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Data Handling and Presentation

Totals from a frequency table

Find totals from a frequency table, using a cricketer's wickets.

Faiz makes a frequency table of the wickets taken by the cricketer Jaspreet Bumrah in his last 30 matches. One column is the number of wickets; the other is in how many matches that happened:

WicketsMatches
02
14
26
38
43
55
61
71

The matches add up to 2 + 4 + 6 + 8 + 3 + 5 + 1 + 1 = 30.

Mayank says: just add 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 to get the total wickets. That gives 28, but it is wrong! It counts each number of wickets only once, as if it happened in just one match. But Bumrah took 3 wickets in 8 different matches.

The right way: multiply each number of wickets by its frequency, then add. 3 wickets in each of 8 matches is 3 × 8 = 24 wickets. Row by row: 0 × 2 = 0, 1 × 4 = 4, 2 × 6 = 12, 3 × 8 = 24, 4 × 3 = 12, 5 × 5 = 25, 6 × 1 = 6, 7 × 1 = 7. Adding: 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90. Bumrah took 90 wickets in those 30 matches.

To find a total from a frequency table, multiply each value by its frequency and add the results; adding the values alone is wrong.
Multiply, then add.

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