32,45,12,17,43,68,75,8,11,29
Five Number Summary:
The Five-Number Summary is a descriptive statistic that provides information about a Set of Observations. It consists of the following statistics:
Given numbers are 180,191,314,243
Firstly, the given numbers are made in an ascending order.
180,191,243,314
From the order of numbers,180 is the minimum number.
Therefore, the Minimum of the given numbers 180,191,314,243 is 180.
Given numbers are 180,191,314,243
Firstly, the given numbers are made in an ascending order.
180,191,243,314
From the order of numbers, 314 is the maximum number.
Therefore, the Maximum of the given numbers 180,191,314,243 is 314.
Median:
The Median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.
Formula for Median of Numbers:
If we have odd set of numbers,the formula will be:
Median=[ (n+1) / 2 ]th item
where n=Set of Numbers
If we have even set of numbers, the formula will be:
Median=Mean of two middle items
i.e., Median=Average of [ n / 2 ]th item and [ n+2 / 2 ]th item
The given numbers are 180,191,314,243
Firstly, the numbers should be set in an ascending order.
180,191,243,314
As these are having Even set of numbers,the Mean of the both middle numbers is the Median
The Set of Numbers, i.e., n = 4
The two middle numbers items will be n / 2 and (n+2) / 2
n / 2 = 4 / 2
n / 2 = 2
(n+2) / 2 = (4+2) / 2
n+2 / 2 = 3
The two middle number items 2 and 3 contains the numbers 191 and 243
Now these numbers should be calculated to know the mean of those numbers
Mean:
The Mean (or Average) of a set of Data Values is the Sum of all of the Data Values divided by the Number of Data Values.
Formula for Mean of Numbers:
Mean (or) Average of Numbers = Sum of the given data / Number of given data
Mean = (x0 +x1 +x2 +x3 .......+xn) / n
X̄ = Σ xn / n
The Given Numbers are 191,243
Number of Data given, i.e., n = 2
Now, the Sum of the Data Values will be
x0 + x1 + x2 + x3 + .... + xi = 191+243
Σ xn = 434
Therefore, the Mean of Data is
X̄ = Σ xn / n
X̄ = 434 / 2
X̄ = 217
The Mean of Data is 217
[ n / 2 + (n+2) / 2] / 2 = (191+243) / 2
Average (or) Mean of two middle numbers is [217]
Median of the numbers is 217
Lower (or) First Quartile:
The Lower Quartile (Q1) is the Median of the lower half of the data set which is the first half of the given data.
Given numbers are 180,191,314,243
Firstly, the numbers should be set in an ascending order.
180,191,243,314
The length of the given data values are 4.
The data can be divided into two halves with 2 numbers each.
The First half of the numbers are 180,191
Now, the Median of the numbers should be calculated.
Median:
The Median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.
Formula for Median of Numbers:
If we have odd set of numbers,the formula will be:
Median=[ (n+1) / 2 ]th item
where n=Set of Numbers
If we have even set of numbers, the formula will be:
Median=Mean of two middle items
i.e., Median=Average of [ n / 2 ]th item and [ n+2 / 2 ]th item
The given numbers are 180, 191
Firstly, the numbers should be set in an ascending order.
180,191
As these are having Even set of numbers,the Mean of the both middle numbers is the Median
The Set of Numbers, i.e., n = 2
The two middle numbers items will be n / 2 and (n+2) / 2
n / 2 = 2 / 2
n / 2 = 1
(n+2) / 2 = (2+2) / 2
n+2 / 2 = 2
The two middle number items 1 and 2 contains the numbers 180 and 191
Now these numbers should be calculated to know the mean of those numbers
Mean:
The Mean (or Average) of a set of Data Values is the Sum of all of the Data Values divided by the Number of Data Values.
Formula for Mean of Numbers:
Mean (or) Average of Numbers = Sum of the given data / Number of given data
Mean = (x0 +x1 +x2 +x3 .......+xn) / n
X̄ = Σ xn / n
The Given Numbers are 180,191
Number of Data given, i.e., n = 2
Now, the Sum of the Data Values will be
x0 + x1 + x2 + x3 + .... + xi = 180+191
Σ xn = 371
Therefore, the Mean of Data is
X̄ = Σ xn / n
X̄ = 371 / 2
X̄ = 185.5
The Mean of Data is 185.5
[ n / 2 + (n+2) / 2] / 2 = (180+191) / 2
Average (or) Mean of two middle numbers is [185.5]
Median of the numbers is 185.5
The Lower (or) First Quartile of the Numbers 180,191,314,243 is 185.5
Upper (or) Third Quartile:
The Upper Quartile (Q3) is the Median of the upper half of the data set which is the second half of the given data.
Given numbers are 180,191,314,243
Firstly, the numbers should be set in an ascending order.
180,191,243,314
The length of the given data values are 4.
The data can be divided into two halves with 2 numbers each.
The Second half of the numbers are 243,314
Now, the Median of the numbers should be calculated.
Median:
The Median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.
Formula for Median of Numbers:
If we have odd set of numbers,the formula will be:
Median=[ (n+1) / 2 ]th item
where n=Set of Numbers
If we have even set of numbers, the formula will be:
Median=Mean of two middle items
i.e., Median=Average of [ n / 2 ]th item and [ n+2 / 2 ]th item
The given numbers are 243, 314
Firstly, the numbers should be set in an ascending order.
243,314
As these are having Even set of numbers,the Mean of the both middle numbers is the Median
The Set of Numbers, i.e., n = 2
The two middle numbers items will be n / 2 and (n+2) / 2
n / 2 = 2 / 2
n / 2 = 1
(n+2) / 2 = (2+2) / 2
n+2 / 2 = 2
The two middle number items 1 and 2 contains the numbers 243 and 314
Now these numbers should be calculated to know the mean of those numbers
Mean:
The Mean (or Average) of a set of Data Values is the Sum of all of the Data Values divided by the Number of Data Values.
Formula for Mean of Numbers:
Mean (or) Average of Numbers = Sum of the given data / Number of given data
Mean = (x0 +x1 +x2 +x3 .......+xn) / n
X̄ = Σ xn / n
The Given Numbers are 243,314
Number of Data given, i.e., n = 2
Now, the Sum of the Data Values will be
x0 + x1 + x2 + x3 + .... + xi = 243+314
Σ xn = 557
Therefore, the Mean of Data is
X̄ = Σ xn / n
X̄ = 557 / 2
X̄ = 278.5
The Mean of Data is 278.5
[ n / 2 + (n+2) / 2] / 2 = (243+314) / 2
Average (or) Mean of two middle numbers is [278.5]
Median of the numbers is 278.5
The Upper (or) Third Quartile of the Numbers 180,191,314,243 is 278.5
1. How to do the Five Number Summary of 180,191,314,243?
You can calculate the 5 number summary of 180,191,314,243 by just arranging the set in ascending order and use the formulas to find the median, first quartile, and third quartile and get the exact results for five-set of observations easily and quickly by hand.
2. What is the Five number summary of numbers 180,191,314,243?
The Five number summary of numbers 180,191,314,243 is the minimum value is 180, the maximum value is 314, the median is 4, the first quartile Q1 is 185.5, and the third quartile Q3 is 278.5.
3. Where do I get exact steps on the 5 number summary of 180,191,314,243?
You can find exact steps on the five (5) number summary of 180,191,314,243 on our page.
