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
|
Class Interval |
Tally |
Classmark (x) |
Freq (f) |
(fx) |
| 21 – 25 |
|
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.