Some Important Statistics

CHAPTER SIX
FUNCTIONS OF RANDOM VARIABLES SAMPLING DISTRIBUTIONS

6.1 Some Important Statistics:

6.1.1 A Population:

A population consists of the total observations with which we are concerned at a particular time.

6.1.2 A Sample:

A sample is a subset of a population.

6.2 Definition: Central Tendency in the Sample:

Any function of the random sample is called a statistic.

6.2.1 The Mean:

6.2.1 Definition: The Mean:

If represent a random sample of size n, then the sample mean is defined by the statistic:

Properties of the Mean:

• The mean is the most commonly used measure of certain location in statistics.
• It employs all available information.
• The mean is affected by extreme values.
• It is easy to calculate and to understand.
• It has a unique value given a set of data.

EX(1):

The length of time, in minutes, that 10 patients waited in a doctor's office before receiving treatment were recorded as follows: 5, 11, 9, 5, 10, 15, 6, 10, 5 and 10. Find the mean.

Solution:

6.2.2 The Median:

• If represent a random sample of size n , arranged in increasing order of magnitude, then the sample median, which is denoted by is defined by the statistic:

Properties of the Median:

1. The median is easy to compute if the number of observations is relatively small.

2. It is not affected by extreme values.

EX(2):

The number of foreign ships arriving at an east cost port

on 7 randomly selected days were 8, 3, 9, 5, 6, 8 and 5.

Find the sample median.

Solution: