PARCC Averages and Rounding Practice Questions 2 — Questions and Answers

Question 1: What is the mean of the data set: 14, 22, 8, 30, 16?

16
18 (Correct answer)
20
22

Correct answer: 18

Add all values: 14 + 22 + 8 + 30 + 16 = 90. Divide by the number of values (5): 90 ÷ 5 = 18.

The mean (arithmetic average) is one of the three measures of central tendency, along with median and mode. To find the mean, you add all the values in the data set and then divide by how many values there are. For the data set 14, 22, 8, 30, 16: Step 1: Add all values: 14 + 22 + 8 + 30 + 16 = 90 Step 2: Count the values: there are 5 values Step 3: Divide the sum by the count: 90 ÷ 5 = 18 The mean is 18. Notice that the mean does not have to be one of the values in the data set. The mean is a useful measure because it accounts for all values equally, but it can be affected by extreme values (outliers). On PARCC math problems, always double-check that you have added all values correctly and divided by the total count of values, not just the distinct values. Organizing your work clearly helps avoid arithmetic errors.

Question 2: A student scored 82, 76, 91, and 85 on four tests. What score does the student need on a fifth test to achieve an average of 85?

85
88
91 (Correct answer)
95

Correct answer: 91

The desired total for 5 tests at an average of 85 is 5 × 85 = 425. Current total: 82 + 76 + 91 + 85 = 334. Needed: 425 − 334 = 91.

This is a reverse-average problem, which requires working backward from a desired average to find a missing value. Step 1: Determine the required total sum. If the average of 5 tests must be 85, then the total of all 5 scores must be 5 × 85 = 425. Step 2: Find the current sum of the four known scores: 82 + 76 + 91 + 85 = 334. Step 3: Subtract to find the missing score: 425 − 334 = 91. The student needs a 91 on the fifth test to achieve an average of 85. This type of problem tests algebraic thinking because you can also set it up as an equation: (334 + x) ÷ 5 = 85, which gives 334 + x = 425, so x = 91. Reverse-average problems are common on the PARCC exam and in real-world situations like calculating the grade needed on a final exam. Practice setting up the equation rather than guessing.

Question 3: Round 3.8472 to the nearest hundredth.

3.84
3.85 (Correct answer)
3.8
3.847

Correct answer: 3.85

The hundredths digit is 4. The digit to the right (thousandths place) is 7, which is ≥ 5, so round up: 3.85.

Rounding to the nearest hundredth means keeping two digits after the decimal point. The rules for rounding are: 1. Identify the digit in the place you are rounding to (the hundredths place). 2. Look at the digit immediately to its right (the thousandths place). 3. If that digit is 5 or greater, round the target digit up by 1. 4. If that digit is less than 5, keep the target digit the same. 5. Drop all digits to the right of the rounded place. For 3.8472: - The hundredths digit is 4 (second digit after the decimal). - The thousandths digit is 7. - Since 7 ≥ 5, round the hundredths digit up: 4 becomes 5. - The rounded value is 3.85. Note that the answer is NOT 3.847, which would be rounding to the nearest thousandth, and NOT 3.8, which would be rounding to the nearest tenth. Understanding which place value you are rounding to is the first and most important step.

Question 4: The temperatures for five days were: 68°F, 74°F, 71°F, 69°F, and 73°F. What is the mean temperature, rounded to the nearest whole number?

70°F
71°F (Correct answer)
72°F
73°F

Correct answer: 71°F

Sum: 68 + 74 + 71 + 69 + 73 = 355. Mean: 355 ÷ 5 = 71. The mean temperature is 71°F.

This problem combines two skills: calculating a mean and applying rounding if necessary. Step 1: Add all the temperatures: 68 + 74 + 71 + 69 + 73 = (68 + 72) + (74 + 71 + 69 + 73 − 72) Let's add directly: 68 + 74 = 142; 142 + 71 = 213; 213 + 69 = 282; 282 + 73 = 355 Step 2: Divide by the number of values: 355 ÷ 5 = 71 The mean temperature is exactly 71°F, so no rounding is needed. In real-world contexts, averages are frequently used with temperature data to describe typical weather patterns, identify climate trends, and plan activities. When a problem asks you to round to the nearest whole number after finding the mean, apply the same rounding rules: look at the first decimal digit, and if it is 5 or greater, round up; if less than 5, round down. In this case the division is exact, so the answer is simply 71°F.

Question 5: Which number, when rounded to the nearest ten, gives 250?

245 (Correct answer)
244
255
261

Correct answer: 245

Numbers from 245 to 254 round to 250 when rounded to the nearest ten. 245 is within this range and rounds up to 250.

When rounding to the nearest ten, you look at the ones digit to decide whether to round up or down. - If the ones digit is 0, 1, 2, 3, or 4, round down (keep the tens digit the same and replace the ones digit with 0). - If the ones digit is 5, 6, 7, 8, or 9, round up (increase the tens digit by 1 and replace the ones digit with 0). Numbers that round to 250 are those from 245 through 254: - 245: ones digit is 5 → round up → 250 ✓ - 244: ones digit is 4 → round down → 240 ✗ - 255: ones digit is 5 → round up → 260 ✗ - 261: ones digit is 1 → round down → 260 ✗ Of the choices given, only 245 rounds to 250. Understanding the range of numbers that round to a given value—not just how to round a specific number—is an important PARCC math skill used in estimation and data analysis.

Question 6: A store sells three items priced at $12.47, $8.95, and $15.63. What is the average price, rounded to the nearest cent?

$12.00
$12.35 (Correct answer)
$12.40
$13.00

Correct answer: $12.35

Sum: $12.47 + $8.95 + $15.63 = $37.05. Mean: $37.05 ÷ 3 = $12.35.

To find the average price of the three items, follow the steps for calculating a mean with decimal values. Step 1: Add all prices: $12.47 + $8.95 = $21.42 $21.42 + $15.63 = $37.05 Step 2: Divide the sum by the number of items: $37.05 ÷ 3 = $12.35 The average price is $12.35. Since the division is exact, no rounding is needed. When working with money, it is important to keep track of decimal places carefully. Adding from right to left and carrying over properly reduces errors. In this problem, note that all three prices have exactly two decimal places, which makes addition straightforward. Averages with decimals and money are frequently tested on the PARCC exam because they appear in real-world contexts such as shopping, budgeting, and data analysis. Always verify your addition before dividing.

PARCC Averages and Rounding Practice Questions 2

What is the mean of the data set: 14, 22, 8, 30, 16?