The ages, in years, of 50 teachers in a school are... | WAEC SSCE - General Mathematics - 2008 (Essay)

Question 1 Report

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

(d) Calculate the mean age.

Answer

(a) Frequency distribution

Age (years)	Tally	Class mark, \(x\)	Frequency, \(f\)	\(fx\)
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
Total			50	1750

(b) Histogram

The continuous class boundaries are \(20.5\), \(25.5\), \(30.5\), \(35.5\), \(40.5\), \(45.5\) and \(50.5\). Since all class widths are 5 years, the bar heights are the frequencies.

graph — Histogram with adjoining bars of equal width 5 years. The class boundaries are 20.5, 25.5, 30.5, 35.5, 40.5, 45.5 and 50.5.

(c) Modal age

The modal class is \(26\text{ - }30\), for which \(L=25.5\), \(f_1=11\), \(f_0=7\), \(f_2=9\), and class width \(h=5\).

\[\text{Mode}=L+\left(\frac{f_1-f_0}{(f_1-f_0)+(f_1-f_2)}\right)h\]

\[=25.5+\left(\frac{11-7}{(11-7)+(11-9)}\right)\times5=25.5+\frac{4}{6}\times5=28.8\]

Hence, the estimated mode is \(28.8\) years.

(d) Mean age

\[\bar{x}=\frac{\sum fx}{\sum f}=\frac{1750}{50}=35\]

Therefore, the mean age is 35 years.

Read lesson note on Sets (JAMB)

Read lesson note on Measures Of Location (JAMB)

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