The mean. The median. The quartiles. An stem and leaf diagram.

Question

Part 1: Explain briefly, in the context of statistical analysis, what is:

1. The mean

2. The median

3. The quartiles

4. An stem and leaf diagram

Hint: you can use examples, give descriptions, explain how you work it out …

Part 2: Here are the heights, in inches, of plants grown using two different kinds of fertilisers.

Organic fertiliser: 23, 18, 38, 52, 46, 9, 36, 39, 40, 49, 50, 42, 47

Chemical fertiliser: 42, 51, 36, 29, 12, 46, 30, 9, 18, 16, 23, 28, 24

1. Make an ordered stem-and-leaf diagram for each fertilizer

2. In each data, how many plants are higher than 40 inches?

3. Find the mean, the median, the lower and upper quartiles of each set of data

4. Which of the two fertilisers is more effective? Explain.

Answer 1

The mean is the sum of the values divided by the number of values

The median is the middle value in an ordered set of data

The first quartile is the 25th percentile, below which 25% of a ordered set of data lies.

The third quartile is the 75th percentile, below which 75% of a ordered set of data lies.

A stem and leaf plot presents quantitative data in a graphical format. Example

0 | 1 2 3 presents data values 1, 2, 3

1 | 3 5 presents data values 13, 15

2 ! 6 9 presents data values 26, 29

Organic fertiliser: 23, 18, 38, 52, 46, 9, 36, 39, 40, 49, 50, 42, 47

Chemical fertiliser: 42, 51, 36, 29, 12, 46, 30, 9, 18, 16, 23, 28, 24

Re-write the data in ascending order;

Organic fertiliser: 9, 18, 23, 36, 38, 39, 40, 42, 46, 47, 49, 50, 52

Chemical fertiliser: 9, 12, 16, 18, 23, 24, 28, 29, 30, 36, 42, 46, 51

Organic:

0 | 9

1 | 8

2 | 3

3 | 6 8 9

4 | 0 2 6 7 9

5 | 0 2

6 plants higher than 40 inches

Mean is 37.8

For any percentile, the slot number of the value is found by taking (percentile)/100 * (n+1), where n is the sample size. For example, for the 50th percentile or median and a sample size (n) of 13, the slot number would be 50/100 * (13 + 1) = 7.

Median is 7th value = 40

1st quartile is average of 3rd and 4th values = 29.5

3rd quartile is average of 10th and 11th values = 48

Chemical:

0 | 9

1 | 2 6 8

2 | 3 4 8 9

3 | 0 6

4 | 2 6

5 | 1

3 plants higher than 40 inches

Mean is 28

Median is 7th value 28

1st quartile is average of 3rd and 4th values = 17

3rd quartile is average of 10th and 11th values = 39

The organic fertilizer is more effective, as the mean and median growth are much greater.