Question

For the following sample of n 5 10 scores:

a. Assume that the scores are measurements of a discrete variable and find the median.
b. Assume that the scores are measurements of a continuous variable and find the median by locating the precise midpoint of the distribution.
Scores: 2, 3, 4, 4, 5, 5, 5, 6, 6, 7

Answer 1

Explanation:

Given that:

scores = 2, 3, 4, 4, 5, 5, 5, 6, 6, 7

Since the scores are already in ascending order; then the median which is the middle number will be:

median = (5th term + 6 term)/2

median = (5+5)/2

median = 10/2

median = 5

Answer 2

Explanation:

Given that:

scores = 2, 3, 4, 4, 5, 5, 5, 6, 6, 7

Since the scores are already in ascending order; then the median which is the middle number will be:

median = (5th term + 6 term)/2

median = (5+5)/2

median = 10/2

meian = 5

b)

Use the cumulative percentage table

X frequency cumulative frequency cumulative percentage

2 1 1 10%

3 1 2 20%

4 2 4 40%

5 3 7 70%

6 2 9 90%

7 1 10 100%

fraction = the no. required to reach 50%/ no. in that interval

= 1/3

Since we have a total of 4 boxes when we reach the value of 4.5

The median of the continuous variable = 4.5 + (1/3)

The median of the continuous variable = 4.833

The median of the continuous variable ≅ 5