# Populations(in hundreds) of 50 towns and villages of a state , taken at random from a census report are: 11, 72, 15, 8, 15, 3, 23, 26, 2, 119, 200, 6, 16, 6, 111, 5,18,140,99,127,3172,18,30,43, 2,1,52,40,3,7,13,5,142,70,86,31,38,70,51,11,52,18,46,89,1,30,25,4,52 Prepare a grouped frequency table for the above data, using class intervals 0-30, 30-60,60-90 and so on. Also find the class with maximum frequency.

To create a grouped frequency table for the given data with class intervals of 30, we can proceed as follows:

Step 1: Sort the given data in ascending order:

1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 11, 11, 13, 15, 15, 16, 18, 18, 23, 25, 26, 30, 31, 38, 40, 43, 46, 51, 52, 52, 52, 70, 70, 72, 86, 89, 99, 111, 119, 127, 140, 142, 200, 3172

Step 2: Determine the range of the data (highest value - lowest value):

Range = 3172 - 1 = 3171

Step 3: Determine the number of class intervals. Since we want class intervals of width 30, we divide the range by 30 and round up to the nearest whole number:

Number of class intervals = ceil(Range/30) = ceil(3171/30) = ceil(105.7) = 106

Step 4: Determine the class boundaries for each interval. We start with the lower boundary of the first interval as 0 and increment by 30 for each subsequent interval:

0-30, 30-60, 60-90, 90-120, 120-150, ...

Step 5: Count the frequency of each interval by counting the number of data points that fall within each interval.

Using the given data, the grouped frequency table is as follows:

Class Interval Frequency

0-30 8

30-60 8

60-90 3

90-120 3

120-150 1

150-180 0

180-210 5

210-240 0

240-270 1

270-300 1

300-330 1

330-360 1

360-390 0

390-420 0

420-450 1

450-480 1

480-510 0

510-540 0

540-570 0

570-600 0

600-630 1

630-660 1

660-690 0

690-720 0

720-750 1

750-780 0

780-810 0

810-840 0

840-870 0

870-900 0

900-930 0

930-960 0

960-990 0

990-1020 0

1020-1050 0

1050-1080 0

1080-1110 0

1110-1140 0

1140-1170 0

1170-1200 0

1200-1230 0

1230-1260 0

1260-1290 0

1290-1320 0

1320-1350 0

1350-1380 0

1380-1410 0

1410-1440 0

1440-1470 0

1470-1500 0

1500-1530 0

1530-1560 0

1560-1590 0

1590-1620 0

1620-1650 0

1650-1680 0

1680-1710 0

1710-1740 0

1740-1770 0

1770-1800 0

1800-1830 0

1830-1860 0

1860-1890 0

1890-1920 0

1920-1950 0

1950-1980 0

1980-2010 0

2010-2040 1

2040-2070 0

2070-2100 0

2100-2130 0

2130-2160 0

2160-2190 0

2190-2220 0

2220-2250 0

2250-2280 0

2280-2310 0

2310-2340 0

2340-2370 0

2370-2400 0

2400-2430 0

2430-2460 0

2460-2490 0

2490-2520 0

2520-2550 0

2550-2580 0

2580-2610 0

2610-2640 0

2640-2670 0

2670-2700 0

2700-2730 0

2730-2760 0

2760-2790 0

2790-2820 0

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