Deck 2: Data Representation

Question 1

A sample distribution of variable X is as follows:

$\begin{array}{cc}X & f \\\hline 2 & 2 \\5 & 5 \\6 & 8 \\8 & 3 \\10 & 4 \\12 & 6 \\15 & 1 \\18 & 5 \\20 & 7 \\\hline\end{array}$

Calculate or draw each of the following for the sample distribution of X. Where possible, Use SPSS to generate the data.
a. Frequency distribution
b. Cumulative relative frequency distribution
c. Histogram (ungrouped)
d. Frequency polygon
e. Q₁
f. Q₂
g. Q₃
h. P₁₀ and P₉₀
i. Box-and-whisker plot

Answer 1

c.
d. frequency polygon

h. P10 and P90
i. box-and-whisker plot

Question 2

A sample distribution of variable X is as follows:

$\begin{array}{cc}X & f \\\hline 15 & 5 \\\hline & \\20 & 3 \\24 & 1 \\28 & 4 \\32 & 2 \\34 & 7 \\36 & 3 \\38 & 8 \\40 & 4 \\\hline\end{array}$
Calculate or draw each of the following for the sample distribution of X. Where possible, use SPSS to generate the data.
a. Frequency distribution
b. Cumulative relative frequency distribution
c. Histogram (ungrouped)
d. Frequency polygon
e. Q₁
f. Q₂
g. Q₃
h. P₁₀ and P₉₀
i. Box-and-whisker plot

Answer 2

c. histogram (ungrouped)

d. frequency polygon

h. P₁₀ and P₉₀

i. box-and-whisker plot

Question 3

A sample distribution of variable X is as follows:

$\begin{array}{cc}X & f \\\hline 75 & 8 \\78 & 5 \\79 & 7 \\81 & 3 \\83 & 6 \\85 & 5 \\86 & 10 \\88 & 5 \\90 & 3 \\\hline\end{array}$
Calculate or draw each of the following for the sample distribution of X. Where possible, use SPSS to generate the data.
a. Frequency distribution
b. Cumulative relative frequency distribution
c. Histogram (ungrouped)
d. Frequency polygon
e. Q₁
f. Q₂
g. Q₃
h. P₁₀ and P₉₀
i. Box-and-whisker plot

Answer 3

c. histogram (ungrouped)

d. frequency polygon

h. P₁₀ and P₉₀

i. box-and-whisker plot

Question 4

A sample distribution of variable X is as follows:

$\begin{array}{cc}X & f \\\hline 100 & 4 \\110 & 8 \\115 & 2 \\120 & 6 \\125 & 10 \\130 & 5 \\135 & 7 \\140 & 3 \\145 & 1 \\\hline\end{array}$
Calculate or draw each of the following for the sample distribution of X. Where possible, use SPSS to generate the data.
a. Frequency distribution
b. Cumulative relative frequency distribution
c. histogram (ungrouped)
d. Frequency polygon
e. Q1
f. Q2
g. Q3
h. P10 and P90
i. Box-and-whisker plot

Question 5

Among the following, what is the preferred method for graphing data pertaining to favorite types of dance of a sample?

A) Bar graph
B) Cumulative frequency polygon
C) Frequency polygon
D) Histogram

Question 6

In examining data collected over the past ten years, researchers at Sea World find that of 1,000 first-time guests: 452 visited during the summer months; 231 visited during the fall; 104 visited during the winter; and 213 visited during the spring. What is the relative frequency for guests who visited during the spring?

A) .45
B) .23
C) .21
D) .10

Question 7

Of 100 research participants, 10 are in group A, 22 in group B, 30 in group C, and 38 in group D. What is the relative frequency for participants in group D?

A) .010
B) .022
C) .030
D) .038