Answer:
let the number of steps taken by friend 1, 2 and 3 be: x, y and z respectively
we know that the mean of the total steps taken by all the friends is 10,350
Since the formula for mean is: sum of all values / number of values
here, the total values is the total number of steps taken
So,
steps taken by friend 1 +steps taken by friend 2 +steps taken by friend 3 +steps taken by friend 4 +steps taken by friend 5 +steps taken by friend 6
all that divided by 6 will give us the mean
so, 7800 + 8000 + 9800 + x + y + z / 6
(25600 + x + y + z)/6 = 10350
25600 + x + y + z = 10350 * 6
x + y + z = 62100 - 25600
x + y + z = 36500
So since the sum of x, y and z is 36500,
we can say that the average value of x , y and z is 12167 (36500/3)
So the next thing to make an equation out of is Median
to find the median, we need to arrange the values in any order you like, i will arrange in descending order
so since the estimated value of all x , y and z is greater than the greatest known value:
x > y > z > 9800 > 8000 > 7800
Since this set of values has an even number of values, we will take the average of the middle 2 values as the median
(9800 + z)/2 = 10000
9800 + z = 20000
z = 10200 -------- we have found one of the three values! getting closer
Now, the final equation will be found from the range
since we already have sorted our data, and the difference of the highest and lowest is the range
x > y > z > 9800 > 8000 > 7800
So, x - 7800 = 7500
x = 15300 ------- now that we have x and z, we can use the first equation to find the value of y and we will be done!
x + y + z = 36500
replacing the values
15300 + y + 10200 = 62100
y = 36500 - 25500
y = 11000
So the three remaining friends walked
15300, 11000 and 10200 steps