FINDING MAXIMUM AND MINIMUM VALUES FROM STEM AND LEAF PLOT

Problem 1 :

a)  Determine the minimum value, maximum value and range of the data.

b)  How many values are greater than 190?

c)  How many values are less than 151?

Solution :

a)  By observing the data values from stem and leaf plot, it is arranged from smaller to larger.

Minimum value = 136

Maximum value = 228

Range = largest value - smallest value

= 228 - 136

Range = 92

b) There are 7 values greater than 190.

c) 5 values are lesser than 151.

Problem 2 :

a)  Determine the minimum value, maximum value and range of the data

b)   How many values are greater than 163?

c)  How many values are less than 177?

Solution :

a)  By observing the data values from stem and leaf plot, it is arranged from smaller to larger.

Minimum value = 121

Maximum value = 218

Range = largest value - smallest value

= 218 - 121

Range = 97

b) There are 18 values greater than 163.

c) 12 values are lesser than 177.

Problem 3 :

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

a) the minimum weight

b) the maximum weight

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

Solution :

a) Minimum weight = 32

b) Maximum weight = 91

c) Number of students with the weight lesser than 48 kg = 7

Converting as fraction = 7/35

Converting as percentage = (7/35) x 100%

= 0.2 (100%)

= 20%

Problem 4 :

For the data set given, find

a) the minimum value    b)  the maximum value

c) the median    d)  The lower quartile

e) the upper quartile   f) the range

g) the interquartile range.

Solution :

a) the minimum value = 3

b)  the maximum value = 42

c) the median

Total number of elements = 23

Median = (23 + 1)/2 ^th element

= 12^th element

Median = 20

d)  The lower quartile 

lower part has 11 elements.

= (11 + 1)/2 ^th element

= 6^th element

Lower quartile = 13

e) the upper quartile

Upper part has 11 elements.

= (11 + 1)/2 ^th element

= 6^th element

upper quartile = 29

f) the range

Range = Largest value - smallest value

= 42 - 3

= 39

g) the interquartile range = IQ₃ - IQ₁

= Upper quartile - lower quartile

= 29 - 13

= 16