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Statistics Worksheets - Page 3

Online Statistics Worksheets 
Statistics Worksheets
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 21.  
The frequency distribution of the highest temperatures (in °F) in 50 states during a season is shown. Find the percentile rank for a temperature of 117.5°F by constructing a percentile graph.
TemperaturesNumber of states
99.5 - 104.52
104.5 - 109.58
109.5 - 114.518
114.5 - 119.513
119.5 - 124.57
124.5 - 129.51
129.5 - 134.51

a.
65th percentile
b.
55th percentile
c.
60th percentile
d.
40th percentile


Solution:

Compute the cumulative frequencies for each class (Temperature).

Compute cumulative percents for each class by using cumulative percent = cumulative frequencyTotal frequency × 100%

For first class, cumulative % = 250 × 100% = 4%


Tabulate the results


Draw a graph with the class boundaries on x - axis and the corresponding cumulative percents on y - axis as shown in the graph.

To find the percentile rank for a temperature of 117.5°F, find 117.5 on the x - axis of the percentile graph, and draw a vertical line to the graph. Then move horizontally to the value on the y - axis.

So, the approximate percentile rank for a temperature of 117.5°F is 60th percentile.


Correct answer : (3)
 22.  
Check the following data set for outliers.
25, 43, 16, 4, 11, 39, 28, 8
a.
no outlier
b.
43
c.
86
d.
4


Solution:

Arrange the data values in increasing order.
4, 8, 11, 16, 25, 28, 39, 43

Q2 = 16+25 / 2= 20.5
[Q2 is the median, which is the mean of the middle values of the data set in the order.]

Q1 = 8+11 / 2= 9.5
[Q1 is the median of the data values less than Q2.]

Q3 = 28+39 / 2= 33.5
[Q3 is the median of the data values greater than Q2.]

Interquartile Range (IQR) = Q3 - Q1= 33.5 - 9.5 = 24

To find the outlier, compute the cut-off points for outliers.

Lower fence = Q1 - 1.5(IQR) = 9.5 - 1.5(24) = - 26.5

Upper fence = Q3 + 1.5(IQR) = 33.5 + 1.5(24) = 69.5

If a data value is less than the lower fence or greater than the upper fence, then it is considered an outlier.

There are no values that are less than - 26.5 or greater than 69.5.

So, there is no outlier.


Correct answer : (1)
 23.  
Find Q1, Q2 and Q3 for the data set.
9, 3, 2, 5, 4, 7, 6, 11, 13.
a.
Q1 = 4.5, Q2 = 6 and Q3 = 10
b.
Q1 = 3.5, Q2 = 6 and Q3 = 11
c.
Q1 = 3.5, Q2 = 7 and Q3 = 10
d.
Q1 = 3.5, Q2 = 6 and Q3 = 10


Solution:

Arrange the data in increasing order.
2, 3, 4, 5, 6, 7, 9, 11, 13

Median = 6.
[Median is the middle value of the data set in the order.]

So, Q2 = 6
[Q2 is the median.]

The median of the data values less than 6 (median) is Q1.

The data values that are less than 6 (median) are 2, 3, 4, 5.

Q1 = 3+4 / 2 = 3.5

The median of the data values greater than 6 (median) is Q3.

The data values that are greater than 6 (median) are 7, 9, 11, 13.

Q3 = 9+11 / 2 = 10.

So, Q1 = 3.5, Q2 = 6 and Q3 = 10.


Correct answer : (4)
 24.  
Amy recorded the number of different flowers used in a bouquet. Which measure of central tendency is most appropriate to describe the data ?
a.
mode
b.
mean
c.
outlier
d.
median


Answer: (a)


Correct answer : (1)
 25.  
Which measure of central tendency is most appropriate for a data that describes the shoe size of the students of your class?
a.
outlier
b.
mode
c.
mean
d.
median


Answer: (c)


Correct answer : (3)
 26.  
Use the stem-and-leaf plot to find the number of data items in the interval 20 - 69.


a.
18
b.
14
c.
20
d.
17


Answer: (d)


Correct answer : (4)
 27.  
The line plot shows the number of chocolates that each student of a class has. How many more chocolates does Smith have than Catherine?

a.
5
b.
3
c.
4


Answer: (a)


Correct answer : (1)
 28.  
Which line plot displays the data set 45, 49, 53, 54, 57, 49, 58, 52 accurately?

a.
Plot 1
b.
Plot 2
c.
Plot 3
d.
Plot 4


Answer: (c)


Correct answer : (3)
 29.  
Which measure of central tendency is most appropriate for a data that describes the favorite color of 5 girls: blue, red, red, green, orange?
a.
outlier
b.
median
c.
mode
d.
mean


Answer: (c)


Correct answer : (3)
 30.  
Which measure of central tendency is most appropriate for the data listed?
        0, 0, 0, 1, 1, 1, 1, 2, 2, 2
a.
median
b.
mean
c.
mode
d.
all of these


Answer: (d)


Correct answer : (4)

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