Displaying and comparing data

Advanced Math 6 · Unit 13 · data-distributions-6 · Teacher edition

data-distributions-6

Name ______________________________Date ______________

1.
Which of these is a statistical question?
1. (A)
  How old am I?
2. (B)
  How tall is the principal?
3. (C)
  How many hours of sleep do sixth graders at our school get on a school night?
4. (D)
  What is $7 \times 8$ ?
2.
Find the median of $3,\ 7,\ 8,\ 12,\ 15,\ 20,\ 21$ .
Answer: ______________
3.
Find the interquartile range (IQR) of $3,\ 7,\ 8,\ 12,\ 15,\ 20,\ 21,\ 25$ .
Answer: ______________
4.
Five students' scores on a quiz were $2,\ 3,\ 3,\ 4,\ 40$ . Which is the better description of a typical score, and why?
1. (A)
  The mean, $10.4$ , because it uses every value
2. (B)
  The median, $3$ , because the $40$ pulls the mean far from where most scores are
3. (C)
  The range, $38$ , because it shows how different the scores are
4. (D)
  The mean, $10.4$ , because it is larger
5.
Find the mean absolute deviation (MAD) of $4,\ 8,\ 5,\ 7,\ 6$ .
Answer: ______________

Answer key — Displaying and comparing data

1.
(C)
How many hours of sleep do sixth graders at our school get on a school night?
data-distributions-6-01
Hours of sleep for sixth graders varies from student to student, so you collect data and describe the distribution. The other three have one fixed answer.
2.
12data-distributions-6-02
Seven values; the $4$ th is $\mathbf{12}$ , with $3, 7, 8$ below and $15, 20, 21$ above.
3.
13data-distributions-6-03
$Q_1 = 7.5$ , $Q_3 = 20.5$ , $IQR = 20.5 - 7.5 = \mathbf{13}$ . (Adding the quartiles gives $28$ , a common error.)
4.
(B)
The median, $3$ , because the $40$ pulls the mean far from where most scores are
data-distributions-6-04
Mean $= 52 \div 5 = 10.4$ — higher than four of the five scores, so it is not typical. The median, $3$ , sits where the data cluster; the outlier $40$ does not move it. The range measures spread, not a typical value.
5.
1.2data-distributions-6-05
Mean $= 6$ . Deviations: $\lvert 4-6 \rvert = 2$ , $\lvert 8-6 \rvert = 2$ , $\lvert 5-6 \rvert = 1$ , $\lvert 7-6 \rvert = 1$ , $\lvert 6-6 \rvert = 0$ . $MAD = \frac{2+2+1+1+0}{5} = \frac{6}{5} = \mathbf{1.2}$ .