The ages of a group of athletes are as follows: 18, 16. 18,20, 17, 16, 19, 17, 18, 17 and 13. (a) Find the range of the distribution. (b) Draw a frequency d...
Question 1 Report
The ages of a group of athletes are as follows: 18, 16. 18,20, 17, 16, 19, 17, 18, 17 and 13. (a) Find the range of the distribution.
(b) Draw a frequency distribution table for the data.
(c) What is the median age?
(d) Calculate, correct to two decimal places, the;
(i) mean age:
(ii) standard deviation.
Answer Details
Data (11 athletes): 18, 16, 18, 20, 17, 16, 19, 17, 18, 17, 13.
(a) Range \(=\) highest \(-\) lowest \(=20-13=7\).
(b) Frequency distribution table
| Age (x) | 13 | 16 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|
| Frequency (f) | 1 | 2 | 3 | 3 | 1 | 1 |
(c) Median. Arranged: 13, 16, 16, 17, 17, 17, 18, 18, 18, 19, 20. With \(n=11\), the median is the \(6^{th}\) value \(= \mathbf{17}\).
(d)(i) Mean. \(\sum fx = 13+32+51+54+19+20 = 189\), \(\sum f = 11\).
\(\bar{x}=\dfrac{189}{11}=17.1818\ldots \approx \mathbf{17.18}\).
(d)(ii) Standard deviation. \(\sum fx^{2}=169+512+867+972+361+400=3281\).
\(\sigma=\sqrt{\dfrac{\sum fx^{2}}{n}-\bar{x}^{2}}=\sqrt{\dfrac{3281}{11}-\left(\dfrac{189}{11}\right)^{2}}=\sqrt{298.2727-295.2149}=\sqrt{3.0579}\).
\(\sigma \approx \mathbf{1.75}\) (2 d.p.).
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