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The students in a 2012 Leaving Certificate class decided to investigate their heights - Leaving Cert Mathematics - Question 6 - 2012
Question 6
The students in a 2012 Leaving Certificate class decided to investigate their heights. They measured the height of each student, in centimetres, and the results were... show full transcript
Worked Solution & Example Answer:The students in a 2012 Leaving Certificate class decided to investigate their heights - Leaving Cert Mathematics - Question 6 - 2012
Step 1
(i) Construct a stem and leaf plot of the above data.
Answer
To construct a stem-and-leaf plot, we first separate the data into stems and leaves. The stems will represent the tens places of the heights, while the leaves will represent the units.
Stem and Leaf Plot
1 | 5 6 6 6 7 7 7 8 8
1 | 6 7 7
1 | 7 8 8
1 | 8 8
2 | 0 2 6
The key indicates that the stem (1) and leaves (5, 6, 6, etc.) together represent heights like 149 cm, 167 cm, etc.
Step 2
(ii) Describe the distribution of the data, by making one statement about each of the three characteristics indicated below.
Answer
Shape of Distribution: The distribution of the heights appears to be roughly symmetrical with a slight positive skew.
Location of Data (Central Tendency / Average): The average height can be calculated to determine the central tendency, which is approximately 171 cm.
Spread of Data (Dispersion): The heights range from a minimum of 149 cm to a maximum of 187 cm, indicating a moderate spread.
Step 3
(iii) State one additional piece of information that you would need in order to decide whether these students are unusually tall?
Answer
To determine if these students are unusually tall, we would need information about the average height of the population of students from which this group is drawn.
Step 4
(i) Construct a back-to-back stem and leaf plot of the above data.
Answer
To create a back-to-back stem-and-leaf plot, we will again separate the data into stems and leaves for both males and females. The left side will represent males and the right side will represent females.
Back-to-Back Stem and Leaf Plot
Males | Females
1 | 7 7 8 8 0 | 1 1 6 6
1 | 5 7 6 6 | 4 6 7 7 7
This plot provides a clear visual comparison between the two groups.
Step 5
(ii) State one difference and one similarity between the two distributions.
Answer
Difference: The male heights generally show a higher central tendency compared to female heights.
Similarity: Both distributions exhibit similar ranges of height, indicating that both groups have comparable extremes.