DRAW THE STEM AND LEAF PLOT FOR THE DATA SET

Problem 1 :

Here are the ages of 14 adults.

42     35     56     39     40     51     47

38     42     55     42     48     49     41

Draw an ordered stem and leaf diagram for these ages.

Solution :

Let us write the ages in the data in ascending order.

35, 38, 39, 40, 41, 42, 42, 42, 47, 48, 49, 51, 55, 56

Problem 2 :

Helen plays darts.

Here are her scores.

55     23     48     29     41     47     36

                   35     40     35     44     34     35

a) Draw an ordered stem and leaf diagram to show her scores.

b) Write down the mode.

c) Work out the range.

Solution :

a)

Let us write the scores in the data in ascending order.

23, 29, 34, 35, 35, 35, 36, 40, 41, 44, 47, 48, 55

b) Mode:

Mode = 35 score

c) Range:

Range = Large value - Small value

= 55 - 23

Range = 32 score

Problem 3 :

Here are the lengths in millimeters of 15 earthworms.

43     19     35     28     21

28     28     18     24     33

31     36     12     41     28

a) Complete an ordered stem and leaf diagram to show this information.

b) How many earthworms are over 40 millimeters?

c) Write down the mode.

d) What fraction of the earthworms are under 20 millimeters?

Solution :

a)

Let us write the observations in the data in ascending order.

12, 18, 19, 21, 24, 28, 28, 28, 28, 31, 33, 35, 36, 41, 43

b) 2 earthworms are over 40 millimeters.

c) Mode:

Mode = 28

d)

3 earthworms are under 20 millimetres.

Fraction = 3/15

= 1/5

Problem 4:

The number of people visiting a café each day, for 11 days, is listed below.

104     131     120     115     109     124    

128     118     116     120     125

a) Complete an ordered stem and leaf diagram for this information. A key has been included.

b) Write down the mode.

c) Write down the median.

d) Write down the range.

Solution :

a)

Let us write the observations in the data in ascending order.

104, 109, 115, 116, 118, 120, 120, 124, 125, 128, 131

Key: 10|4 means 104

b) Mode :

Mode = 120

c) Median :

Median = 120

d) Range :

Range = Large value - Small value

= 131 - 104

Range = 27

Problem 5 :

The number of passengers on 10 buses was recorded. The stem and leaf diagram shows this information.

a) Work out the median.

A bus is selected at random.

b) What is the probability the bus has more than 20 passengers?

The next bus has 32 passengers.

c) Find the range.

Solution :

7, 9, 14, 15, 16, 18, 18, 21, 23, 30

a)   Median:

Median = (16 + 18) / 2

= 34/2

Median = 17

b) P (more than 20 passengers) = 3/10

c) Tick the box to show how this will effect the range.

Range = large value - small value

30 - 7 = 23

So, the range is 23.

Problem 6 :

The weights of books on a shelf are recorded in a stem and leaf diagram.

Key: 0|1 means 0.1 kg

(a) Write down the median.

(b) Work out the total weight of books on the shelf.

A book weighting 1.8 kg is added to the shelf.

Peter says the median will remain the same.

(c) Is peter correct? Explain your answer.

Solution :

0.1, 0.1, 0.1, 0.2, 0.2, 0.3, 0.4, 0.4, 0.5, 1.0, 1.0, 1.2, 1.3, 1.7, 2.2

a) Median

Median = 0.4 kg

b)

Total weight = 0.1+ 0.1+ 0.1+ 0.2 + 0.2 + 0.3 + 0.4 + 0.4 + 0.5 + 1.0 + 1.0 + 1.2 + 1.3 + 1.7 + 2.2

= 10.7 kg

c)  No, it would increase to 0.45 kg.