TOPIC 11: STATISTICS ~ MATHEMATICS FORM 2
Statistics is the study of the collection, analysis, interpretation, presentation and organization of data. Statistics helps to present information using picture or illustration. Illustration may be in the form of tables,
Illustration may be in the form of tables, diagrams, charts or graphs.
- The month that had the highest temperature was August.
- The month with the lowest temperature was February.
- The difference in temperature between February and may is (320-290)=30C.
- The total number of months that had temperature more than 300C was 9.
survey about pupils interests in subjects is as follows: 30 pupils
prefer English, 40 pupils refer French and 50 pupils prefer Kiswahili.
Show this information in a pie chart.
2: divide each value by the total and then multiply by 360 degrees to
figure out how many degrees for each “pie slice” (we call pie slice a
sector) We multiply by 360 degrees because a full circle has a total of
3: draw a circle of a size that will be enough to show all information
required. Use a protractor to measure degrees of each sector. It will
look like the one here below:
angle of this section is 36 degrees. The question says there are 30
pupils in the class. So the number of pupils of height 121 – 130 cm is:
is how often something occurs. For example; Amina plays netball twice
on Monday, once on Tuesday and thrice on Wednesday. Twice, once and
thrice are frequencies.
- how often 1 occurs? (2 times)
- how often 2 occurs? (5 times)
- how often 3 occurs? (4 times)
- how often 4 occurs? (2 times)
- how often 5 occurs? (1 times)
is very useful when the scores have many different values. For example;
Alex measured the lengths of leaves on the Oak tree (to the nearest cm)
16, 13, 7, 8, 4, 18, 10, 17, 18, 9, 12, 5, 9, 9, 16, 1, 8, 17, 1, 10,
5, 9, 11, 15, 6, 14, 9, 1, 12, 5, 16, 4, 16, 8, 15, 14, 17.
Put the numbers in order. 1, 1, 1, 4, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 9,
9, 9, 9, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 16, 16,
17, 17, 17, 18, 18,
Find the size of each group. Calculate an approximate size of the
group by dividing the range by how many groups you would like. then,
round that group size up to some simple value like 4 instead of 4.25
and so on.
that is less than or equal to the smallest value. Try to make it a
multiple of a group size if you can. In our case a start value of 0 make the most sense.
our case, starting at 0 and with a group size of 4 we get 0, 4, 8, 12,
16. Write down the groups. Include the end value of each group. (must
be less than the next group):
For instance 3 cm means the actual value could have been any were
between 2.5 cm to 3.5 cm. Alex just rounded numbers to whole numbers.
And 0 means the actual value have been any where between -0.5 cm to 0.5
cm. but we can’t say length is negative. 3.5 cm is called upper real limit or upper boundary while –0.5 cm is called lower real limit or lower boundary. But since we don’t have negative length we will just use 0. So regarding our example the lower real limit is 0.
is a central (middle) value of a class interval. It is a value which is
half way between the class limits. It is sometimes called mid-point of a
class interval. Class mark is obtained by dividing the sum of the upper
and lower class limits by 2. i.e.
in the survey are most likely to have 1 person in them as this is the
tallest bar – 6 of the cars in the survey had one occupant.
a frequency polygon, one interval is added below the lowest interval
and another interval is added above the highest interval and they are
both assigned zero frequency. The points showing the frequency of each
class mark are placed directly over the class marks of each class
interval. The points are then joined with straight lines.
group of professional basketball players. Use the frequency polygon to
answer the following questions:
example; you measure the height of every tree in the orchard in
Centimeters (cm) and notice that, their height vary from 100 cm to 340
cm. And you decide to put the data into groups of 50 cm. the results
were like here below:
- Percentage of the job applicants scored between 30 and 40 is10%
- Percentage of the job applicants scored below 60 is90%
- Job applicants scored between 10 and 30 is100
March, we continue to add up. The total earned so far is Tsh 12 000 +
Tsh 15 000 + Tsh 13 000 = 40 000 or simply take the cumulative of
February add that of March i.e. Tsh 27 000 + Tsh 13 000 = Tsh 40 000.
2. The following table represent the number of pupils with their corresponding height.