# Computing the mode in R

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In R there isn’t a function for computing the mode. This statistic is not often used but it is very useful for categorical and discrete data.

The mode is defined as “the most common value occurring in a set of observations.” Mathematically, for numerical data, the mode is the centre of order zero mode = arg min_m sum [x_i – m]^0, where 0^0 is defined as equal to 0.

This definition is not complete because in a set of data there can be one or many or no mode. For example: in a set with 10 apples, 5 pears and 2 bananas the mode is apple, in a set with 5 apples, 5 pears and 2 bananas the modes are apple and pear, in a set with 5 apples, 5 pears and 5 bananas there is no mode. This is shown in the figure below.

ta = table(x)

tam = max(ta)

if (all(ta == tam))

mod = NA

else

if(is.numeric(x))

mod = as.numeric(names(ta)[ta == tam])

else

mod = names(ta)[ta == tam]

return(mod)

}

Let’s see how it works for

**nominal data**:

One mode

fruit = c(rep(“apple”, 10), rep(“pear”, 5), rep(“banana”, 2))

Mode(fruit)

# [1] “apple”

Two modes

fruit2 = c(rep(“apple”, 5), rep(“pear”, 5), rep(“banana”, 2))

Mode(fruit2)

# [1] “apple” “pear”

No mode

fruit3 = c(rep(“apple”, 5), rep(“pear”, 5), rep(“banana”, 5))

Mode(fruit3)

# [1] NA

Works fine for nominal data. Let’s check for **numerical data**:

One mode

count1 = c(rep(1, 10), rep(2, 5), rep(3, 2))

Mode(count1)

# [1] 1

Two modes

count2 = c(rep(1, 5), rep(2, 5), rep(3, 2))

Mode(count2)

# [1] 1 2

No mode

count3 = c(rep(1, 5), rep(2, 5), rep(3, 5))

Mode(count3)

# [1] NA

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