calcuate the mean medain and standard deviation of the following data set.?

Question

round to 1 decimal place

15.88, 19.20, 15.92, 4.81, 3.22, 12.67, 16.87, 9.49,

now damb it ! i own a t1-83 but it dose not show me how to work it out on paper .

rsmith

Answer 1

Salty got the answer, but her answers don't agree with mine. And I worked the problem twice to be sure.

Anyway, I'll try to tell you how to do it. First, sort the numbers:

3.22 4.81 9.49 12.67 15.88 15.92 16.87 19.20

There are 8 numbers (n=8). The is right in the middle, halfway between 12.67 and 15.88.

So Median = (12.67 + 15.88) / 2 = 14.275

Now add them up. The total of the 8 numbers is sum(x) = 98.06. Divide by n=8 to get the average or .

So Mean = sum(x)/n = 98.06 / 8 = 12.2575

There are different formulas for the standard deviation. In "standard form", you use the deviations (differences) from the mean or average, but for computational purposes, I prefer this formula:

S.D. = sqrt[n sum(x^2) - (sum x)^2] / n

We already know sum(x) = 98.06. Now we need to add the of all the numbers to get sum(x^2) = 1442.9512.

Now we can calculate the standard deviation:

S.D. = sqrt(8 * 1442.9512 - 98.06^2) / 8
S.D. = sqrt(11543.6096 - 9615.7636) / 8
S.D. = sqrt(1927.846) / 8
S.D. = 43.9072 / 8 = 5.488

This number, 5.49 (rounded to the nearest hundredth) is the . But because we have such a small (less than 30), we lose a , and instead of dividing by n = 8, we're going to divide by sqrt[n(n-1)] = sqrt(8*7) = sqrt(56) = 7.4833.

The standard deviation we'll finally use is

S.D. = sqrt(1927.846 / 56) = 5.867, rounded off to 5.87.

Since standard deviation is a measure of dispersion, the higher number (5.87) is better when the sample size is small. When you have enough data (more than 30 observations), you don't have to worry about degrees of freedom.

Anyway, that's how you calculate what you're interested in.

To repeat your answers, Mean = 12.26, Median = 14.28, and Standard Deviation = 5.87 (5.49 if you just divide by n=8).

Oh -- you have to round to one decimal. Then your answers are Mean = 12.3, Median = 14.3, and Standard Deviation = 5.9 (or 5.5, depending on your formula).

Answer 2

Go to http://statpages.org/ and find links to Javascript calculators for every statistical distribution you have ever heard of (including a couple that *I* had never heard of ☺)


Doug

Answer 3

mean 11.599
median 15.88
sd dev 6.01

Answer 4

try to use your calculator.