# Luka and Anja each measured the height of their friend three times. Their friend is 59 inches tall. They recorded their measurements as shown. Luka: 59 in., 58, in., 58 in. Anja: 59.3 in., 59.6 in., 58.2 in. Which statement is true? Luka’s measurements are more precise and more accurate. Anja’s measurements are more precise and more accurate. Luka’s measurements are more precise, but Anja’s measurements are more accurate. Luka’s measurements are more accurate, but Anja’s measurements are more precise

Question
Measurement
Luka and Anja each measured the height of their friend three times. Their friend is 59 inches tall. They recorded their measurements as shown. Luka: 59 in., 58, in., 58 in. Anja: 59.3 in., 59.6 in., 58.2 in. Which statement is true?
Luka’s measurements are more precise and more accurate. Anja’s measurements are more precise and more accurate. Luka’s measurements are more precise, but Anja’s measurements are more accurate. Luka’s measurements are more accurate, but Anja’s measurements are more precise

2020-12-16
Step 1
Define accuracy and precision of values.
An accurate value is judged to be closer to true to value, whereas precision is the consistency between values obtained by repeated measurements.
Here, Luka's measurements are 59 in,58 in, 58 in and Anja's measurements are 59.3 in, 59.6 in,58.2 in
Step 2
The average of Luka's measurements is,
$$A=\frac{59+58+58}{3}=58.33\in$$
The average of Anja's measurements is,
$$A=\frac{59.3+59.6+58.2}{3}=59.03\in$$
The Anja's measurements are more close towards true value. Thus, it is more accurate.
The recordings of Luka is more precise, because the degree of closeness is high compared to Anja.
Therefore, Option (C) is correct.

### Relevant Questions

1.After several tries of measuring, Lydia gets the results of 2.75, 2.76, 2.30 cm. She realized that the results of measurement is closest to the actual measurement which is 3.25. What is the implication of her measurements? Is it Accurate and precise?
2.I measured the length of cabinet 3 times. The results of my measurements are 3.44 m, 3.55 m, 3.47 m. Afterwards, I compared it to the results with each other. What did I was trying to find out? Is it precision?
One hundred adults and children were randomly selected and asked whether they spoke more than one language fluently. The data were recorded in a two-way table. Maria and Brennan each used the data to make the tables of joint relative frequencies shown below, but their results are slightly different. The difference is shaded. Can you tell by looking at the tables which of them made an error? Explain.
$$\begin{array}{c|c}&Yes&No\\\hline\text{Children}&0.15&0.25\\\hline\text{Adults}&0.1&0.6\end{array}$$
A certain scale has an uncertainty of 3 g and a bias of 2 g. a) A single measurement is made on this scale. What are the bias and uncertainty in this measurement? b) Four independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements? c) Four hundred independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements? d) As more measurements are made, does the uncertainty get smaller, get larger, or stay the same? e) As more measurements are made, does the bias get smaller, get larger, or stay the same?
A certain scale has an uncertainty of 3 g and a bias of 2 g.
a) A single measurement is made on this scale. What are the bias and uncertainty in this measurement?
b) Four independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements? c) Four hundred independent measurements are made on this scale. What are the bias and uncertainty in the average of these measurements?
d) As more measurements are made, does the uncertainty get smaller, get larger, or stay the same?
e) As more measurements are made, does the bias get smaller, get larger, or stay the same?
The weight of an object is given as $$67.2 \pm 0.3g$$. True or false:
a) The weight was measured to be 67.2 g.
b) The true weight of the object is 67.2 g.
c) The bias in the measurement is 0.3 g.
d) The uncertainty in the measurement is 0.3 g.
(Measure the longest dimension of the room twice, using two different techniques. Do the measurement in feet and inches. Then convert to meters.) Below is what I got.
$$Tape Measure - 146 inches > 3.7084 meters / 12 feet and 2 inches = 12.1667 feet > 3.70840 meters$$
$$Ruler - 144.5 inches (144 + 1/2) = 3.6703 meters / 12.0416 feet = 3.67027 meters$$
Case: Dr. Jung’s Diamonds Selection
With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.
After a bit of searching, Dr. Jung located a number of earring sets that he would consider purchasing. But he knew the pricing of diamonds varied considerably. To assist in his decision making, Dr. Jung decided to use regression analysis to develop a model to predict the retail price of different sets of round-cut earrings based on their color, clarity, and carat scores. He assembled the data in the file Diamonds.xls for this purpose. Use this data to answer the following questions for Dr. Jung.
1) Prepare scatter plots showing the relationship between the earring prices (Y) and each of the potential independent variables. What sort of relationship does each plot suggest?
2) Let X1, X2, and X3 represent diamond color, clarity, and carats, respectively. If Dr. Jung wanted to build a linear regression model to estimate earring prices using these variables, which variables would you recommend that he use? Why?
3) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
4) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
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6) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
7) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must actually square the model’s estimates to convert them to price estimates.) Which sets of earring appears to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
8) Dr. Jung now also remembers that it sometimes helps to include interaction terms in a regression model—where you create a new independent variable as the product of two of the original variables. Modify your spreadsheet to include three new independent variables, X4, X5, and X6, representing interaction terms where: X4 = X1 × X2, X5 = X1 × X3, and X6 = X2 × X3. There are now six potential independent variables. If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?
9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?
10) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must square the model’s estimates to convert them to actual price estimates.) Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?
Juan makes a measurement in a chemistry laboratory and records the result in his lab report. The stardard deviation of lab measurements made by students is $$\sigma=10$$ milligrams. Juan repeats the measurement 3 times and records the mean xbar of his 3 measurements.