Statistics1.Arithmetic Mean (Averages)
A number expressing the central/typical value of data set.
A.M. =\frac{Sum of terms}{No. of terms}
2. Median(The Middle Number)
It is the value that separates the higher half from the lower half of a data set.
Depending on the number of data points, median can be calculated in two ways:-
> ODD no. of values : Median is the unique middle value when the data is arranged in increasing/decreasing order.
> EVEN no. of values : Median is the average of the two middle values when the data is arranged in increasing/decreasing order.
3. Standard Deviation (S.D.)
It describes the spread/variation of data in a set.
Though calculating the S.D. is never required on the GMAT, knowing the nature of the S.D. sometimes is very helpful in typical problems. It can be done easily by following steps
a) Find MEAN(M) of the data set.
b) Find the difference(D) of each of the numbers from the MEAN.
c) Square the differences(D^2) and find the Mean of the Differences.
d) Find the \sqrt{Mean of the Differences}
A small S.D. --> set is closely cluttered around the mean.
A large S.D. --> set is spread out widely, with some points appearing far from mean.
Though not very common on the GMAT, just remember that this too gives the spread of the numbers from their mean.
It is calculated by squaring the Standard Deviation.
IMPORTANT POINTS TO REMEMBER WHILE ANSWERING STATITICS PROBLEMS >> Mean value is never the highest/lowest value of the data set.
>> Unlike Mean the MEDIAN only depends on the middle number(ODD no. data points) or the average of the two middle numbers(EVEN no. of data points). Hence we can find median even when there is unknown data.
>> When the same number is ADDED to or SUBTRACTED from all elements of a data set -
New MEAN = Old mean + ADDED no.
-OR-
New MEAN = Old mean - SUBTRACTED no.
New MEDIAN = Old median + ADDED no.
-OR-
New MEDIAN = Old median - SUBTRACTED no.
"NO CHANGE" to Standard deviation.
>> When all elements of a data set are multiplied by a number 'n' -
New MEAN = Old mean * n
New MEDIAN = Old median * n
New Standard deviation = Old Standard Deviation * n
>> The statement "Within 'n' of the S.D. of the MEAN means" -
the Range = {MEAN - (n* S.D.) , MEAN + (n* S.D.) }
I hope this is helpful
Please let me know in case I missed out anything.