ACT Math : Data Analysis

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #54 : Statistics

A group of 8 friends collect baseball cards. After years of collecting the students count how many cards they personally own. The quantity of each collection is listed as follows:

\displaystyle 112, 160, 64, 25, 115, 12, 184, 64.

What is the mean value of baseball cards each friend owns?

Possible Answers:

\displaystyle 64

\displaystyle 112

\displaystyle 92

\displaystyle 172

\displaystyle 82

Correct answer:

\displaystyle 92

Explanation:

To find the arithmetic mean, you simply add up all of the data and divide by the number of data points there are.

In this case there are 8 data points. 

\displaystyle \frac{112+160+64+ 25+ 115+ 12+184+ 64}{8}=92.

Example Question #51 : How To Find Arithmetic Mean

For a fundraiser, six students attempt to collect as many canned goods as possible. After a week of collecting, student individually collected the following amounts of cans:

\displaystyle 18, 8, 10, 2, 8, 8.

What is the mean value of cans collected per student?

Possible Answers:

\displaystyle 9

\displaystyle 4

\displaystyle 10

\displaystyle 8

\displaystyle 16

Correct answer:

\displaystyle 9

Explanation:

To find the arithmetic mean, you simply add up all of the data and divide by the number of data points there are.

In this case there are 6 data points. 

\displaystyle \frac{18+ 8+ 10+ 2+ 8+ 8}{6}=9.

Example Question #52 : How To Find Arithmetic Mean

The day of the month that seven students were born on is recorded below (note, the month they were born is irrelevant, only the day of the month matters):

\displaystyle 1,20,9,17,18,18,31

what is the average day of the month the students were born on? Round your answer to the nearest tenth if necessary.

Possible Answers:

\displaystyle 16.3

\displaystyle 18

\displaystyle 16.2

\displaystyle 1

\displaystyle 31

Correct answer:

\displaystyle 16.3

Explanation:

The arithmetic average is found by calculating the sum of the given data set, then dividing by the total number of numbers in the data set:

\displaystyle \\\frac{1+20+9+17+18+18+31}{7} \\= 16.286 \\= 16.3

Example Question #71 : Data Analysis

A sequence of five unknown numbers follows the following pattern:

\displaystyle x+2

\displaystyle x+1

\displaystyle x

\displaystyle x-1

\displaystyle x-2

If the average of this sequence is \displaystyle 25, what is \displaystyle x?

Possible Answers:

\displaystyle 25

\displaystyle 10

\displaystyle -5

\displaystyle 5

\displaystyle 0

Correct answer:

\displaystyle 25

Explanation:

The average of a set of numbers involves adding up all of the numbers and dividing by the number of terms:

\displaystyle average = \frac{total sum}{number\: of\: terms}

In this problem, since we do not know what the values are, we add the sequence in terms of \displaystyle x.  

\displaystyle \frac{(x+2) + (x-1) +(x) + (x-1) + (x-2)}{5} 

\displaystyle \frac{x+2+x-1+x+x-1+x-2}{5}=\frac{5x}{5}=25. 

Therefore, \displaystyle x=25.

Example Question #61 : Statistics

Find the mean of the following set of numbers.

\displaystyle \textup{2,5,6,8,9,11,15}

Possible Answers:

\displaystyle 2

\displaystyle 15

\displaystyle 13

\displaystyle 8

Correct answer:

\displaystyle 8

Explanation:

To find mean, simply total the numbers and divide by 7.

\displaystyle \textup{mean}=\frac{2+5+6+8+9+11+15}{7}=\frac{56}{7}=8

Example Question #62 : Statistics

Find the mean of the following set of numbers:

\displaystyle 3,5,8,9,11,12,15,17

Possible Answers:

\displaystyle 9

\displaystyle 15

\displaystyle 10

\displaystyle 11

Correct answer:

\displaystyle 10

Explanation:

To find the mean, simply sum all of the numbers and divide by how many there are.

Thus,

\displaystyle \frac{3+5+8+9+11+12+15+17}{8}=10

Example Question #71 : Data Analysis

Find the mean of the following set of numbers:

\displaystyle \textup{1,1,5,6,8,9}

Possible Answers:

\displaystyle 1

\displaystyle 5

\displaystyle 8

\displaystyle 10

\displaystyle 6

Correct answer:

\displaystyle 5

Explanation:

To find the mean, simply sum up the numbers and divide by the amount there are. Thus,

\displaystyle \textup{mean}=\frac{1+1+5+6+8+9}{6}=5

Example Question #64 : Statistics

Restaurant

From the menu above, what is the average price of a sandwich?  Round to the nearest cent.

Possible Answers:

$5.03

$4.99

$5.09

$5.07

$5.11

Correct answer:

$5.07

Explanation:

Average  = Sum of the Options / # of Options

= (4.75 + 5.25 + 4.75 + 4.50 + 5.00 +5.25 + 6.00) / 7 = 35.50 / 7 = 5.07

Example Question #1 : Median

Gradechart

Refer to the chart above. What is the Median of Exam 1?

Possible Answers:

83

82

85

84

79

Correct answer:

82

Explanation:

To find the median, one must arrange all the heights from the lowest to the highest value and then pick the middle value.

All Values: 82 72 75 96 85 77 79 84 98

In Order: 72 75 77 79 82 84 85 96 98

Median: 82

Example Question #65 : Statistics

Find the median of the given set of data:

{1,4,3,2,5,6,6}

Possible Answers:

3

6

1

2

4

Correct answer:

4

Explanation:

First you must order the elements from least to greatest. In order, the set is {1,2,3,4,5,6,6}. There are 7 terms in this set, so the median will be the 4th term of the set, which happens to be 4.

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