Answer:
let the missing values be a , b , c ,d and e
So the mean of these values is $ 2225
<em>(a + b + c + d + e + 1900 + 2300 + 3000)/8 = 2225</em>
<em>a + b + c + d + e + 7200 = 2225*8</em>
<em>a + b + c + d + e = 17800 - 7200</em>
a + b + c + d + e = 10600 -------------------- let this be our first equation
Since the range is 3000 and the data is already in increasing order:
3000 - a = 2100
a = $ 900 --------- one down, 4 to go
Now lets get another equation through Median:
So the median value is 2450, since median is the middle value when the given set is written in increasing or decreasing order
since we are already given the increasing order of the numbers, we will make use of that
So, since there is no middle number since there are even amount of numbers, the average of the 2 mid numbers will be the Median
so, (2300 + c)/2 = 2450
2300 + c = 4900
c = $ 2600 ---------------------- two down, 3 to go
Now we will try to get another equation through mode
We are given that the mode of the numbers is 2900
we will take some help from the first equation for this part
a + b + c + d + e = 10600
900 + 2600 + b + d + e = 10600
b + d + e = 10600 - 3500
b + d + e = 7100
Since the mode is 2900, lets check if b + d + e = 3 (2900) since that would mean that 2900 is repeated 3 times
b + d + e = 2.45(2900)
since b + d + e is 2.45 times 2900 and 2900 is the most repeated number,
we can say that 2 of the 3 values is 2900
so,
2900 + 2900 + b = 7100
e = 7100 - 5800
e = $ 1300
so the complete list is: 900 , 1300 , 1900 , 2300 , 2600 , 2900 , 2900 , 3000
