Suppose a person takes data (say counts per minute of cars going past his window), for a long time. Then he loses his data, but knows that he counted 5 cars more often than any other number. What is the likely range for the average count rate? I tried to solve this by saying the mode is 5, so the distribution peaks around 5. Which means that if I differentiate the Poisson distribution with respect to a parameter μ, which I assume is the mean of the distribution, then find the value at which the maximum occurs, I can find the mean in terms of the mode 5. So I know the mean, and the standard deviation, which gives me the range of the average count rate. Carrying this out, I got the mean to be 5 also. Is this correct? Can anyone help me? Or am I completely on the wrong track?