11.3 CHAPTER 11. STATISTICS
(c) What mark must oneobtain in order to be inthe top 2% of the class?
(d) Approximately 84% of the pupils passed thetest. What was the passmark?
(e) Is the distribution normal or skewed?- In a road safety study, the speed of 175 cars was monitored along a specific stretch of highway
in order to find out whether there existed any link between high speed and the large number of
accidents along the route. A frequency table ofthe results is drawn up below.
Speed (km.h−^1 ) Number of cars (Frequency)
50 19
60 28
70 23
80 56
90 20
100 16
110 8
120 5The mean speed was determined to be around 82 km·hr−^1 while the median speedwas worked
out to be around 84 , 5 km·hr−^1.(a) Draw a frequency polygon to visualise the data in the table above.
(b) Is this distribution symmetrical or skewed left or right? Give a reasonfro your answer.More practice video solutions or help at http://www.everythingmaths.co.za(1.) 01aw (2.) 01ax (3.) 01ay11.3 Extracting a Sample Population
EMCCW
Suppose you are tryingto find out what percentage of South Africa’s population owns a car. One way
of doing this might be tosend questionnaires to peoples homes, asking them whether they own acar.
However, you quickly run into a problem: youcannot hope to send every person in the country a
questionnaire, it wouldbe far to expensive. Also, not everyone wouldreply. The best you cando is
send it to a few people,see what percentage ofthese own a car, and then use this to estimate what
percentage of the entirecountry own cars. Thissmaller group of peopleis called the sample popula-
tion.The sample populationmust be carefully chosen, in order to avoid biased results. How do we do
this?
First, it must be representative. If all of our sample population comes from a very rich area, then almost
all will have cars. But we obviously cannot conclude from this that almost everyone in the country has
a car! We need to sendthe questionnaire to richas well as poor people.
Secondly, the size of the sample population must be large enough. It is no good havinga sample
population consisting of only two people, for example. Both may verywell not have cars. Butwe
obviously cannot conclude that no one in thecountry has a car! Thelarger the sample population
size, the more likely it isthat the statistics of oursample population corresponds to the statistics of the
entire population.