Gazer's Digest

MEASURES OF CENTER - USING THE STEM & LEAF DIAGRAM

Median, Mean, and Mode of data

March 07, 2021

To describe the center of a list of values, the most commonly used numerical measures are the mean and the median.

EXAMPLE  2

The heights (mm) of a different variety of plants are as follows.

65, 32, 40, 27, 35, 49, 53, 33, 47, 56, 45, 30, 48, 67, 56, 37, 56, 41, 38, 52

Let’s show the heights in an ordered (in increasing order) stem and leaf diagram.

STEM
LEAF
2
7
3
0
2
3
5
7
8
4
0
1
5
7
8
9
5
2
3
6
6
6
6
5
7

2 | 7 = represents 27 mm plant

 

MEDIAN

What is the median height?

You can use the stem and leaf diagram to find the middle value. Cross out the smallest and  the highest value from each end. The smallest value is 27 mm and the highest value is 67 mm.

STEM
LEAF
2
7
/
3
0
/
2
/
3
/
5
/
7
/
8
/
4
0
/
1
/
5
7
8
/
9
/
5
2
/
3
/
6
/
6
/
6
/
6
5
/
7
/

There are two center values in the ordered stem and leaf diagram, 45 and 47.

(45 + 47) ÷ 2 = 46 mm is the median.

 

MODE

What is the most frequently occurring height? 56 appears three times, the other heights appear only once.

STEM
LEAF
2
7
3
0
2
3
5
7
8
4
0
1
5
7
8
9
5
2
3
6
6
6
6
5
7

56 mm is the mode.

 

MEAN

What is the average height?

27 + 30 + 32 + 33 + 35 + 37 + 38 + 40 + 41 + 45 + 47 + 48 + 49 + 52 + 53 + 56 + 56 + 56 + 65 + 67 = 907

907 ÷ 20 = 45.35

45.35 mm is the mean.

 

 

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