What is a Median ?
The median is the middle value of a given data when those values are arranged from ascending to descending order.
Median = Middle value
To find the median from ungrouped data, we have to consider if n is odd or even.
If n is odd, then using the formula
Median = (n+1)^{th} term/2
If n is even, then using the formula
Median = [(n/2)^{th} term + (n/2+1)^{th} term]/2
Problem 1 :
121, 115, 135, 109, 136, 147, 127, 119, 110
Solution :
Let's arrange the data in ascending order.
109, 110, 115, 119, 121, 127, 135, 136, and 147
So, Median = Middle value
Median = 121
Problem 2 :
4, 8, 1, 5, 14, 3, 1, 12
Solution :
Let's arrange the data in ascending order.
1, 1, 3, 4, 5, 8, 12, 14
It is an ungrouped data. Here n is 8.
If n is even, we are using the formula
Median = [(n/2)^{th} term + (n/2+1)^{th} term]/2
Median = [(8/2)^{th} term + (8/2+1)^{th} term]/2
Median = (4^{th }term + 5^{th})/2
Median = (4 + 5)/2
Median = (9)/2
Median = 4.5
Problem 3 :
3, 9, 2, 6, 20, 3, 3, 10
Solution :
Let's arrange the data in ascending order.
2, 3, 3, 3, 6, 9, 10, 20
It is an ungrouped data. Here n is 8.
If n is even, we are using the formula
Median = [(n/2)^{th} term + (n/2+1)^{th} term]/2
Median = [(8/2)^{th} term + (8/2+1)^{th} term]/2
Median = (4^{th }term + 5^{th})/2
Median = (3 + 6)/2
Median = (9)/ 2
Median = 4.5
Problem 4 :
99.2, 101.9, 98.6, 99.5, 100.8, 99.8
Solution :
Given data, 98.6, 99.2, 99.5, 99.8, 100.8, 101.9 in ascending order.
It is an ungrouped data. Here n is 6.
If n is even, we are using the formula
Median = [(n/2)^{th} term + (n/2+1)^{th} term]/2
Median = [(6/2)^{th} term + (6/2+1)^{th} term]/2
Median = (3^{th }term + 4^{th})/2
Median = (99.5 + 99.8) / 2
Median = 199.3 / 2
Median = 99.65
Problem 5 :
28.8, 32.9, 32.5, 27.9, 30.4, 32.5, 31.6, 32.7
Solution :
Let's arrange the data in ascending order.
27.9, 28.8, 30.4, 31.6, 32.5, 32.5, 32.7, 32.9
It is an ungrouped data. Here n is 8.
If n is even, we are using the formula
Median = [(n/2)^{th} term + (n/2+1)^{th} term]/2
Median = [(8/2)^{th} term + (8/2+1)^{th} term]/2
Median = (4^{th }term + 5^{th})/2
Median = (31.6 + 32.5) 2
Median = (64.1)/2
Median = 32.05
Problem 6 :
Last week ray recorded how much he spent for lunch each workday. He spent $6.50, $7.25, $4.90, $5.30, and $12.00. Find the median.
Solution :
He spent the money for lunch each day are $6.50, $7.25, $4.90, $5.30, and $12.00.
Let's arrange the money in ascending order.
4.90, 5.30, 6.50, 7.25, 12.00
So, Median = Middle value
Median = 6.50
So, the average money is $6.50.
Problem 7 :
Michaela is in charge of 6 two year olds at a day care centre. Their ages, in months, are 25, 24, 28, 32, 29, and 31. Find the median age.
Solution :
Their ages 25, 24, 28, 32, 29, and 31 on months.
Let's arrange the ages in ascending order.
24, 25, 28, 29, 31, 32
It is an ungrouped data. Here n is 6.
If n is even,
Median = [(n/2)^{th} term + (n/2+1)^{th} term]/2
Median = [(6/2)^{th} term + (6/2+1)^{th} term]/2
Median = (3^{th }term + 4^{th})/2
Median = (28 + 29) / 2
Median = 57 / 2
Median = 28.5
The median age is 28.5.
Problem 8 :
Brian is teaching a swim class for 6 three-year olds. Their ages, in months, are 38, 41, 45, 36, 40, and 42. Find the median age.
Solution :
Their ages 38, 41, 45, 36, 40, and 42 on months.
Let's arrange the ages in ascending order.
36, 38, 40, 41, 42, 45
It is an ungrouped data. Here n is 6.
If n is even,
Median = [(n/2)^{th} term + (n/2+1)^{th} term]/2
Median = [(6/2)^{th} term + (6/2+1)^{th} term]/2
Median = (3^{th }term + 4^{th})/2
Median = (40 + 41) / 2
Median = 81 / 2
Median = 40.5
The median age is 40.5.
Problem 9 :
Sal recorded the amount he spent for gas each week for the past 8 weeks. The amounts were past 8 weeks. The amounts were $38.65, $32.18, $40.23, $51.50, $43.68, $30.96, $41.37, and $44.72. Find the median amount.
Solution :
He spent the amount for gas in each week are 38.65, 32.18, 40.23, 51.50, 43.68, 30.96, 41.37, and 44.72
Lets arrange the amount in ascending order.
30.96, 32.18, 38.65, 40.23, 41.37, 43.68, 44.72, 51.50
It is an ungrouped data. Here n is 8.
If n is even, we are using the formula
Median = [(n/2)^{th} term + (n/2+1)^{th} term]/2
Median = [(8/2)^{th} term + (8/2+1)^{th} term]/2
Median = (4^{th }term + 5^{th})/2
Median = (40.23 + 41.37) / 2
Median = 95.18 / 2
Median = 47.59
The median amount is $47.59.
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