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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.
VarIntTo 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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