HOW TO FIND MINIMUM AND MAXIMUM VALUE OF STEM AND LEAF PLOT

Problem 1 :

The test score out of 40 marks was recorded for a group of 30 students:

25   18   35   32   34   28   24   39   29   33

22   34   39   31   36   35   36   33   35   40

26   25   20   18   9     40   32   23   28   27

a) Construct a stem-and-leaf plot for this data using 0, 1, 2, 3 and 4 as the stems.

b) Redraw the stem-and-leaf plot so that it is ordered.

c) What advantage does the stem-and-leaf plot have over a frequency table?

d) What was the

i. highest

ii. lowest mark scored for the test?

e) If an 'A' was awarded to students who scored 36 or or more for the test, what percentage of students scored an 'A'?

Solution:

a)

b)

c)  The stem and leaf plot displays all the actual data values.

d) 

Highest mark = 40

Lowest mark = 9

e) 

Score 36 or more = 6 students

Percentage = (6/30) × 100

= 20%

Problem 2 :

For the following sample of weights (in kg) of year 10 students, find:

a) the minimum weight

b) the maximum weight

c) the number of students with a weight greater than 52 kg

d) the number of students with a weight of at least 70 kg

e) the percentage of students with a weight less than 48 kg.

Solution:

a) The minimum weight is 32 kg.

b) The maximum weight is 91 kg

c) The number of students with a weight greater than 52 kg is 20.

d) The number of students with a weight of at least 70 kg is 5.

e) The percentage of students with a weight less than 48 kg 

= (7/35) × 100

= 20%

Problem 3 :

The data below is the scores (out of 100) for a Mathematics examination for 45 students.

a) Construct a stem and leaf plot for this data using 3, 4, 5, 6, 7, 8 and 9 as the stems.

b) Redraw the stem and leaf plot so that it is ordered.

c) What advantages does a stem and leaf plot have over a frequency table?

d) What is the

i. highest

ii. lowest mark scored for the examination?

e) If an 'A' was awarded to students who scored 85 or more for the examination, what percentage of students scored an 'A' ?

f) Would you describe this distribution as:

i. symmetric    ii. skewed      iii. neither symmetric nor skewed?

Solution:

a)

b)

c)

The stem and leaf plot displays all the actual data values.

d)

 Highest mark = 97.

 Lowest mark = 31

e)

Score 85 or more = 9 students

= (9/45) × 100

= 20%

f) By observing the shape from the stem and leaf plot, it is not symmetric, it is positively skewed.