Chpt 11 - Statistics & Probability

STATISTICS & PROBABILITY Mathematics Preparatory Course for Direct Entry to Higher Nitec 11-1 Chapter 11 11.1 Statistical Presentations Mrs Fung has to handle her family’s finances now. She finds that she has to invest some of their savings as the interest paid by banks hardly covers the increase in the cost of living due to inflation. She has to consult her stockbroker and browse through newspapers and company reports. It is not an easy task and she laments the fact that she was not taught statistics during her schooldays. Statistical data presented graphically, as shown below, confound her. Mrs Fung’s problem is a common one that many of us face in this modern world. Studying statistics helps us to tackle this problem. 1. In pictograms, pictures are used to represent data. The pictures attract immediate attention as they depict the objects under discussion. However, they are not accurate as the fractional parts of the pictures are only approximations.

STATISTICS & PROBABILITY Mathematics Preparatory Course for Direct Entry to Higher Nitec 11-2 2. Bar charts can be horizontal or vertical. The bars or columns must be of equal width. The length of a bar or the height of a column represents the frequency. The lengths give a better comparison of values than the sectors in a pie chart. 3. In a pie chart, the angle of the sector is proportional to the frequency of the category represented by the sector. 4. In a histogram, the area of each column represents the frequency of each class. If all the columns are of equal widths, we can use the height of the column to represent the frequency. 5. A frequency polygon is formed by joining the midpoints at the top of the rectangular columns in a histogram by straight lines. Example 1 A class of 36 pupils was asked to name their favourite colour. Their choices are represented on a given pie chart. (a) If 16 said they liked red, calculate the value of x°. (b) Find the number who said they liked green. (c) Find the percentage of the class who said they liked blue.

STATISTICS & PROBABILITY Mathematics Preparatory Course for Direct Entry to Higher Nitec 11-3 11.2 Statistical Averages The mean of a distribution is found by dividing the sum of the values by the number of values. The median of a distribution is the value below which half the data lies. The mode of a distribution is the value that occurs most frequently. Example 2 Find the mean, the mode and the median of 2, 7, 6, 6, 2, 4, 5, 6. Example 3 A six-sided die is thrown 19 times. The results are tabulated as shown. (a) Write down (i) the mode, (ii) the median. (b) The die is thrown one more time. If the mean of the 20 throws is 2.8, find the number shown on the die.

STATISTICS & PROBABILITY Mathematics Preparatory Course for Direct Entry to Higher Nitec