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.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(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)
Source: Myschool Past Questions Archive (Record #56455)