Question

A psychologist wanted to study distraction and attention. To begin, 21 study participants were put in a room with many gadgets and gizmos and asked to take a quiz while waiting for the researcher to arrive with more instructions. Time (in seconds) was measured to determine how long until the participants became distracted by an object in the room:

16, 18, 22, 22, 23, 23, 24, 26, 29, 32, 34, 36, 42, 43, 46, 46, 49, 57

1.Compute the Median. Type your answer in numerals only

2. Compute the Lower Quartile. Type your answer in numerals only

3.Compute the Upper Quartile. Type your answer in numerals only

Answer 1

Answer

Data is provided in ascneding order for 18 students, so we can start our calculation without modifying the data.

(1) we know the formula for median when we even number of data values is given as

Median =

((n/2)term + ((n/2) +1)term)/2

where n = 18

so, we get

Median=

((18/2)term +((18/2)+1)term)/2- (9th + 10th)/:2

where 9th term = 29 and 10th term = 32

setting the values, we get

Median =

so, median is 30.5

(2) We have a total of 18 data values, so we will divide the data into two equal halves

So, we get 9 values in first half and 9 values in the second half

16, 18, 22, 22, 23, 23, 24, 26, 29

Now, total data values = 9, i.e. odd number

So, lower quartile = median of first half = [(n+1)/2]th term

where n = 9

so, we get

lower quartile =(9+1)/2 = 10/2 = 5th term

5th term = 23

So, lower quartile is 23

(3) we get 9 values in first half and 9 values in the second half

32, 34, 36, 42, 43, 46, 46, 49, 57

Now, total data values = 9, i.e. odd number

So, upper = median of second half = [(n+1)/2]th term

where n = 9

so, we get

upper quartile =(9+1)/2 = 10/2 = 5th term

5th term = 43

So, upper quartile is 43