Question

The table below shows the mass (in kg) of the first 11 fish caught on a fishing trip.
(a) For the above data find the mean, median, mode, range, quartiles and interquartile range.

Answer 1

Answer:

To calculate the range, you need to find the largest observed value of a variable (the maximum) and subtract the smallest observed value (the minimum). The range only takes into account these two values and ignore the data points between the two extremities of the distribution. It's used as a supplement to other measures, but it is rarely used as the sole measure of dispersion because it’s sensitive to extreme values.

The interquartile range and semi-interquartile range give a better idea of the dispersion of data. To calculate these two measures, you need to know the values of the lower and upper quartiles. The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. The upper quartile, or third quartile (Q3), is the value under which 75% of data points are found when arranged in increasing order. The median is considered the second quartile (Q2). The interquartile range is the difference between upper and lower quartiles. The semi-interquartile range is half the interquartile range.