Question 13:
Data in Table 1 shows the height, in cm, of a group of 10 volleyball players.
Table 1
(a) Determine
(i) the first quartile
(ii) median
(iii) the third quartile
(iv) the interquartile range
[4 marks]
(b) Table 2.1 shows the number of words typed by a group of participants in a Shorthand and Secretarial Workshop within the duration of 5 minutes.
Table 2.1
Complete Table 2.2 in the answer space 13(b).
Calculate standard deviation of the data.
[6 marks]
Answer:
(b)
Solution:
142, 154, 157 (Q1), 158, 162, | 162, 168, 169 (Q3), 172, 183
(a)(i) the first quartile, Q1 = 157
(a)(ii)
(a)(iii) the third quartile, Q3 = 169
(a)(iv) the interquartile range = Q3 – Q1 = 169 – 157 = 12
(b)
Data in Table 1 shows the height, in cm, of a group of 10 volleyball players.
142 | 168 | 162 | 154 | 172 |
162 | 157 | 158 | 169 | 181 |
(a) Determine
(i) the first quartile
(ii) median
(iii) the third quartile
(iv) the interquartile range
[4 marks]
(b) Table 2.1 shows the number of words typed by a group of participants in a Shorthand and Secretarial Workshop within the duration of 5 minutes.
Number of words | Frequency |
121 – 125 | 6 |
126 – 130 | 9 |
131 – 135 | 13 |
136 – 140 | 18 |
141 – 145 | 14 |
146 – 150 | 10 |
Complete Table 2.2 in the answer space 13(b).
Calculate standard deviation of the data.
[6 marks]
Answer:
(b)
f | Midpoint | fx | x2 | fx2 |
6 | 123 | |||
9 | 128 | |||
13 | 133 | |||
18 | 138 | |||
14 | 143 | |||
10 | 148 | |||
Σ f = 70 | Σ fx = | Σ x2 = | Σ fx2 = |
Solution:
142, 154, 157 (Q1), 158, 162, | 162, 168, 169 (Q3), 172, 183
(a)(i) the first quartile, Q1 = 157
(a)(ii)
(a)(iii) the third quartile, Q3 = 169
(a)(iv) the interquartile range = Q3 – Q1 = 169 – 157 = 12
(b)
f | Midpoint | fx | x2 | fx2 |
6 | 123 | 738 | 15 129 | 90 774 |
9 | 128 | 1 152 | 16 384 | 147 456 |
13 | 133 | 1 729 | 17 689 | 229 957 |
18 | 138 | 2 484 | 19 044 | 342 792 |
14 | 143 | 2 002 | 20 449 | 286 286 |
10 | 148 | 1 480 | 21 904 | 219 040 |
Σ f = 70 | Σ fx = 9 585 | Σ x2 = 110 599 | Σ fx2 = 1 316 305 |