Median from a Histogram Flashcards

All 6 cards in this deck

What are the steps to estimate the median from a histogram?

e.g. a histogram showing $43$ runners' times

1. Find the total frequency: $43$
2. Find the median position: $43 \div 2 = 21.5$
3. Add bar frequencies until you reach it, then use proportion across that bar: e.g. $16 + \frac{9.5}{16} \times 4 = 18.375$

For $n$ values shown in a histogram, which position do you use to estimate the median?

The $\frac{n}{2}$ th value (using $\frac{n+1}{2}$ is also accepted).

For $n$ values shown in a histogram, which positions do you use to estimate the lower and upper quartiles?

The $\frac{n}{4}$ th and $\frac{3n}{4}$ th values.

e.g. for $n = 23$: $5.75$ and $17.25$

What is the formula for the interquartile range?

$\text{IQR} = \text{upper quartile} - \text{lower quartile}$

How do you find the median value once you know which bar it lies in?

e.g. $10$ more values needed into a bar of frequency $16$ covering $16 < t \le 20$

Go that fraction of the way across the interval and add it to the lower bound.

e.g. $16 + \frac{10}{16} \times 4 = 18.5$

True or false? The median of data in a histogram is the midpoint of the interval with the tallest bar.

False. You find the interval containing the $\frac{n}{2}$ th value using the bar areas, then use proportion within it.