## Subjects

# Statistics: Mode and median

How do you find the median of an even number of values?

## Statistics: Mode and median

Mikhail's school has 39 teachers. Mikhail asked each of them how tall they are. Just like Lina, when she was comparing different municipalities, Mikhail made a frequency table. This is what it looks like. The height is in the left column divided into five centimeter intervals.

The right column shows the number of teachers whose height falls within the interval. Mikhail drew a bar graph as well. Here it is. Mikhail compares his graph of the teacher's heights with Lina's graph, which shows the population of municipalities. The bars form completely different patterns.

Among the municipalities, the highest bars which show the most common population sizes are to the left. But in the chart of the teachers' heights, the highest bar is in the middle. The highest bar is the most common measurement, the observation with the highest frequency. The value with the highest frequency is called the mode. The mode for the teachers' height is 170 to 175 centimeters.

The mode for the municipality's population is 10,000 to 20,000. Lina is not happy knowing the mode, which is the most frequent value. She wants to know which municipality lies in the middle. In other words, a municipality of what size is smaller than half of the other municipalities and larger than the other half of them? To get the answer, she arranges her list in increasing order and calculates.

of 290 municipalities, the middle is between positions 145 and 146. This is [Safle?] in Hallsberg. They have about 15,300 inhabitants each. This middle value that Lina calculated has a name. It's the median.

The median is the middle value when the data is arranged in increasing order to be precise the median is the middle value if you have an odd number of observations. But we have 290 municipalities and this is an even number, so the median is the average of the two observations in the middle. Lina calculates that the median is 15,332 so the median population of a Swedish municipality is within the interval that Lina identified as the mode. Mikhail also calculates the median among his teachers just like Lina he sorts the observations in increasing order and he finds the middle value. Mikhail has 39 teachers in his survey, so the 20th by height teacher is exactly in the middle.

That's Eva. She's 174 cm tall. The number of teachers taller than Eva equals the number of teachers who are shorter. Lina is still not completely satisfied. She calculated the most common value, the mode, and the center value, the median, but among the municipalities, there are several very big ones and neither the mode nor the median is affected by their size.

Find the video on the mean value to find out how Lina deals with that problem.