Finding the Mean

Question

For the following three questions, a team of psychologists studying narcolepsy (a sleep disorder characterized by sudden nodding off during the day) decided to follow 20 narcoleptic volunteers throughout the course of one day and record how many times they each fell asleep. The data they collected have been arranged in the following simple frequency distribution:

Number of times asleep	f
7	2
6	1
5	3
4	5
3	3
2	4
1	2
N=20

Answer 1

Hi Nitara! Great question. It sounds like this question is asking you to interpret data from a frequency table, which can be a little bit non-intuitive if you're not used to seeing numbers presented this way. Basically, the key to understanding this is understanding that "f" column is telling us the number of times we see each observation in the data. In other words, we can re-write the table as follows:

Number of times fallen asleep: Number of people who fell asleep this many times (f):

7 times 2

6 times 1

5 times 3

4 times 5

3 times 3

2 times 4

1 time 2

There are two ways I might approach this:

I) Put the observations in a list and sum it explicitly, then divide by 20. Let's re-write this data again in a list format you're likely more used to. The table above is telling me that there are two 7s, one 6, three 5s, five 4s, three 3s, four 2s, and two 1s:

7 7 6 5 5 5 4 4 4 4 4 3 3 3 2 2 2 2 1 1

We know that there are 20 observations, so we can calculate the average directly by taking the sum of the above list and dividing by 20.

Sum of list above: 74

Average: 3.7

II) Use multiplication to find the sum, then divide by 20. The sum can also be calculated by multiplying each cell of the rows together, then taking the sum of the results. Here's what that would look like:

Number of times fallen asleep: f Product of columns:

7 times 2 7 x 2 = 14

6 times 1 6 x 1 = 6

5 times 3 5 x 3 = 15

4 times 5 4 x 5 = 25

3 times 3 3 x 3 = 12

2 times 4 2 x 4 = 8

1 time 2 1 x 2 = 2

Sum of third column = 74

Average = 82/20 = 3.7

Hope this helps! :)