Significant Digits, Mean, Median, Mode

1) If 10 items in a shopping cart ranged in price from $1.23 to $5.98, is it possible for the mean price to be $7.49?

Yes

No

Maybe

The mean price is the average of all the prices in the shopping cart. Since the prices range from $1.23 to $5.98, it is not possible for the mean price to be $7.49. The mean price can only be within the range of $1.23 to $5.98.

Explanation

The mean price is the average of all the prices in the shopping cart. Since the prices range from $1.23 to $5.98, it is not possible for the mean price to be $7.49. The mean price can only be within the range of $1.23 to $5.98.

2) A science class of 11 students had the following quiz scores. What is the mean, median, and mode:
10, 10, 9, 6, 5, 6, 5, 4, 5, 8, 9

Mean = 6, median = 7, mode = 9

Mean = 7, median = 6, mode = none

Mean = 7, median = 6, mode = 5

Mean = 6, median = 5, mode = 5

The mean is calculated by adding up all the scores and dividing by the total number of scores. In this case, the sum of all the scores is 78, and there are 11 students, so the mean is 78/11 = 7.

The median is the middle value when the scores are arranged in ascending order. In this case, when the scores are arranged in ascending order, the middle value is 6, so the median is 6.

The mode is the value that appears most frequently. In this case, the value 5 appears three times, which is more than any other value, so the mode is 5.

Therefore, the correct answer is mean = 7, median = 6, mode = 5.

Explanation

The mean is calculated by adding up all the scores and dividing by the total number of scores. In this case, the sum of all the scores is 78, and there are 11 students, so the mean is 78/11 = 7.

The median is the middle value when the scores are arranged in ascending order. In this case, when the scores are arranged in ascending order, the middle value is 6, so the median is 6.

The mode is the value that appears most frequently. In this case, the value 5 appears three times, which is more than any other value, so the mode is 5.

Therefore, the correct answer is mean = 7, median = 6, mode = 5.

3) Round off the following number to 3 significant digits: 410.900

410

410.9

411

41

The number 410.900 has four significant digits. When rounding off to three significant digits, we look at the digit after the third significant digit, which is 0. Since 0 is less than 5, we do not round up the last significant digit. Therefore, the correct answer is 411.

Explanation

The number 410.900 has four significant digits. When rounding off to three significant digits, we look at the digit after the third significant digit, which is 0. Since 0 is less than 5, we do not round up the last significant digit. Therefore, the correct answer is 411.

4) How many significant digits are there in the following number: 0.001010

Two

Three

Four

Seven

The number 0.001010 has four significant digits. Significant digits are the digits that contribute to the precision of a number. In this case, the zeros before the first non-zero digit are not significant, so they are not counted. The first non-zero digit is 1, followed by 0, 1, and 0, which are all significant. Therefore, there are four significant digits in the given number.

Explanation

The number 0.001010 has four significant digits. Significant digits are the digits that contribute to the precision of a number. In this case, the zeros before the first non-zero digit are not significant, so they are not counted. The first non-zero digit is 1, followed by 0, 1, and 0, which are all significant. Therefore, there are four significant digits in the given number.

5) If everybody in a room had a watch that all showed a time of exactly 10:02 AM, but if the actual time was 10:05 AM, which statement below best describes those watches?

The watches were all very accurate.

The watches were very precisely synchronized, but not accurate.

The watches were both precise and accurate.

The watches were neither precise nor accurate.

The watches in the room are synchronized because they all show the same time, 10:02 AM. However, they are not accurate because the actual time is 10:05 AM. This means that while the watches are synchronized with each other, they are not synchronized with the correct time. Therefore, the statement "The watches were very precisely synchronized, but not accurate" best describes the situation.

Explanation

The watches in the room are synchronized because they all show the same time, 10:02 AM. However, they are not accurate because the actual time is 10:05 AM. This means that while the watches are synchronized with each other, they are not synchronized with the correct time. Therefore, the statement "The watches were very precisely synchronized, but not accurate" best describes the situation.

6) It is possible for a series of measurements made by the same instrument to be very precise but not very accurate.

True

False

Precision refers to the consistency and reproducibility of measurements, while accuracy refers to how close the measurements are to the true value. In this case, it is possible for a series of measurements made by the same instrument to be very consistent and reproducible (precise), but still consistently deviate from the true value (not accurate). This could be due to systematic errors or biases in the instrument or measurement technique. Therefore, the statement is true.

Explanation

Precision refers to the consistency and reproducibility of measurements, while accuracy refers to how close the measurements are to the true value. In this case, it is possible for a series of measurements made by the same instrument to be very consistent and reproducible (precise), but still consistently deviate from the true value (not accurate). This could be due to systematic errors or biases in the instrument or measurement technique. Therefore, the statement is true.

7) A grocery list contains 25 items ranging in price from 0.49 to 5.32. If the median item cost $2.03, how many items on the list cost more than $2.03?

13

12

11

Not enough information to tell

The median item cost is $2.03, which means that there are 12 items on the list that cost more than $2.03. This is because the median divides the list into two equal halves, so there are 12 items on one side that cost more than $2.03, and 12 items on the other side that cost less than $2.03.

Explanation

The median item cost is $2.03, which means that there are 12 items on the list that cost more than $2.03. This is because the median divides the list into two equal halves, so there are 12 items on one side that cost more than $2.03, and 12 items on the other side that cost less than $2.03.

8) Which one of the following rulers are the most precise AND the most accurate?

A ruler divided into 1/10th centimeters with clean, sharp edges

A ruler divided into centimeters with clean, sharp edges

A ruler divided into 1/10th centimeters with rough, worn down edges

A ruler divided into 10-centimeter lengths with clean, sharp eduges

The ruler divided into 1/10th centimeters with clean, sharp edges is the most precise and accurate because it allows for measurements to be made with greater precision due to the smaller divisions. Additionally, the clean and sharp edges ensure that the measurements can be taken accurately without any distortion or misalignment. The other options either have rough and worn down edges, which can affect the accuracy of the measurements, or have larger divisions (centimeters or 10-centimeter lengths), which reduce the precision of the ruler.

Explanation

The ruler divided into 1/10th centimeters with clean, sharp edges is the most precise and accurate because it allows for measurements to be made with greater precision due to the smaller divisions. Additionally, the clean and sharp edges ensure that the measurements can be taken accurately without any distortion or misalignment. The other options either have rough and worn down edges, which can affect the accuracy of the measurements, or have larger divisions (centimeters or 10-centimeter lengths), which reduce the precision of the ruler.

9) It is possible for a series of measurements made by the same instrument to be very accurate, but not very precise.

True

False

It is not possible for a series of measurements made by the same instrument to be very accurate but not very precise. Accuracy refers to how close the measurements are to the true or accepted value, while precision refers to how close the measurements are to each other. If the measurements are accurate, it means they are close to the true value. If they are precise, it means they are close to each other. Therefore, if the measurements are accurate, they are also precise, and vice versa.

Explanation

It is not possible for a series of measurements made by the same instrument to be very accurate but not very precise. Accuracy refers to how close the measurements are to the true or accepted value, while precision refers to how close the measurements are to each other. If the measurements are accurate, it means they are close to the true value. If they are precise, it means they are close to each other. Therefore, if the measurements are accurate, they are also precise, and vice versa.

10) How many significant digits are there in the following number: 101.010

Three

Five

Six

None

The number 101.010 has six significant digits. A significant digit is any digit that is not zero and contributes to the precision of the number. In this case, all the digits (1, 0, 1, 0, 1, and 0) are significant because they are not zero and they all contribute to the precision of the number. Therefore, the number has six significant digits.

Explanation

The number 101.010 has six significant digits. A significant digit is any digit that is not zero and contributes to the precision of the number. In this case, all the digits (1, 0, 1, 0, 1, and 0) are significant because they are not zero and they all contribute to the precision of the number. Therefore, the number has six significant digits.

11) In a baseball game, the pitcher threw high and inside more than 80 percent of the time. Describe his accuracy and precision.

His pitches were both accurate and precise.

His pitches were neither accurate nor precise.

His pitches were accurate but not precise.

His pitches were precise but not accurate.

The pitcher's pitches were precise but not accurate. Precision refers to the consistency and repeatability of the results, while accuracy refers to how close the results are to the target. Since the pitcher consistently threw high and inside, his pitches were precise. However, if the majority of his pitches missed the intended target, they were not accurate.

Explanation

The pitcher's pitches were precise but not accurate. Precision refers to the consistency and repeatability of the results, while accuracy refers to how close the results are to the target. Since the pitcher consistently threw high and inside, his pitches were precise. However, if the majority of his pitches missed the intended target, they were not accurate.

12) Round off the following number to the hundredth's place: 211.02954

211.03

211.02

211

200

The given number, 211.02954, is rounded off to the hundredth's place, which means we need to look at the digit in the thousandth's place, which is 9. Since 9 is greater than or equal to 5, we round up the digit in the hundredth's place, which is 2, to the next higher digit, which is 3. Therefore, the correct rounded off number is 211.03.

Explanation

The given number, 211.02954, is rounded off to the hundredth's place, which means we need to look at the digit in the thousandth's place, which is 9. Since 9 is greater than or equal to 5, we round up the digit in the hundredth's place, which is 2, to the next higher digit, which is 3. Therefore, the correct rounded off number is 211.03.