Statistics " Measures of Central Location" Group one presentation.

This is Statics power point presentation on topic of measures of central location.

1. MEASURES OF CENTRAL LOCATION Group One Presentation

2. DEFINITION A measure of central location is a single value that best represents characteristics such as age or height of a group or individuals. It can also be defined as the statistical measure that represents the single value of the entire distribution or a dataset. ( Byjus, 2022) The central location of the dataset can be found by using the three important measures . These measures include; mean, median, mode and mid range.

3. MEAN Is the sum of the value, divided by the total number of the values The symbol that represents mean is The mean in most cases is not an actual data value. It should be rounded to one more decimal place that occurs in the raw data. Formula used to find mean is as follows;  

4. EXAMPLE For Example mean of 1,16,3,5,6,6 Using formula Mean= 1+16+3+5+6+6 6 6.2 Mean =6.2  

5. MEAN CONT’D Types Of Mean Generalized mean Geometric mean Harmonic mean Weighted arithmetic mean I nterquartile mean T rimmed mean

6. MODE This is the most occurring value in a distribution. It was discovered by English mathematicians Karl Pearson(1857-1936) The advantage of mode over other measures is that it can be found for both numeric /non numeric numbers. However , it is limited because : it cannot reflect the centre of the distribution very well. Thus , there can be more than one mode of the same distribution ( i.e., bi-modal and multimodal). This can limit the ability of the mode in describing the centre of the distribution because a single value to describe the centre cannot be identified .

7. MODE CONTI…. For example , if all data are different ( i.e., scores of boys and girls in a class) mode is different in these distribution. However, to overcome these problems : group the data to find modal class or use mean and median to find the centre of the distribution. TYPES OF MODE Unimodal Bimodal Multimodal

8. EXAMPLE Find the mode of the signing bonuses of eight NFL player for a specific year. The bonuses in millions of dollars are, 54, 58 , 60 ,54 , 55, 56,57, 57 , 58, 60 , 54, 54 , 54, 54, 55, 56,57, 57, 58, 58, 60, 60 Since 54 occurred 3 times- a frequency larger than any other number therefore mode is 54 Mode = 54

9. MEDIAN It is the mid point of the data array Steps in computing the median of the data array Step 1 : Arrange the data in order Step 2 : Select the mid point

10. Example The number of children with asthma during a specific year in seven local districts is shown . Find the median 253,125,328,417,201,70,90 Solution 70,90,125, 201 ,253,328,417 201 is median, since is at the of the distribution

11. MID RANGE This a rough estimate of the middle . It is found by adding the lowest and the highest value in the data set and dividing by 2 Formula = MR = LOWEST VALUE + HIGHEST VALUE 2

12. Example Find the midrange of data set : 54, 57, 58, 60,55, 56, Solution Using formula MR = LOWEST VALUE + HIGHEST VALUE 2 54 , 55, 56,57, 58, 60 Highest value =60 Lowest value =54 MR = 54+60 2 = 114 2 57

13. IMPORTANCE OF MEASURES OF CENTRAL LOCATION It was invented by Edmund( enclopedia.com,2022) The terms is first found in the mid 1960s in writings o Edmund H alley (1656-1742) It has been used to summarize observation of a variable since the time of Galileo (1564-1642) Importances Include: Condense the data set down to one representative value, which is useful when you are working with large amount of data Measures of central location are used often by individuals who work in human resources departments of companies For example; Mean, human resource managers often calculate the mean salary of individual in a certain field so that they know what type average salary to give to new employees

14. Reference List Bluman,A.G . (2012). Elementary statistics : A Step by Step Approach. (8 th Ed). McGraw-hill .

15. Group Members Patricia Phungu BBC/20/SS/063 Maureen Mkandawire BBC/20/SS/043 Nancy Mwamadi BBC/20/SS/053 Michael Chitanda BBC/20/SS/008 MacEvice Majoni BBC/20/SS/035 Grace Mwenelupembe BBC/19/SS/040