الأسبوع 12 · رسم المدرجات التكرارية والمخطط الصندوقي واختيار التمثيل · 3 دروس
3
Choosing the best display for a question
Discover Mathematics P6: Term 1, Unit 6, Lessons 3–5
GoalCompare a dot plot, a histogram and a box plot of the same data and choose the display that answers a question best.
New words
display · a picture of data such as a dot plot, histogram or box plotspread · how far apart the data values arecompare · to look at two data sets side by side
Explanation
Each display tells a different story. A dot plot shows every single value, so it is best for small data sets and for questions such as “Which value is the most common?” A histogram groups the values into intervals, so it is best for large data sets and for the overall shape. A box plot shows the five-number summary, so it is best for the centre and the spread, and for comparing two groups; but it hides the individual values and the number of values. To choose, read the question first and ask what you need to see.
Display
Shows best
Hides
Dot plot
every value, peak, gaps
nothing, but gets crowded
Histogram
overall shape of many values
exact values
Box plot
centre and spread, comparing groups
shape details and the count
Worked examples
Eleven pupils gave the minutes they study each day: 10, 15, 15, 20, 20, 20, 25, 25, 30, 35, 45. In the dot plot we see each value: the peak is 20 minutes (3 pupils) and there is a gap at 40.
The same data in a histogram with the width 10: 3 pupils in 10–19, 5 in 20–29, 2 in 30–39 and 1 in 40–49 (3 + 5 + 2 + 1 = 11). We see the overall shape, a peak in 20–29 and a tail to the right, but not the exact values.
The same data in a box plot: minimum 10, Q1 = 15, median 20, Q3 = 30, maximum 45. We see at once that half of the pupils study between 15 and 30 minutes, but we cannot tell how many pupils there are.
Class
Min
Q1
Median
Q3
Max
A
10
20
30
40
50
B
20
25
30
35
40
Two classes timed how long they take to get to school. Both have the median 30 minutes, but the box of Class A (from 20 to 40) is longer than the box of Class B (from 25 to 35). So the times of Class A are more spread out, while Class B pupils are more alike. Side-by-side box plots are the best display for this question.
Class activity
Which display? A grown-up reads five questions about data (for example: “Which shoe size is the most common in the class?”, “How are the ages of 300 people spread?”). For each one, you say dot plot, histogram or box plot, and explain in one sentence.
Practice
1
Choose the best display: (a) which exact quiz score appears most among 12 pupils, (b) the grouped heights of 200 pupils, (c) the median and spread of two classes’ travel times.
(a) a dot plot, (b) a histogram, (c) box plots side by side.
2
In this box plot of study times, Seif says: “More than half of the pupils studied longer than 30 minutes.” Is he right?
No. The median is 30, so about half studied 30 minutes or less and about half studied more. It is not more than half.
3
Which of the three displays cannot tell you how many pupils were asked?
The box plot: it shows only five summary numbers.
4
Rana says: “The histogram shows that the highest score is exactly 49.” Is she right?
No. A histogram only shows that the highest score is in the last interval, for example 40–49.
5
The dot plot shows the number of goals in 12 matches. Write its five-number summary.
