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Worked Examples · Example 5.3

Q.In the list of height of students, mode is 110 as its frequency of occurrence in the list is 3, which is larger than the frequency of rest of the values.

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The mode is the observation with the highest frequency — the most typical value actually present in the data. Height 110 cm occurs 3 times (all others occur once or twice), so the mode is 110 cm.

The idea

Mean and median answer "where is the centre?"; the mode answers "which value is most common?". Unlike the mean, the mode is always an actual observed value, and it is the only measure of central tendency that also works for non-numeric data (e.g. the most common uniform colour).

Counting the frequencies

Height (cm)Frequency
851
902
1001
1021
1103
1151

The highest frequency is 3, belonging to 110 cm — that is the mode. (90 cm, with frequency 2, is the runner-up, not a mode.)

In Python

import statistics

heights = [90, 102, 110, 115, 85, 90, 100, 110, 110]
print(statistics.mode(heights))
110

To see the frequency table the way we built it by hand, collections.Counter is perfect:

from collections import Counter
print(Counter(heights))
Counter({110: 3, 90: 2, 102: 1, 115: 1, 85: 1, 100: 1})
``` …

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