Mean and median

The number of observations is usually denoted by the letter n

In your observation n = 10

To find the mean (average), you add all your observations (x) together and divide by the number of observations (n)

$$ \overline{x} = \frac{x_1 + x_2 + x_3 +.....x_n}{10} \Leftrightarrow $$

$$ \overline{x} = \frac{176 + 172 + 160..... + 158}{10} \Leftrightarrow $$

$$ \overline{x} = \frac{1648}{10} \Leftrightarrow $$

$$ Mean = 164.8 cm $$

The mean is one measure of what is typical in a data set. Another important measure is the median.

If you sort your observations from smallest to largest, the median will be the observation right in the middle.

There will be the same number of observations on each side of the median.

If there are 5 observations, the median is the third (so there are two on each side).

In our case, there is an even number of observations, so the median will be the average of the 5th and 6th observation.

5th observation = Sophia 161 cm

6th observation = Ava 167 cm

Average = 164

The median is equal to 164 cm.

The mean and the median can give different results.

If a data set has very high or very low values, the mean can be pulled in that direction, while the median is more robust.