ASSIGNMENT 1 & 2

ASSIGNMENT 1 & 2



ASSIGNMENT 1 & 2

Descriptive Statistics

Mean

In statistics, Mean is the measures of central tendency and it is defined as the sum of all the observation divided by total number of observation. We can find the value of mean by using the formula (Balduzzi,et.al,1998,pp.62-72).

X = ?xi / n

Where n defines the number of observations

?xi defines the sum of all the observations

Median

Median of an observation is the value that divides the data in partially. It is also identified as the 50th percentile of the data set. We have two kinds of method for classifying the median value.

• When we have even data set, then arrange the data first in an ascending order, then add the middle two values, add them and then divide by 2 (Newman,1939,pp.20-30).

• When we have odd data set, and then arrange the data first in an ascending order, the middle value which cuts the data set exactly as half is they median of odd data set.

Standard Deviation

In Probability distribution or Statistics, standard deviation is defined as how far is varaiated from the average value of the observation. The standard deviation tends to very close to the average value and great variation in the data describes that the values are scattered out from the mean value. It is represented by Greek symbol s (Koenkar,2005).

Confidence Intervals

In statistics Confidence interval is a kind of interval estimation of a parameter that is used to specify the dependability of an estimation.

Range

Range can be finf by subtracting maximum value from the minimum value, the result obtains is the range of the observation.

ASSIGNMENT 1

Section A

Descriptive statistics

Mean

66.25

Median

67

Standard Deviation

10.41717

 

 

The results from the above table show that the average marks obtained is 66.25 with the median marks of 67. It can easily be seen that the mean and median of the marks distribution is fairly close to each other thus we conclude reliable results and also the standard deviation is also not very high i.e. lying within the normal range.

The box plot graph defines the outliers of the observation values. In the data , those values who are on the near and approx the trend line they are close to the mean value. Values which are far away from the trend line they signifies as a outliers. The main purpose of box plot is to recognize the outliers. Errors in the box plot shows that Grade B, Grade C and Grade D have higher standard deviation because of higher box plot ranges. The box plot of Grade E shows minimum errors because it is fairly close to mean. In fact the standard deviation in Grade A only increases on one - sided way. Normal distribution has bell shaped curve that described by the average value and the standard deviation. The curve is symmetrical in shape which defines the normal distribution. It is calculated by using the formula:

= 1/s (under root 2?) * e-1/2 (x-µ/s)^2

From the results it can be determined that the data is normally distributed as majority of the values lies ...