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Answer:
The median is -8°F
Step-by-step explanation:
Attached Table.
The median is the "middle" value from all the numbers arranged from least to greatest.
Looking at the table, we need to arrange the numbers (first week numbers) from least to greatest.
-31, -29, -9, -8, 3, 4, 6
There are 7 numbers and the middle number is the 4th one, which is -8
The median is -8°F
Answer:
The mean of the distribution is about 53.9 and standard deviation is about 16.5 marks.
Step-by-step explanation:
Use the trick of transforming the given random variable one that is standard normal distributed, aka a z-score, then look up the two percentile values in z-score tables to get two equations with two unknowns.
So, let x be the variable describing the marks of a student, and
the standardized equivalent of that (mu - mean, sigma - standard deviation).
We are looking for values of mu and sigma. At this point we'd be out of luck, but, wait, we're given two bits of info: the 10% point (aka, 90th percentile) and the 20% point (can be interpreted as 100-20th percentile). For each point we can use z-score tables to look up the corresponding values of z (just search for z tables). I found:
z-score for the 10% point: z_10=1.28
z-score for the 20% point: z_20=-0.84
That gives us two equations:
and can be solved for mu and sigma (do the work on your end, I am showing my result):
The mean of the distribution is about 53.9 and standard deviation is about 16.5 marks.