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ACT Math : Statistics

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Example Question #21 : Arithmetic Mean

The average of four numbers is 27. A new number, $\dpi{100} \small x$ , is added to these four, and the new average of the five numbers is 25. What is the value of $\dpi{100} \small x$ ?

Possible Answers:

$\dpi{100} \small 18$

$\dpi{100} \small 14$

$\dpi{100} \small 15$

$\dpi{100} \small 17$

$\dpi{100} \small 21$

Correct answer:

$\dpi{100} \small 17$

Explanation:

The value of $\dpi{100} \small x$ is $\dpi{100} \small 17$ . Suppose we call the sum of the original four numbers $\dpi{100} \small z$ . We know that $\frac{z}{4}=27$ , so $\dpi{100} \small z=108$ . Now, when $\dpi{100} \small x$ is added to $\dpi{100} \small z$ , we know that $\frac{x+z}{5}=25$ . This means that $x+z=125$ , and thus $x=125-z$ . Since $\dpi{100} \small z=108$ , $\dpi{100} \small x$ must equal $\dpi{100} \small 17$ .

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Example Question #21 : How To Find Arithmetic Mean

Jameson received four grades on his algebra tests, which brought his average to an 88. What grade would he have to make on his final test in order to bring his average up to a 90?

Possible Answers:

100

Correct answer:

Explanation:

To start, we have to understand the concept behind averages. To average something, take all your numbers, add them together and then divide by the total amount of numbers. Also, the definition of an average is a quantity intermediate to a set of quantities, or in other words, the exact middle.

In this particular problem, we know that the average of the first four tests is an 88, which means that the summation of the first four tests divided by 4 must equal 88. We can extrapolate from the definition of an average that the first four tests can all be estimated at 88.

When adding in the fifth test, we must then account for 5 tests as opposed to 4. We can set up and solve the formula for the fifth test's grade as such:

( = fifth test)

$\frac{88+88+88+88+x}{5}=90$

Multiply both sides by 5.

352+x=450

x=98

Jameson must score a 98 on his last test to bring his average up to a 90.

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Example Question #21 : Arithmetic Mean

If Point $X$ is located at $-10$ on a number line and Point $Z$ is located at $101$ on the same line. What is the midpoint of line $XZ$ ?

Possible Answers:

$43.5$

$44.5$

$46.5$

$55.5$

$45.5$

Correct answer:

$45.5$

Explanation:

The line is 111 points long, meaning the midpoint is 55.5 away from either end. Simply subtract 55.5 from 101 to yield 45.5.

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Example Question #21 : Arithmetic Mean

Brenda's cat gave birth to 6 kittens. The kittens weights are listed below.

$1.6\ oz.$

$1.8\ oz.$

$2.3\ oz.$

$3\ oz.$

$0.98\ oz.$

$1.2\ oz.$

What is the average weight of one of Brenda's kittens?

Possible Answers:

$1.62\ oz.$

$1.81\ oz.$

$3\ oz.$

$10.5\ oz.$

$2.8\ oz.$

Correct answer:

$1.81\ oz.$

Explanation:

Sum of the weights divided by 6.

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Example Question #21 : How To Find Arithmetic Mean

A graduating class has 300 women and 250 men. The women's ages average to 27 and the men's ages average to 29. What is the average age of the class?

Possible Answers:

$28$

$27.9$

$27.5$

$27$

$Cannot\ be\ determined$

Correct answer:

$27.9$

Explanation:

$\small \frac{(300)(27) + (250)(29)}{550}$

$\small \frac{8100+7250}{550}= 27.9$

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Example Question #26 : Arithmetic Mean

In Town A, the average price of gas at all 45 gas stations is $3.31 per gallon. In Town B, the average price of gas at all 20 gas stations is $3.22 per gallon. What is the average combined average price of gas in both towns?

Possible Answers:

$\dpi{100} \$3.30\ per\ gallon$

$\dpi{100} \$3.27\ per\ gallon$

$\dpi{100} \$3.26\ per\ gallon$

$\$3.28\ per\ gallon$

$\dpi{100} \$3.29\ per\ gallon$

Correct answer:

$\$3.28\ per\ gallon$

Explanation:

Assume that all gas stations in Town A are selling the gas at $3.31 per gallon and all gas stations in Town B are selling the gas at $3.22 per gallon. To find the average price per gallon across all stores, you write the following formula:

$\frac{45(3.31)+20(3.22)}{65}$

$\frac{148.95+64.4}{65}$

$\frac{213.35}{65}$

$3.28$

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Example Question #21 : Arithmetic Mean

On the last Algebra exam, Sarah scored 87, Amy scored 63, and Jessica scored lower than Sarah but higher than Amy. What is Jessica's score if the mean of their three scores is 52 points higher than the range of their scores?

Possible Answers:

Correct answer:

Explanation:

The range of a set of data is the difference between the highest and lowest values in the set. Since Jessica scored between Sarah and Amy, the range must be the difference between Sarah and Amy's scores. 87 - 63 = 24

If the mean is 52 points higher than the range, the mean must be 52 +24 = 76 .

The mean is the sum of the values in the set divided by the number of values in the set.

Let Jessica's score be denoted by .

$\frac{87 + J + 63}{3} = 76$

Solve for .

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Example Question #28 : Arithmetic Mean

Last week, gas sold in the 92 gas stations in Jonestown for an average of $3.32 per gallon, and gas sold for an average of $3.42 per gallon in the 142 gas stations in Smithsville. What was the average price of gas per gallon in all of the gas stations of Jonestown and Smithsville together?

Possible Answers:

$\dpi{100} \$3.37\ per\ gallon$

$\dpi{100} \$3.39\ per\ gallon$

$\dpi{100} \$3.36\ per\ gallon$

$\dpi{100} \$3.40\ per\ gallon$

$\$3.38\ per\ gallon$

Correct answer:

$\$3.38\ per\ gallon$

Explanation:

Assume that the price of gas in every gas station of each town is exactly the average price. The equation you would write would then be as follows:

$\frac{92(\$ 3.32)+142(\$3.42)}{(92+142)}$

The correct answer is $3.38 per gallon.

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Example Question #21 : Arithmetic Mean

Susan checked her grades and saw that she had averaged an 88% on the last four tests. After taking the fifth test, her average grade was now 90%. What grade did she get on her fifth test?

Possible Answers:

$96\%$

$90\%$

$92\%$

$98\%$

$100\%$

Correct answer:

$98\%$

Explanation:

Because her average grade after 5 tests was 90% and the first four tests averaged 88%, write the following expression:

$\frac{4(88)+x}{5}=90$

$4(88)+x=450$

$x=98$

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Example Question #30 : Arithmetic Mean

What is the sum of the range, mean, mode and median of the following data set:

15, 2, 7, 3, 11, 5, 12, 2, 6

Possible Answers:

Correct answer:

Explanation:

Arrange the data set from smallest to largest:

2, 2, 3, 5, 6, 7, 11, 12, 15

Range: $largest\ \# - smallest\ \#$ or 15 - 2 = 13

Median: number in the middle, or

Mode: number most often repeated, or

Mean: the sum of all numbers divided by the total number of data points, or $\frac{63}{9} = 7$

The sum of all these measures is .

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ACT Math : Statistics

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #21 : Arithmetic Mean

Example Question #21 : How To Find Arithmetic Mean

Example Question #21 : Arithmetic Mean

Example Question #21 : Arithmetic Mean

Example Question #21 : How To Find Arithmetic Mean

Example Question #26 : Arithmetic Mean

Example Question #21 : Arithmetic Mean

Example Question #28 : Arithmetic Mean

Example Question #21 : Arithmetic Mean

Example Question #30 : Arithmetic Mean

All ACT Math Resources

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