The ages, in years, of 50 teachers in a school are given below : 21 37 49 27 49 42 26 33 46 40 50 29 23 24 29 31 36 22 27 38 30 26 42 39 34 23 21 32 41 46 46 31 33 29 28 43 47 40 34 44 26 38 34 49 45 27 25 33 39 40 (a) Form a frequency distribution table of the data using the intervals : 21 - 25, 26 - 30, 31 - 35 etc. (b) Draw the histogram of the distribution (c) Use your histogram to estimate the mode (d) Calculate the mean age.
Explanation
ClassInterval
Tally
Classmark(x)
Freq(f)
\(fx\)
21 - 25
IIII ||
23
7
161
26 - 30
|||| |||| |
28
11
308
31 - 35
|||| ||||
33
9
297
36 - 40
|||| ||||
38
9
342
41 - 45
|||| |
43
6
258
46 - 50
|||| |||
48
8
384
\(\sum\)
50
1750
(b) (c) Mode : \(L_{1} + (\frac{f_{0} - f_{1}}{2f_{0} - f_{1} - f_{2}})t\) Where \(L_{1}\) = lower class boundary of modal class = 25.5 \(f_{0}\) = frequency of modal class = 11 \(f_{1}\) = frequency of pre-modal class = 7 \(f_{2}\) = frequency of post modal class = 9 \(t\) = interval mark = 5. Mode : \(25.5 + (\frac{11 - 7}{22 - 7 - 9})\times 5 = 25.5 + 3.3\) = 28.8. (d) Mean : \(\frac{\sum fx}{\sum f} = \frac{1750}{50}\) = 35.
