ordinal data - can you provide mean and sd?
Message posted by Shelly (via 64.228.61.150) on October 22, 2001 at 7:22 PM (ET)

I have a variable which has ordinal values (0=never; 1=once; 2=2-3times; 3=4-10 times; 4=more than 10 times).

Can I provide in my writeup of my study the MEAN and STANDARD DEVIATION of these variable? Does that mean anything?

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Re: ordinal data - can you provide mean and sd?
Message posted by Tomi (via 154.32.142.7) on October 22, 2001 at 10:32 PM (ET)

However your variable is based on a real numerical variable: the number of times something occurs, by the sound of it. If you can identify the maximum possible (or likely) value for the "more than 10 times" response, you can calculate a meaningful mean and sd by using the techniques for grouped data.

Suppose that you replace the "more than 10 times" response with "11-19" times (obviously with no knowledge of the context I have no idea whether 19 is a sensible maximum value). The following example gives the calculations for mean and sd.

[variable]#[mid point]#[frequency]#[mid point * frequency]#[frequency*(mid point)^2]

[0]#[0]#[5]#[0]#[0]
[1]#[1]#[8]#[8]#[8]
[2-3]#[2.5]#[12]#[30]#[75]
[4-10]#[7]#[9]#[63]#[441]
[11-19]#[15]#[6]#[90]#[1350]

[Totals]#[n/a]#[40]#[1874]

Mean = sum(mid point*frequency)/sum(frequency) = 191/40=4.775

Variance = (sum(frequency*(mid point)^2)/sum(frequency) - (mean)^2 = 1874/40 - 4.4775^2 = 24.05 (2 d.p)

sd = sqrt(Variance) = 4.9 (1 d.p)

These measures will give good estimates of the sample mean and standard deviation. Note that they are only estimates because you are assuming that within each group values tend to be at the centre of the group (the mid point). This may not be true, especially with the "more than 10 times" group.

Hope this helps.

Re: ordinal data - can you provide mean and sd?
Message posted by Tomi (via 154.32.142.7) on October 22, 2001 at 11:05 PM (ET)

[Totals]#[n/a]#[40]#[191]#[1874]