Bar Chart

Definition: These are rectangular bars with varying heights but the same width with equal spaces or gaps separating the bars. The height of each bar represents the frequency of each value. The bars may be drawn vertically or horizontally. A bar chart can be used to display qualitative and discrete quantitative data.

Example 1

Solution:

(a)

(b)

Sum of items produced = 4100 + 2500 + 1500 + 1800 + 9200 = 19100

Number of years = 5

∴ Average Production = \( \frac{19100}{5} \)

Example 2

Solution:

(a) No. of Students who took the test = 2 + 5 + 3 + 8 + 10 + 7 + 6 + 4 = 45

(b) The highest bar gives the mode (i.e. the marks which occur most often).

i.e. 10 students got 4 marks

Therefore, Modal mark = 4.

(c) Recall that the median is the middle mark obtained after the marks have been arranged in order of size. There are 45 students, so the median is the mark obtained by the 23^rd student. By counting, the 23^rd student got 4 marks. Thus the median mark is 4.

(d) Lowest Mark = 0, Highest Mark = 7. Thus, the range of the mark is from 0 to 7.

⇒ Range = Highest Mark – Lowest Mark

⇒ Range = 7 – 0

= 7.

(e) 7 Students scored 5 marks, 6 students scored 6 marks and 4 students scored 7 marks.

No of Students who scored 5 marks and above = 7 + 6 + 4 = 17

(f) 10 students scored 4 marks

∴ the fraction of students who scored 4 marks = \( \frac{10}{45} = \frac{2}{9} \)

(g) Number of students who scored 5 and above = 17.

Students who failed the test = 45 – 17 = 28

∴ the Percentage of students who failed the test

= \( \frac{28}{45} \scriptsize \: \times \: 100 = 62.22 \%\)

\( \scriptsize \approx 62 \%\)

Example 3

Solution:

(a) Number of vehicles produced in February

= 40 + 25 + 30 = 95

(b) Fraction of the vehicle manufactured in February that were Cars

=\( \frac{40}{95} = \frac{8}{19} \)

(c) Number of buses produced from January to March

= 20 + 30 + 50 = 100

(d) The ratio of Lorries produced in February to that in March = 25:30

i.e. = 5:6

⇒ ratio = 5:6