Math: Exercise 1

Set Theory

1) There are 50 people on tour. One day, 26 people went on the morning cruise and 29 to the evening barbecue. Using Venn diagrams, or otherwise, answer the following questions.

(a) It was thought that 4 people went to both events and 1 person to neither. Explain why this was not possible.

(b) Find the least number and the greatest number of people who could have gone to both events.

2) Mary has 50 counters. Some of the counters are square, the remainder are round. There are 11 square counters that are green. There are 15 square counters that are not green. Of the round counters, the number that are not green is double the number that are green.

By drawing Venn diagram, or otherwise, find the number of counters that are

(a) round, (b) round and green, (c) not green.

Statistical Data

1) For each of the data set given below, identify whether it is discrete or continuous.

(a) The number of students in Cosmopolitan college in the year of 2013
(b) The time taken for a laptop to shut down

2) For each of the following, state whether it is a primary or a secondary data.

(a) A student recorded the time taken by a batch of desktops to shut down.
(b) Jamilah is the owner of a book store. She is looking onto the account prepared by her clerks to find out the amount of profit she made in last month.

3) From the following information, distinguish whether it is quantitative or qualitative.

(a) The height of each football player
(b) The colour of car passing by maria's house

Statistical Representation

1) Cameron observed the make of 100 cars passing his house. Draw a pie chart to show him results. Calculate the fraction of the whole that each sector represents.

2) (a) An article in a newspaper reported that the number of crimes had been reduced by half from 1991 to 2001. The article contained the bar chart shown here. Explain why this bar chart might considered misleading.

(b) The histogram alongside shows distribution of times taken by a group of students to travel to school. 11 students took at least 5 but less than 10 minutes. Complete the table in the answer space.