The weekly wages (in Rs.) of 30 workers in a factory are given:

Question:

The weekly wages (in Rs.) of 30 workers in a factory are given:

830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840

Mark a frequency table with intervals as 800-810, 810-820 and so on, using tally marks. Also, draw a histogram and answer the following questions:

(i) Which group has the maximum number of workers?

(ii) How many workers earn Rs 850 and more?

(iii) How many workers earn less than Rs 850?

Solution:

The frequency table with intervals $800-820,810-820, \ldots 890-900$ is given below:

Wage (in Rs) Tally Wage Frequency Tally marks
800-">-810 804, 808, 806 III
810-">-820 810, 812 2 II
820-">-830 820 1 I
830-">-840 830, 835, 835, 836, 832, 833, 835, 835, 836 9 IIII IIII
840-">-850 845, 845, 840, 840, 840 5 IIII
850-">-860 855 1 I
860-">-870 869, 860, 868 3 III
870-">-880 878 1 I
880-">-890 885 1 I
890-">-900 890, 898, 890, 890 4 IIII

The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:

(i) The group that has the maximum number of workers is represented as the highest rectangle. It is in the interval $830-840$.

(ii) The number of workers who earn Rs 850 or more can be calculated from frequency table in the following manner:

$1+3+1+1+4=10$

(iii) The number of workers who earn less than Rs 850 can be calculated from frequency table in the following manner:

$3+2+1+9+5=20$

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