In a college, the number of absentees recorded over a period of 30 days was as shown in the frequency distribution table
Number of absentees
0-4
5-9
10-14
15-19
20-24
Number of Days
1
5
10
9
5
Calculate the : (a) Mean
(b) Standard deviation , correct to two decimal places.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
\(x\)
mid-value
\(f\)
\(fx\)
\((x - \bar{x})\)
\((x - \bar{x})^{2}\)
\(f(x - \bar{x})^{2}\)
0 - 4
2
1
2
-12
144
144
5 - 9
7
5
35
-7
49
245
10 - 14
12
10
120
-2
4
40
15 - 19
17
9
153
3
9
81
20 - 24
22
5
110
8
64
320
\(\sum \)
30
420
830
(a) Mean \(\bar{x}\) = \(\frac{\sum fx}{\sum f}\)
= \(\frac{420}{30} = 14\)
(b) Standard deviation = \(\sqrt{\frac{\sum f(x - \bar{x})^{2}}{\sum f}\)
= \(\sqrt{\frac{830}{30}}\)
= \(\sqrt{27.66}\)
= 5.26.
Source: Myschool Past Questions Archive (Record #53009)