The range of the numbers of legs in the image is 120, and the interquartile range is 80. This means that the middle 50% of the data is between 40 and 120 legs.
The range is the difference between the largest and smallest values in the data set. In this case, the largest value is 120 and the smallest value is 40, so the range is 120 - 40 = 80.
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). The third quartile is the median of the upper half of the data set, and the first quartile is the median of the lower half of the data set.
To find the IQR, we first need to find the median of the entire data set. The median is the middle value when the data is arranged in order, or the mean of the two middle values if there are an even number of values. In this case, the median is 80.
Next, we need to find the medians of the upper and lower halves of the data set. To do this, we split the data set in half at the median. The upper half of the data set is {80, 120}, and the lower half of the data set is {40, 80}.
The median of the upper half of the data set is 120, and the median of the lower half of the data set is 40. Therefore, the IQR is 120 - 40 = 80.
The box plot above shows the distribution of the numbers of legs. The IQR is represented by the length of the box. As you can see, the IQR is 80, which means that the middle 50% of the data is between 40 and 120 legs