Question

The water tax bills (in rupees) of 30 houses in a locality are given below. Find the range : 30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88, 40, 14, 20,15, 35, 44, 66, 75, 84, 95, 96,102,110, 88, 74, 112, 14, 34, 44 \[\]

Answer 1

Hint: We recall the definition of range of data sample as a difference of maximum data value and minimum data value. We arrange the given data values in ascending order and find the maximum data value and minimum data value and then subtract minimum data value from maximum data value. \[\]

Complete step-by-step answer:
We know that when we arrange the data from smallest to highest we call the process sorting in ascending order and when we arrange the data from highest to smallest we call the process sorting in descending order. \[\]
We know that a data sample is data obtained with a finite number of experiments and outcomes of each experiment is called data values. The outcomes here are the water tax bills (in rupees) of 30 houses in a locality which are given as 30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88, 40, 14, 20,15, 35, 44, 66, 75, 84, 95, 96,102,110, 88, 74, 112, 14, 34, 44. \[\]
We know that that range of the data sample is the difference between maximum data value and minimum data value. Let us arrange the given data values in ascending order. We have: 14,14,15,20,30,32,34,35,40,44,44,45,54,66,66,74,74,75,76,78,84,88,88,95,96,102,108,110,112,112. \[\]
So the maximum data value is 112 and minimum data value is 14. So the range is $ 112-14=98 $ . \[\]

Note: We note that we can also solve by arranging the data in descending order. The range of the data sample helps the observer to evaluate maximum and minimum cost for the operation of population size. The number of times a data value appears in the data sample is called its frequency.