Applied Statistics

Name: Amr Mohamed Badawy

Course: Applied Statistics

Assignment

Submitted to: DR.Alaa Ibrahim

Theoretical Questions

Question 1 : Define the Following terms briefly :

1. The Central Tendency measures :

• Used To summarize a large no of data with one value which is the central value.

1. The Dispersion measures :

• To measure the distance between the observations and the central point. For example Standard deviation.

1. The first quartile :

• The first quartile it is the value on the distance of 25% from the beginning after arranging the data in ascending order.

1. The continuous random variable :

• It is a measurable variable
• It is a variable whose value is changeable in a very short period of time
• It is a variable which take many value between two successive.

For example: Weight.

1. The discrete variable :

• It is a countable variable
• It is a variable that take a specific value doesn’t change in a very short period of time
• It is a variable which doesn’t contain any interval (doesn’t take any value between Two successive.

For example: number of children in a family, absence day.

1. The Third quartile :

• The Third quartile it is the value on the distance of 75 % from the beginning after arranging the data in ascending order.

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Question 2 : State whether the following statements are true or false and give a brief explanation (Note that no marks will be given for a simple true/false answer):

1.        If the distribution of the data is skewed, then the best central measure is the mean and the best dispersion measure is the variance:

1. False  

• Explanation:

• We have extreme value , The best Central measure : is the median  and the best dispersion measure : is the interquartile range (IQR)

        2. The standard deviation can have a negative value and can’t be zero:

1. False

• Explanation :

• , because it measure the distance between the observation and the central point.

3.        We always depend on the value of the variance in comparing the homogeneity between the different groups:

1.  False

• Explanation :

• Because the variance have the two problem :

1. The change in unit measure
2. The difference between the 2 mean.

4.        The first quartile is the value on the distance 25% from the beginning after arranging the data in the descending order:

1. False

• Explanation :

• Is the value on the distance 25% from the beginning after arranging the data in the Ascending order.

1. If the value of the mean is greater than the value of the median, and the value of the median is greater than the value of the mode and there is a great difference between their values, then the data is skewed to the left:

[pic 1]

1. False  

• Explanation :

• The data is Skewed to the Right.

6) The first quartile is the value on the distance 25% from the beginning:

1. False

• Explanation :

• After arranging the data in the Ascending order.

7) the descriptive data which is not ordered, the best central measure is the mode and the best dispersion measure is the quartile range :

7. False

• Explanation :

• There is no dispersion measure for Descriptive data
• There is no distance to measure .

 8)If the data doesn't contain any extreme value then the distribution of this data is symmetric:

   8.False

Explanation :

•  if the data contain extreme value, then it is skewed , but if the data doesn’t include an extreme value it doesn't mean it is symmetric it may be skewed or symmetric and to know we should apply the test of stem and leaf.

Question 3  Answer the following questions briefly:        

1. What are the characteristics of a set of data for which the mean, median and mode are identical?

Symmetric Data

Mean: data should be symmetric and quantitative

Median data should be qualitative, ordered and odd and quantitative skewed

Mode data qualitative ordered, not ordered

1. Which of the central tendency measures can assume more than one value for a data set? And which can be calculated for quantitative data only?

• The Central Tendency measures can assume more than one value is the Mode.
• Mean that can be calculated for quantitative data only .

1. What is the difference between the absolute and relative dispersion measures?  

•  The Absolute dispersion measure: used to describe the data only.
• The relative dispersion measure: to compare the homogeneity between different group to find which is most homogenous.

1. What are the four sampling techniques?

• Simple random sample
• Stratified random sample
• Systematic random sample
• Cluster ( Multi-stage) random

Conditions:

1.  Simple random Sample:

If the individual in the population are equally likely (have the same chance to chosen)

1. Stratified random sample :

If the population is divided to a different group so there is homogeneity inside each group and heterogeneity between each group.