Question

14. An animal researcher records the time (in seconds) it takes a group of maze-bright rats to complete a maze. Locate the lower median, and upper quartiles for the following times. Hint: Firstarrange the data in numerical order. 21 Time Frequency 4 3 6 8 12 6 N 16

Answer 1

Answer

We have 5 data values for the time recorded. It means that we have odd number of data values.

First, we need to arrange the data in ascending order or increasing order from smallest number to largest number.

4, 5, 6, 8, 12

Now, we have to find the median. Formula for median in case of odd number of data values is given as

Median = (n+1)/2 term

where n is the number of data values, so we have n = 5

setting the values, we get

Median= (5+1)/2 term = (6/2)th term = 3rd term = 6 (because 6 is the 3rd term in the given data values)

So, median is 6

Now, we will divide the data values into two parts excluding the median

so, we get 4,5 and 8,12, i.e. 2 data values in first half and 2 data values in second half

Formula for first quartile is given as average of 2 data values term

i.e. lower quartile = (n1+ n2)/2 = (4+5)/2 = 9/8 = 4.5

Similarly, upper quartile = average of two data values = (n1+n2)/2 = (8+12)/2 = 20/2 = 10

So, lower quartile is 4.5, median is 6 and upper quartile is 10