The following frequency distribution shows the results of a test on an air intake vent on an F1 car. From the diagram calculate:?

It is not clear what level of accuracy you require. Mean and SD could be ESTIMATED from the red curve, or CALCULATED from the underlying blue histogram of grouped frequencies.

Normally distributed data has an infinite range, so 'range/6' is not reliable. The 'range' used would have to specify eg 'range at 10% of peak value'.

The normal frequency distribution has the form

f(x) = Aexp[-(1/2)t^2]

where t=(x-m)/s, m is mean and s is standard deviation.

Assuming the red curve is the gaussian best fit to the grouped data, then estimating from the curve the peak is approx. f=320. When f = 50 then x1=838 and x2=845 approx. You can use any other frequency instead of 50, eg 100. The point is to obtain a 'range' which is as broad as possible - so as to minimise % errors when reading off corresponding x values - while also trying to avoid taking readings where the slope is either horizontal or vertical - a place where the slope is 45 degrees is best.

So

m=(x1+x2)/2=841.5.

The ratio of frequencies is

320/50 = exp[(1/2)t^2]

(1/2)t^2 = ln(320/50) = 1.856

t = (x2-x1)/2s = 3.5 / s = +/-1.927

s = 3.5 / 1.927= 1.82.

The standard deviation is approx. 1.8.

You could get a better estimate by measuring from a large print of the image, ruling lines and interpolating values.

Range is 834 to 849

mean ~ midpoint of range ~ 841.5

sd ~ range/6 ~ 15/6 ~ 2.5