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.
Explanation
(a) The range; 20 - 15 = 5.
(b) They drew the frequency distribution table as
\(\sum\) f = 11\(\sum\) fx = 191 \(\sum\)f\(^2\) = 3337
| Age(x) | Tally |
Freq (f) |
Com. Freq |
fx | fx\(^2\) | |
|
15 16 17 18 19 20 |
I II III III I I |
1 2 3 3 1 1 |
1 3 6 9 10 11 |
15 32 51 54 19 20 |
225 512 867 972 361 400 |
(c) Median age as 17.
(d)(i) Mean = \(\frac{\sum fx}{\sum f}\) = \(\frac{191}{11}\) = 17.3636
(d)(ii). The standard deviation was \(\sqrt{\frac{2227}{11} - (\frac{191}{11})^2}\)
= \(\sqrt{1.8677}\) = 1.37(correct to two decimal places)