Hi, I can normally calculate the standard deviation if I were to be given grouped/raw data, but I've found these two confusing and I'm not really sure what to do, so would be grateful for some help.
1. Three statistics students, Ali, Les and Sam spent the day fishing, and they caught three different types of fish and recorded the type and mass of each fish caught. At 4p.m, they summarised the results as follows. (I'll only enter data for Sam, as that's the data required)
Sam. 1 perch. 1 roach 0 tench. mean mass 1kg. standard deviation.
a) How can you deduce that each fish caught by Sam was 1kg?
- Would this be sufficient "As the standard deviation was 0, this means that the values must've all lied on the mean, so each value must be 1kg" - Could someone help make it clearer?
b) Before leaving the waterside, Sam catches one more fish and weighs it. He then announces that if this extra fish is included with the other two fish he caught, the standard deviation is 1.00kg. Find the mass of this extra fish.
How would you do this?
I've got something like 1 (s.d.) = square root (1/3 * sigmax^2 - mean^2).
But I'm missing 2 variables, so I'm not sure if I'm doing it all wrong :/
2. The depth of water in a lake was measured at 50 different points on the surface of the lake. The depths, x metres are summarised by sigmax = 934.5 and sigmax^2=19275.81.
a) Find the mean and the variance of the depths.
Mean = 934.5/50 = 18.69
Variance = (sigmafx^2)/sigmaf - mean^2
But I don't/can't get fx^2 data though? :/
b) Some weeks later the water level in the lake rose by 0.23m. What would be the mean and variance of the depths taken at the same points on the lake as before?
I'm not really sure how to approach this, but I guess doing the first bit may help.
I'd be really grateful if someone can help me with these questions :/