Sunday, November 8, 2009

GMAT/CAT PREPARATION EMAIL COURSE DAY 20

AVERAGE, MEDIAN AND MODE

Average or Arithmetic Mean

To find the average of a set of numbers, find the sum and divide by the number of numbers.

Average = Sum of the terms/Number of terms

To find the average of the five numbers 12, 15, 23, 40, and 50, first add them:
12 + 15 + 23 + 40 + 50 = 140.

Then divide the sum by 5: 140 / 5 = 28.

If Average is known to Find the Sum:

Sum = (Average) X (Number of terms)

If the average of ten numbers is 70, then their sum is 10 X 70, or 700.

To Find a Missing Number:

To find a missing number when the average is given , use the sum.

If the average of four numbers is 8, then the sum of those four numbers is 4 X 8, or 32.
Suppose three of the numbers are 4, 7, and 8.

These three numbers add up to 19 .
Which leaves 13 for the fourth number.

Median:

The median of a set of numbers is the value that falls in the middle of the set.

If you have five test scores, and they are 88, 85, 59, 94, and 73, you must first list the scores in increasing or decreasing order: 59,73, 85, 88, 94.The median is the middle number, or 85.

If there is an even number of values in a set (six test scores, for instance), simply take the average of the two middle numbers.

Mode:

The mode of a set of numbers is the value that appears most often.

If your test scores were 89, 56, 68, 88,99, 95, 95, 84, and 95, the mode of the scores would be 95 because it appears more often than any other score.

If there are two most common value in a set, the set has more than one mode.

Standard Deviation

The standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance.

Standard deviation is a widely used measure of the variability or dispersion. It may be thought of as the average difference of the scores from the mean of distribution, how far they are away from the mean.

A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.