STATISTIC AND PROBABILITY

Question

A random sample of 60 students in the business statistics course answered a survey on the

average number of hours they spent on statistics each week. Unfortunately, the original data were

lost, and all that remains is the frequency table below. From these data, calculate the estimated

sample mean. Show the complete calculation steps.

CLASS	HOURS	N
1	0-3	18
2	4-7	16
3	8-11	14
4	12-15	10
5	16-19	2

Answer 1

Hi Umi! Good question - thankfully, all we need is a frequency table to come up with an estimate.

Since we don't know anything about the exact number of hours each person studied (except the range given in this table), I'd start by calculating the midpoint of each range. In particular, what's the value that's exactly between the endpoints of each category? Remember, we calculate the halfway point between two numbers by adding them together and dividing them by two:

HOURS	MIDPOINT	N
0-3	(3+0)/2 = 1.5	18
4-7	(7+4)/2 = 5.5	16
8-11	(11+8)/2 = 9.5	14
12-15	(15+12)/2 = 13.5	10
16-19	(19+16)/2 = 17.5	2

Now note that the column "N" denotes the number of times we see an observation that corresponds to a certain category. That means that we see eighteen observations between 0 and 3 hours, sixteen observations between 4-7 hours, fourteen observations between 8 and 11 hours, ten observations between 12 and 15 hours, and two observations between 16 and 19 hours.

Now, all we need to do is multiply each "MIDPOINT" and "N" value within a given row, and then take the sum:

MIDPOINT	N	MIDPOINT x N
1.5 (0-3 hours)	18	1.5 x 18 = 27
5.5 (4-7 hours)	16	5.5 x 16 =88
9.5 (8-11 hours)	14	9.5 x 14 = 133
13.5 (12-15 hours)	10	13.5 x 10 = 135
17.5 (16-19 hours)	2	17.5 x 2 = 35

Now, let's add the last column together: 27 + 88 + 133 + 135 + 35 = 418.

We've now estimated the total number of hours that the students have spent studying all together. Now, to get the average, we simply divide by the total number of students in the class. In this problem, we get that number by simply adding the N column together: 18+16+14+10+2 = 60.

Our final answer, therefore, is 418/60 = about 7.

Hope this helps!