# Can the Median and mean be “zero”? [closed]

I have a data set with 32 variables. I take the summary of these variables. I found that some of these variables have a Mean or Median equal to zero. Is that Ok? Can I still work with this data set? Why they are equal to zero?

My data is Ionosphere (I worked with the variables 3:34). The data is available online from KEEl. The description of the data is:

Ionosphere data set

1: Description.

This data set is a modified version of the Ionosphere database present in the UCI repository. The second attribute has been removed due it only a single value (0) was present for it.

The task is to determine if a given signal is Good (g) or Bad (b).

2: Type.            Classification
3: Origin.          Real world
4: Instances.       351
5: Features.        33
6: Classes.         2
7: Missing values.  No

@relation ionosphere
@attribute Pulse1 integer [0, 1]
@attribute Pulse3 real [-1.0, 1.0]
@attribute Pulse4 real [-1.0, 1.0]
@attribute Pulse5 real [-1.0, 1.0]
@attribute Pulse6 real [-1.0, 1.0]
@attribute Pulse7 real [-1.0, 1.0]
@attribute Pulse8 real [-1.0, 1.0]
@attribute Pulse9 real [-1.0, 1.0]
@attribute Pulse10 real [-1.0, 1.0]
@attribute Pulse11 real [-1.0, 1.0]
@attribute Pulse12 real [-1.0, 1.0]
@attribute Pulse13 real [-1.0, 1.0]
@attribute Pulse14 real [-1.0, 1.0]
@attribute Pulse15 real [-1.0, 1.0]
@attribute Pulse16 real [-1.0, 1.0]
@attribute Pulse17 real [-1.0, 1.0]
@attribute Pulse18 real [-1.0, 1.0]
@attribute Pulse19 real [-1.0, 1.0]
@attribute Pulse20 real [-1.0, 1.0]
@attribute Pulse21 real [-1.0, 1.0]
@attribute Pulse22 real [-1.0, 1.0]
@attribute Pulse23 real [-1.0, 1.0]
@attribute Pulse24 real [-1.0, 1.0]
@attribute Pulse25 real [-1.0, 1.0]
@attribute Pulse26 real [-1.0, 1.0]
@attribute Pulse27 real [-1.0, 1.0]
@attribute Pulse28 real [-1.0, 1.0]
@attribute Pulse29 real [-1.0, 1.0]
@attribute Pulse30 real [-1.0, 1.0]
@attribute Pulse31 real [-1.0, 1.0]
@attribute Pulse32 real [-1.0, 1.0]
@attribute Pulse33 real [-1.0, 1.0]
@attribute Pulse34 real [-1.0, 1.0]
@attribute Class {g, b}
@inputs Pulse1, Pulse3, Pulse4, Pulse5, Pulse6,
Pulse7, Pulse8, Pulse9, Pulse10, Pulse11, Pulse12, Pulse13, Pulse14,
Pulse15, Pulse16, Pulse17, Pulse18, Pulse19, Pulse20, Pulse21,
Pulse22, Pulse23, Pulse24, Pulse25, Pulse26, Pulse27, Pulse28,
Pulse29, Pulse30, Pulse31, Pulse32, Pulse33, Pulse34

@outputs Class


This is an example of one variable (20 observations out of 351).

 1  0.605
2 -0.517
3  0.546
4 -1
5  0.344
6 -0.0457
7  0.746
8  0
9  0.904
10 -0.337
11  0.907
12  1
13  0.937
14  1
15  1
16 -1
17  0.942
18  1
19  0.786
20  0

• You have provided a very little information about your data set and it is very difficult to say if the mean and median of the variables can be zero or not unless we know the variables, still I don't see why we cannot have mean and median zero. We can have mean and median zero. – Prasad Dalvi Jun 25 '19 at 7:34
• @PrasadDalvi Thank you for your comment and sorry for my little information. I will provide much more details about my data. – Mary Jun 25 '19 at 7:42
• Much better to give an example. Ionosphere and KEEI won't mean much to most readers without their doing a web search. – Nick Cox Jun 25 '19 at 7:47
• @NickCox Thank you for your comment. I have added a description of the data with their domain. – Mary Jun 25 '19 at 7:56
• Does the interval notation $[-1, 1]$ and $[0, 1]$ used by your unnamed software have the standard mathematical meaning? – Nick Cox Jun 25 '19 at 7:59

There is no rule that the mean and median cannot be zero.

This can be expanded a little:

1. A variable that is always zero will necessarily have mean and median zero.

2. A variable that can in principle be only zero or positive can only have mean zero if all values in practice are zero. On the other hand, such a variable can and will have median zero if more than half of the values are zero. Such variables are very common and include counts and indicators (commonly, variables that are 1 or 0).

3. Point 2 applies also to variables that can in principle be negative or zero, although such variables seem less common.

4. A variable that can be negative, zero, or positive can also have mean and median zero.

5. It's even possible to have mean and median zero for a variable that cannot be zero, as contemplation of $$-1, -1, 1, 1$$ will make clear.

Being puzzled by this implies that looking more closely at your data (graphs of distributions, other summary statistics) is needed.

• Thank you so much for your help. Is that OK for 1st Quantile as well? – Mary Jun 25 '19 at 7:48
• I guess you mean first quartile. But all the arguments used for median apply also with modification to any other quantile. – Nick Cox Jun 25 '19 at 7:50

If you have a random variable following a standard normal distribution, then we would expect its mean to be 0 so this is perfectly possible.