# Measures of central tendancy

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The mode, median and mean are called measures of central tendancy.

# Mode

The value that is most common in a row of data is the mode. In other words, it is the value with the highest frequency. With a distribution in classes is the class with the highest frequency the modal class. If there are two values with the highest frequency, there is no mode.

## Example

Given is the row: 1, 2, 2, 3, 3, 4, 5, 6, 6, 6, 6, 7
The number 6 is most common. So 6 is the mode.

# Median

The median is the middle value in a row of data in ascending order.
The median divides the data in two, 50% of the values is lower than the median and 50% higher than the median.

Odd number of values: take the middle number

Even number of values: there is no middle number...but there are two numbers who make up the middle. The mean of those two numbers is the median.

## How do you calculate which value is the middle value?

Use number of the middle value = (total number of values + 1) ÷ 2.

## Example 1

What is the median of 1, 6, 4, 3, 2, 8, 7, 6, 12 and 3?

1. First put them in ascending order: 1, 2, 3, 3, 4, 6, 6, 7, 8, 12.
2. There are 10 values, so the middle value is the (10 + 1) ÷ 2 = 5.5th number.
3. Therefore you need the fifth and sixth value. Those middle values are 4 and 6.
4. The median is (4 + 6) ÷ 2 = 5.

There is a total of 3 + 4 + 5 + 6 + 2 + 4 = 24 values.
The middle value is the (24 + 1) ÷ 2 = 12.5th number.
So you need to find the 12th and 13th number.
Start counting from the top, using the frequencies.
The 12th number is a 6. The 13th number is a 7.
The median is therefore (6 + 7) ÷ 2 = 6.5.

# Mean

The mean can be calculated in the following way: mean = (sum of the values) ÷ (total number of values).

# Mean of a distribution in classes

What if you have a distribution in classes? In that case you can only make an estimation of the mean.

1. Calculate the midpoint of each class.
2. Multiply the midpoint with the frequency and add the outcomes.
3. Divide the sum of the outcomes by the sum of the frequencies.

Estimation of the mean is 3130 ÷ 18 ≈ 173.9 cm.