1. 1 Wai Yin Poon Department of Statistics The Chinese University of Hong Kong What is Statistics? What is Statistics? –Some very basic concepts Applications of Statistics in daily life Applications of Statistics in daily life

2. 2 Statistics A powerful guide to the unknown. A powerful guide to the unknown. There has been increasing use of statistics, in work or in daily life. There has been increasing use of statistics, in work or in daily life. –People today make reference to relevant statistical information in decision-making and for better understanding of various social and economic issues.

3. 3 The word “statistics” is derived from the Latin word “status” meaning “state”. The word “statistics” is derived from the Latin word “status” meaning “state”. Three major components Three major components –Gathering information –Analysis of data –Inferential statistics »From a part to the whole.

4. 4 Gathering Information What is your objectives ? Question 1: For the students in this class, how much money do they have with them right now, in change only? - What are the monthly incomes of HK males aged 30-40? - Hong Kong citizen’s household incomes. Question 2: Do the students like the Professor? - Do citizens like Mr. Tung?

5. 5 Census: A complete enumeration of the population. Census: A complete enumeration of the population. –The population is large –Time –Accuracy May need to draw conclusions about populations from samples. May need to draw conclusions about populations from samples.

6. 6 Population versus Sample All students in this class All students in this class –20 selected students in this class HK male aged 30-40 HK male aged 30-40 –200 HK male aged 30-40 Find a “representative” sample to elicit useful information. Find a “representative” sample to elicit useful information.

7. 7 A “representative” sample? Obtain samples by the method of simple random sampling. Obtain samples by the method of simple random sampling. –Can be very expensive »Large population –Other sampling methods are available.

8. 8 Data Analysis Graphical representations of the data. Graphical representations of the data. –Example: Bar Chart

9. 9 A B C D 30% 35% 25% 10% A: Students with less than $1 C: Students with $5.1-$9 B: Students with $1.1-$5 D: Students with more than $9

10. 10 There are various methods to construct graphical displays to better describe different kinds of data. There are various methods to construct graphical displays to better describe different kinds of data.

11. 11 Descriptive Statistics Mean for measuring central tendency. Mean for measuring central tendency.Example: The amounts of money in 7 selected students: {4 8 3 0 11 12 4} The mean is (4+8+3+0+11+12+4)/7 = 6

12. 12 {4 8 3 0 11 82 4} The mean becomes (4+8+3+0+11+82+4)/7 = 16 The mean is highly influenced by outliers.

13. 13 Another popular measure of central tendency: Median {4 8 3 0 11 12 4} {0 3 4 4 8 11 12} Median = 4 {4 8 3 0 11 82 14} {4 8 3 0 11 82 14} {0 3 4 4 8 11 82} Median = 4 {0 3 4 4 8 11 82} Median = 4 Median is less susceptible to outliers. Median is less susceptible to outliers.

14. 14 Measures of dispersion In order to better understand your data, other measures are required to complement the measures of central tendency. In order to better understand your data, other measures are required to complement the measures of central tendency.

15. 15 {2 2 2 2 2 2 2 2 2 2} Mean = 2 {2 2 2 2 2 2 2 2 2 2} Mean = 2 {1 1 1 1 1 3 3 3 3 3} Mean = 2 {1 1 1 1 1 3 3 3 3 3} Mean = 2 The dispersion in the first data set is smaller. Various kinds of dispersion measures are available. Various kinds of dispersion measures are available.

16. 16 Inferential statistics From the sample to the population From the sample to the population –The average amount of money (change only) for the 20 students is 15.8 –Infer the average amount of money (change only) for all students in this class is “approximately” 15.8. »How accurate is the approximation? Is your sample representative? Is your sample representative? Is the size of your sample large enough? Is the size of your sample large enough? »Statistical methods are available to help assess the accuracy of the approximation.

17. 17 Living with statistics: How likely I can win a game? How likely I can win a game? Is the game fair? Is the game fair? Opinion Poll Opinion Poll Quality control Quality control Drug test Drug test Government decisions Government decisions –Housing development –Consumer price index Business decisions Business decisions –Usually made under uncertainty.