__Example 1:__

The stem and leaf plot below shows the grade point averages of 18 students. The digit in the stem represents the ones and the digit in the leaf represents the tenths. So for example 0 | 8 = 0.8, 1 | 2 = 1.2 and so on.

a) What is the range of the data in the stem and leaf plot?

b) How many students have a grade of 2 or more?

c) What is the mode of the grades?

d) What is the median of the grades?

__Solution to Example 1:__

a) range = maximum value - minimum value = 4.0 - 0.8 = 3.2

b) 7 + 4 + 1 = 12 students

c) two modes: 1.4 and 2.5

d) There are 18 data values and already ordered in the stem and leaf diagram.

median = (the 9th value + the 10th value) / 2 = (2.5 + 2.5) / 2 = 2.5

__Example 2:__

The back to back stem and leaf plot below shows the exam grades (out of 100) of two sections. The digit in the stem represents the tens and the digit in the leaf represents the ones. So for example 5 | 3 = 53 and so on.

a) How many students scored higher than 60 in section 1?

b) How many students scored higher than 60 in section 2?

c) What are the minimum and maximum scores in section 1?

d) What are the minimum and maximum scores in section 2?

e) Without counting, which section has more students scoring 80 or more?

f) Without counting, which section has more students scoring 50 or less?

__Solution to Example 2:__

a) 6 + 7 + 5 + 4 = 22 students

b) 8 + 6 + 2 + 2 = 18 students

c) minimum = 40 , maximum = 95

d) minimum = 41 , maximum = 91

e) section 1

f) section 2

__Example 3:__

The back to back stem and leaf plot below shows the LDL cholesterol levels (in milligram per deciliter mg/dL) of two groups of people, smokers and non smokers. The digits in the stem represents the hundreds and tens and the digit in the leaf represents the ones. So for example 11 | 8 = 118 and so on.

a) People with a cholesterol level of 129 or less are said to have a near ideal level of cholesterol. How many people, in each group, have a near ideal level of cholesterol?

b) People with a cholesterol level between 130 and 159 inclusive are said to be in the border high. How many people, in each group, are in the border high?

c) People with a cholesterol level between 160 and 189 inclusive are said to have a high level of cholesterol. How many people, in each group, have a high level of cholesterol?

d) People with a cholesterol level of 190 or above are said to have a very high level of cholesterol. How many people, in each group, have a very high level of cholesterol?

e) Comparing the two groups, which group has more people with a higher level of cholesterol?

__Solution to Example 3:__

a) smokers: 1 + 2 = 3 people , non smokers: 2 + 4 + 7 = 13 people

b) smokers: 3 + 4 + 5 = 12 people , non smokers: 7 + 6 + 3 = 16 people

c) smokers: 6 + 5 + 4 = 15 people , non smokers: 3 + 2 + 1 = 6 people

d) smokers: 3 + 2 = 5 people , non smokers: none

e) The group of smokers have more people with higher cholesterol.

### More References and links

elementary statistics and probabilities.

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