**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

The number of items produced by a company over a five-year period is given below:

Year | 1978 | 1979 | 1980 | 1981 | 1982 |

Number Produced | 4100 | 2500 | 1500 | 9200 | 1800 |

**(a) **Plot a bar chart for this information.

**(b)** What is the average production for the five-year period? (WAEC)

**Solution:**

**(a)**

**(b)**

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

Number of years = 5

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

### Example 2

The diagram below is a bar chart showing the distribution of marks scored in a mathematics test. Use the bar chart to answer the following questions.

**(a)** How many students took the test?

**(b) **What was the modal mark?

**(c)** What was the median class?

**(d)** What was the range of marks?

**(e) **How many students scored 5 marks and above?

**(f) **What fraction of the students scored 4?

**(g)** If the pass mark is 5, what percentage of the students failed the test?

**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

The diagram below shows the bar charts representing the number of vehicles ___ Cars, Buses and Lorries manufactured by a company in January, February and March, 1992.

### Number of Vehicles manufactured From January – March 1992

**(a)** How many vehicles were produced in February?

**(b)** What fraction of the vehicles manufactured in February were Cars?

**(c) **How many buses were produced altogether from January to March, 1992?

**(d)** Find the ratio of Lorries produced in February to that in March. (WAEC)

**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

**Exercise**

Small nails are sold in packets which have printed on them, “Average contents 200 nails”. The contents of 100 packets, picked at random, were counted and the results are as given in the table below:

Nails per Packet | 185-189 | 190-194 | 195-199 | 200-204 | 205-209 | 210-214 |

Frequency | 2 | 4 | 6 | 2 | 4 | 6 |

(i) Draw a histogram for the distribution

(ii) Estimate the mode of the distribution

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