Listed are 32 ages for Academy Award winning best actors in order from smallest to largest.

Question

17;18;21;22;25;27;29;30;31;34;36;37;37;41;42;47;52;54;57;58;62;63;67;69;71;72;73;74;76;77

Find the following (rounding to 2 decimal places when needed, part f give answer rounded to a whole number)

a) Mean:

b) Median:

c) First Quartile:

d) Third Quartile:

e) Standard deviation:

f) 10th percentile:

g) percentile of 34:

Answer 1

a) Mean:

To compute the mean add all the values together then divide by the number of values (n)

b) Median:

To determine which value is the median, choose the (n+1)/2th value of the ordered values.

for n = 32, that would be the 16.5th value. Since not an even integer, the median would be the average of the 16th and 17th value.

c) First Quartile:

choose the (n+1)/4th value of the ordered values. for n = 32 that would be the 8.5th value. Since not an even integer, the first quartile would be the average of the 8th and 9th values.

d) Third Quartile:

choose the 3(n+1)/4th value of the ordered values. for n = 32 that would be the 24.75th value. Since not an even integer, the third quartile would be the average of the 24th and 25th values.

e) Standard deviation:

the variance is computed as: sum of (values - mean)^2 / (n-1). Standard deviation is the square root of the variance.

f) 10th percentile:

the value that is the 10th percentile is the 10(n+1) th value or the (n+1)/10 th value, which for n = 32

----------

100

is the 3.3th value. Since not an even integer, the 10th percentile would be the average of the 3rd and 4th values.

g) percentile of 34:

the value that is the 34th percentile is the 34(n+1) th value which for n = 32

----------

100

is the 10.88th value. Since not an even integer, the 34th percentile would be the average of the 10th and 11th values.