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.
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.
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Correct Answer: Option n
Explanation:
(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.
| 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.