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Exercises · Q10

Q.Prepare a frequency distribution by inclusive method taking class interval of 7 from the following data. 28 17 15 22 29 21 23 27 18 12 7 2 9 4
1 8 3 10 5 20 16 12 8 4 33 27 21 15
3 36 27 18 9 2 4 6 32 31 29 18 14 13
15 11 9 7 1 5 37 32 28 26 24 20 19 25
19 20 6 9

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With a class interval of 7 and the inclusive method (both limits included, a gap left between classes), the full 60-value data are grouped into 1–7, 8–14, 15–21, 22–28, 29–35 and 36–42 — six classes, not five, since the data itself contains values up to 37. Tallying every value gives frequencies 15, 12, 15, 10, 6 and 2, summing to the full 60 observations.

Method: inclusive classification with width 7

In the inclusive method both the lower and upper limits belong to the same class and consecutive classes are separated by a gap (…7, then 8…). A class width of 7 means each class spans seven whole numbers. Starting from 1, the classes needed to cover the data's full range (up to 37) are:

1–7,8–14,15–21,22–28,29–35,36–421\text{–}7,\quad 8\text{–}14,\quad 15\text{–}21,\quad 22\text{–}28,\quad 29\text{–}35,\quad 36\text{–}42

Tally (from the complete 60-value stem data)

Tallying every one of the 60 recorded observations into these six classes:

Class interval (inclusive)Frequency
1 – 715
8 – 1412
15 – 2115
22 – 2810
29 – 356
36 – 422
Total60

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