Question

3. Ten college students watch 3 half-hour news programs. Then, they are asked to recall as many of the news items as they can remember. Listed is the number of items they recalled.

1 7 4 3 4 4 3 8 5 2

a. (6 points) What is the mean? The median? The mode?

b. (8 points) The range? The variance? The standard deviation?

Answer 1

(a)

(i)

Mean () is given by:

(ii)

Arranging numbers in ascending order, we get:

1,2,3,3,4,4,4,5,7,8

n = 10

Median is (10+1)/2th item = Average of 5th & 6th items = (4 + 4)/2 = 4

So,

Median = 4

(iii)

Mode = 4

since 4 occurs the maximum number of times.

(b)

(i) Range = Maximum - Minimum

            = 8 - 1 = 7

So,

Range = 7

(ii)

From the given data, the following Table is calculated:

x	(x - )	(x - )2
1	- 3.1	9.61
7	2.9	8.41
4	- 0.1	0.01
3	- 1.1	1.21
4	- 0.1	0.01
4	- 0.1	0.01
3	- 1.1	1.21
8	3.9	15.21
5	0.9	0.81
2	- 2.1	4.41
Total =		40.9

Variance (s²) is given by:

So,

The variance = 4.5444

(iii)

The standard deviation =