Researchers count 30 tagged zebras and 150 total zebras in an area of a game reserve. If researchers had previously tagged 80 total zebras at the game reserve, about how many total zebras live at the game reserve?Write a proportion to estimate the total population.
One possible proportion to estimate the total population of zebras at the game reserve is:
tagged zebras / total zebras = tagged zebras previously / total zebras previously
This proportion assumes that the ratio of tagged to total zebras is roughly the same for the current sample as for the previous sample, and that the population size has not changed drastically between the two samples. Using the values given in the problem, we can set up the proportion as follows:
30 / 150 = 80 / x
where x is the estimated total population we want to find. To solve for x, we can cross-multiply and simplify:
30x = 150 x 80
30x = 12000
x ≈ 400
Therefore, an estimate for the total number of zebras living at the game reserve is about 400. This assumes that the proportion of tagged zebras to total zebras is the same for the current and previous samples, and that there are no other sources of error or bias in the sampling method.
can you make it way shorter and simpler
Sure! Here's a shorter and simpler version:
- We know that 30 out of 150 zebras in the game reserve are tagged, and that 80 zebras were previously tagged.
- We can set up a proportion to estimate the total number of zebras in the game reserve: tagged zebras / total zebras = tagged zebras previously / total zebras previously.
- Solving for the unknown variable, we get: total zebras ≈ (tagged zebras / tagged zebras previously) x total zebras previously.
- Plugging in the values, we get: total zebras ≈ (30 / 80) x 80 = 30.
- Therefore, an estimate for the total number of zebras in the game reserve is about 30. This assumes that the tagged zebras are representative of the entire zebra population and that the ratio of tagged zebras to total zebras is consistent across different samples.
can you make it even more shorter and more simpler
Yes, I can! Here's a simplified version:
- Researchers have tagged 30 out of 150 zebras in the game reserve and previously tagged 80 total zebras.
- To estimate the total number of zebras in the game reserve, we can use the proportion: tagged zebras / total zebras = tagged zebras previously / total zebras previously.
- The estimated total zebras is about (30 / 80) x 80 = 30.
- Therefore, the estimated total number of zebras in the game reserve is 30.
Maria has the following scores on exams in her social studies class: 86, 75, 97, 58, 94, and 58.
Find the mean, median, and mode of the scores.
Should Maria’s social studies teacher use the mean, median, or mode of the exam scores to convince Maria that she needs to study more regularly for her exams?
To find the mean of the scores, we add them up and divide by the total number of scores:
Mean = (86 + 75 + 97 + 58 + 94 + 58) / 6 = 78
To find the median of the scores, we first need to put them in order from smallest to largest:
58, 58, 75, 86, 94, 97
The median is the middle score, which is 86.
To find the mode of the scores, we look for the score(s) that appear most frequently. In this case, there are two scores that appear twice each, which are 58 and 94, so the mode is not unique.
Based on these measures, we can see that Maria's scores are relatively spread out, with a mean of 78, a median of 86, and no clear mode. However, for her teacher to convince Maria that she needs to study more regularly, it might be more effective to use the lowest scores as evidence. In this case, Maria got two scores of 58, which are well below the mean and median. Therefore, the teacher could focus on these low scores and suggest that Maria needs to improve her studying habits to perform better on exams.
The stem-and-leaf plot shows the heights in centimeters of Teddy Bear sunflowers grown in two different types of soil.
Soil A Soil B
5 9
5 2 1 1 6 3 9
5 1 0 7 0 2 3 6 7 8
2 1 8 3
0 9
Key: 9|6 means 69 Key: 5|8 means 58
Calculate the mean of each data set.
Calculate the mean absolute deviation (MAD) of each data set.
Which set is more variable? How do you know?
To calculate the mean of each data set, we need to use the stem-and-leaf plots to find the individual heights and add them up, then divide by the number of heights in each data set.
For Soil A:
- There are 11 heights, ranging from 50 cm to 58 cm.
- Summing the heights gives: 50 + 51 + 51 + 52 + 53 + 58 + 58 + 58 + 59 + 61 + 80 = 571 cm.
- Dividing by the number of heights gives: 571 / 11 = 51.9 cm.
For Soil B:
- There are 16 heights, ranging from 59 cm to 83 cm.
- Summing the heights gives: 60 + 63 + 67 + 68 + 70 + 70 + 73 + 73 + 73 + 76 + 78 + 78 + 78 + 79 + 80 + 83 = 1156 cm.
- Dividing by the number of heights gives: 1156 / 16 = 72.3 cm.
To calculate the mean absolute deviation (MAD) of each data set, we first need to find the deviations from the mean for each height, then take the absolute value of each deviation, then find the mean of the absolute deviations. This measures how spread out the data is on average, regardless of whether the deviations are positive or negative.
For Soil A:
- The mean is 51.9 cm.
- The deviations from the mean are: -1.9, -0.9, -0.9, -0.9, +1.1, +6.1, +6.1, +6.1, +7.1, +9.1, +28.1.
- The absolute deviations are: 1.9, 0.9, 0.9, 0.9, 1.1, 6.1, 6.1, 6.1, 7.1, 9.1, 28.1.
- The mean of the absolute deviations is: (1.9 + 0.9 + 0.9 + 0.9 + 1.1 + 6.1 + 6.1 + 6.1 + 7.1 + 9.1 + 28.1) / 11 = 6.73 cm.
For Soil B:
- The mean is 72.3 cm.
- The deviations from the mean are: -13.3, -9.3, -5.3, -4.3, -2.3, -2.3, +0.7, +0.7, +0.7, +3.7, +5.7, +5.7, +5.7, +6.7, +7.7, +10.7.
- The absolute deviations are: 13.3, 9.3, 5.3, 4.3, 2.3, 2.3, 0.7, 0.7, 0.7, 3.7, 5.7, 5.7, 5.7, 6.7, 7.7, 10.7.
- The mean of the absolute deviations is: (13.3 + 9.3 + 5.3 + 4.3 + 2.3 + 2.3 + 0.7 + 0.7 + 0.7 + 3.7 + 5.7 + 5.7 + 5.7 + 6.7 + 7.7 + 10.7) / 16 = 5.56 cm.
To determine which set is more variable, we can compare the MADs. A larger MAD indicates more variability, because the absolute deviations from the mean are on average farther apart. In this case, Soil A has a MAD of 6.73 cm, while Soil B has a MAD of 5.56 cm. Therefore, Soil A is more variable than Soil B.
To estimate the total zebra population at the game reserve, we can use a proportion.
Let's denote the total population of zebras as "x". We know that there are 30 tagged zebras out of a total of 150 zebras in the sampled area. We can set up a proportion using this information:
30 tagged zebras / 150 total zebras = 80 tagged zebras / x total zebras
To estimate the total population, we can cross-multiply and solve for "x":
30x = 150 * 80
Now we can solve for "x" by dividing both sides of the equation by 30:
x ≈ (150 * 80) / 30
Using a calculator, we find that x is approximately 400.
Therefore, the estimated total zebra population at the game reserve is around 400 zebras.