# Find a range of four numbers given a mode, median and mean

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#1
Hi
I have some homework revision and am looking for some clarity on approach. Consider the question:

Four numbers have a mode of 100, a median of 101 and a mean of 102. What is their range?

My approach:

We have four numbers but they're not given. Let's assume they are:

x1 x2 x3 x4

Given:
mode = 100
median = 101
mean = 102

The median is the middle number in a list of numbers ordered from smallest to largest. Hence;

x1 x2 101 x3 x4

The mode is the value that appears most often in a set of data.

100 100 101 102 x4

Given that our mean value is 102

100 + 100 + 101 + 102 + x4 = 510 , since 510 / 5 = 102 our mean value, thus

=> x4 = 107

We can say our full set of numbers are:

100 100 101 102 107

We can deduce the range of this set of numbers is: 107 - 100 = 7.

Does this appear correct?
0
1 year ago
#2
"100 + 100 + 101 + 102 + x4 = 510 , since 510 / 5 = 102 our mean value, thus"

not sure why you have 5 numbers ? it says there are 4 ?
0
#3
(Original post by the bear)
"100 + 100 + 101 + 102 + x4 = 510 , since 510 / 5 = 102 our mean value, thus"

not sure why you have 5 numbers ? it says there are 4 ?
Yes, the middle value threw me a little. It has to be four then?
0
#4
(Original post by Im_with_stupid->)
Yes, the middle value threw me a little. It has to be four then?
With four values

x1 101 x3 x4

is not central?
0
1 year ago
#5
Yes it does - how you you get the median of 4 numbers?
0
1 year ago
#6
the mode must appear more than once.

it cannot appear 3 times because then the median would be the same as the mode....
0
#7
(Original post by Muttley79)
Yes it does - how you you get the median of 4 numbers?
Of course,
If there is an even number of terms, add the two middle terms and divide by 2.
Thanks
0
#8
So my revised list of numbers (with middle two summed and divided by 2) looks like:

100 100 100.5 x

For the mean value;

(100 + 100 + 100.5 + x) / 4 = 102

(300.5 + x) / 4 = 102

x = 107.5

check
[100 + 100 + 100.5 + 107.5] / 4 = 408/4 = 102

final set of numbers is;

100 100 100.5 107.5

The range is the difference between the lowest value and the highest value,

107.5 - 100 = 7.5

Is this more correct?
Last edited by Im_with_stupid->; 1 year ago
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