A bar graph uses bars of equal width separated by spaces to represent data. It shows the frequency distribution of scores from a student test. The document then provides solutions to 10 multiple choice questions about values that can be determined from the bar graph like the total number of students, mean score, median, range, and interquartile range.

1. BAR CHART
A bar graph uses bars of equal width with spaces between them to
represent information
0
1
2
3
4
5
6
Category 1 Category 2 Category 3 Category 4
Frequency
Variable
Bar Chart
Series 1 Series 2 Series 3

2. JAMB 1984
Solution
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑢𝑒𝑛𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑙𝑎𝑠𝑠
= 4 + 6 + 8 + 9 + 5 + 2
= 34

3. JAMB
Solution
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑠
= 3 + 4 + 8 + 2 + 6 + 2
= 25
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑦𝑒𝑙𝑙𝑜𝑤 𝑐𝑎𝑟𝑠 = 3
⇒ 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑜𝑓𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟
𝑜𝑓 𝑐𝑎𝑟𝑠 𝑎𝑟𝑒 𝑌𝑒𝑙𝑙𝑜𝑤 =
3
25

4. WASSCE July 2005
The scores obtained by
students in a test are
21,25,27,25,27,21,24,
23,23 and 24. Draw a
bar chart to illustrate the
information.
Solution
The corresponding frequency
table is 𝑺𝒄𝒐𝒓𝒆𝒔 𝑻𝒂𝒍𝒍𝒚 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚
21 // 2
23 // 2
24 // 2
25 // 2
27 // 2

5. WASSCE July 2012
The bar chart is the
frequency distribution of
marks scored by
students in a test.
How many students
took the test?
Solution
The number of students who
took the test is equal to the total
frequency= 6 + 8 + 6 + 5 = 25

6. 1. The bar chart represents the frequency distribution of students in a
test. How many students took the test?
A. 23
B. 42
C. 25
D. 24
E. 32
The correct answer is 23

7. 1. The bar chart represents the frequency distribution of students in a
test. How many students took the test?
A. 23
B. 42
C. 25
D. 24
E. 32
The correct answer is 23
Solution
The number of students who took the test = total frequency
= 2 + 4 + 3 + 3 + 6 + 4 + 1 = 23

8. 2. The bar chart represents the frequency distribution of students in a
test. What is the mean score correct to one decimal place?
A. 4.9
B. 4.1
C. 5.0
D. 6.0
E. 4.0
The correct answer is 5.0

9. 2. The bar chart represents the frequency distribution of students in a
test. What is the mean score correct to one decimal place?
A. 4.9
B. 4.1
C. 5.0
D. 6.0
E. 4.0
The correct answer is 5.0
Solution
The corresponding frequency table is given as follows
𝑺𝒄𝒐𝒓𝒆 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒇𝒙
2 2 4
3 4 12
4 3 12
5 3 15
6 6 36
7 4 28
8 1 8
𝑓 = 23 𝑓𝑥 = 115
Mean=
𝑓𝑥
𝑓
=
115
23
= 5.0

10. 3. The bar chart represents the frequency distribution of students in a
test. What is the maximum score?
A. 6
B. 8
C. 4
D. 6
E. 5
The correct answer is 8

11. 3. The bar chart represents the frequency distribution of students in a
test. What is the maximum score?
A. 6
B. 8
C. 4
D. 6
E. 5
The correct answer is 8
Solution
The highest score is 8, so the maximum is 8

12. 4. The bar chart represents the frequency distribution of students in a
test. What is the median score?
A. 6
B. 8
C. 4
D. 6
E. 5
The correct answer is 5

13. 4. The bar chart represents the frequency distribution of students in a
test. What is the median score?
A. 6
B. 8
C. 4
D. 6
E. 5
The correct answer is 5
Solution
The corresponding frequency table is given as follows
𝑺𝒄𝒐𝒓𝒆 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒇𝒙
2 2 4
3 4 12
4 3 12
5 3 15
6 6 36
7 4 28
8 1 8
𝑓 = 23 𝑓𝑥 = 115
The median score corresponds to the score in
1
2
𝑓 + 1 𝑡ℎ position
=
1
2
(23 + 1) position
= 12th position
Adding cumulatively on the frequency table , the 12th value

14. 5. The bar chart represents the frequency distribution of students in a
test. What is the modal score?
A. 6
B. 8
C. 4
D. 6
E. 5
The correct answer is 6

15. 5. The bar chart represents the frequency distribution of students in a
test. What is the modal score?
A. 6
B. 8
C. 4
D. 6
E. 5
The correct answer is 6
Solution
The score with the highest bar(frequency) is 6 , hence 6
is the mode

16. 6. The bar chart represents the frequency distribution of students in a
test. What is the first quartile?
A. 2
B. 3
C. 4
D. 6
E. 5
The correct answer is 3

17. 6. The bar chart represents the frequency distribution of students in a
test. What is the first quartile?
A. 2
B. 3
C. 4
D. 6
E. 5
The correct answer is 3
Solution
The corresponding frequency table is given as follows
𝑺𝒄𝒐𝒓𝒆 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒇𝒙
2 2 4
3 4 12
4 3 12
5 3 15
6 6 36
7 4 28
8 1 8
𝑓 = 23 𝑓𝑥 = 115
The median score corresponds to the score in
1
4
𝑓 + 1 𝑡ℎ position
=
1
4
(23 + 1) position
= 6th position
Adding cumulatively on the frequency table , the 6th value =

18. 7. The bar chart represents the frequency distribution of students in a
test. What is the third quartile?
A. 2
B. 3
C. 4
D. 6
E. 5
The correct answer is 6

19. 7. The bar chart represents the frequency distribution of students in a
test. What is the third quartile?
A. 2
B. 3
C. 4
D. 6
E. 5
The correct answer is 6
Solution
The corresponding frequency table is given as follows
𝑺𝒄𝒐𝒓𝒆 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒇𝒙
2 2 4
3 4 12
4 3 12
5 3 15
6 6 36
7 4 28
8 1 8
𝑓 = 23 𝑓𝑥 = 115
The median score corresponds to the score in
3
4
𝑓 + 1 𝑡ℎ position
=
3
4
(23 + 1) position
=18th position
Adding cumulatively on the frequency table , the 18th value

20. 8. The bar chart represents the frequency distribution of students in a
test. What is the range?
A. 2
B. 3
C. 4
D. 6
E. 5
The correct answer is 6

21. 8. The bar chart represents the frequency distribution of students in a
test. What is the range?
A. 2
B. 3
C. 4
D. 6
E. 5
The correct answer is 6
Solution
The range= The highest score – the least score
= 8 − 2
= 6

22. 9. The bar chart represents the frequency distribution of students in a
test. What is the interquartile range?
A. 2
B. 3
C. 4
D. 6
E. 5
The correct answer is 3

23. 9. The bar chart represents the frequency distribution of students in a
test. What is the interquartile range?
A. 2
B. 3
C. 4
D. 6
E. 5
The correct answer is 3
Solution
The interquartile range = the third quartile – the first
quartile
= 6 − 3
= 3

24. 10. The bar chart represents the frequency distribution of students in a
test. What is the semi-interquartile range?
A. 1.6
B. 2.8
C. 1.4
D. 0.2
E. 1.5
The correct answer is 1.5

25. 10. The bar chart represents the frequency distribution of students in a
test. What is the semi-interquartile range?
A. 1.6
B. 2.8
C. 1.4
D. 0.2
E. 1.5
The correct answer is 1.5
Solution
The semi interquartile range =
1
2
(𝑖𝑛𝑡𝑒𝑟𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝑟𝑎𝑛𝑔𝑒)
=
3
2
= 1.5

26. BAR CHART
You can always construct a frequency distribution table from a bar graph an
Use it to answer related follow up questions.