1. Travis is testing how far he can throw a baseball to prepare himself for the season. He makes 16
throws and records the length of each throw in feet. The results are provided in the accompanying table.
236 240 232 242 238 235 228 245
247 239 234 238 241 227 243 238
Travis says that the histogram provided below could be used to represent the data.
Show whether the histogram Travis created is correct and, if not, explain how the histogram could be corrected.
It is not possible to determine if Travis' histogram is correct without seeing the actual histogram. However, if the histogram accurately represents the data, then it should show the frequency of each range of throw lengths. One way to correct the histogram would be to adjust the range of each bar so that they accurately represent the frequency of the data. Additionally, Travis could label the x-axis with the range of throw lengths and the y-axis with the frequency or number of throws.
1. For a project, Fay kept track of the total annual amount of precipitation in inches for two cities over the last 12
years. The results are shown in the table below.
City A 41.50 69.43 48.15 39.23 37.03 66.02 47.62 68.38 38.69 52.48 70.03 43.74
City M 48.14 61.59 44.05 33.14 32.41 72.92 48.49 50.21 33.70 48.69 49.06 44.47
Find the mean and standard deviation for each city, and then compare the means and standard deviations. Round the means and standard deviations to two decimal places.
To find the mean for each city, we will add up all the precipitation amounts for that city and divide by the number of years (12).
For City A:
Mean = (41.50 + 69.43 + 48.15 + 39.23 + 37.03 + 66.02 + 47.62 + 68.38 + 38.69 + 52.48 + 70.03 + 43.74) / 12
Mean = 52.30 inches
For City M:
Mean = (48.14 + 61.59 + 44.05 + 33.14 + 32.41 + 72.92 + 48.49 + 50.21 + 33.70 + 48.69 + 49.06 + 44.47) / 12
Mean = 46.26 inches
To find the standard deviation for each city, we can use the following formula:
s = √[(Σx - μ)² / (n - 1)]
where s is the standard deviation, Σx is the sum of all the data points, μ is the mean, and n is the number of data points.
For City A:
s = √[((41.50 - 52.30)² + (69.43 - 52.30)² + ... + (43.74 - 52.30)²) / (12 - 1)]
s = 13.97 inches
For City M:
s = √[((48.14 - 46.26)² + (61.59 - 46.26)² + ... + (44.47 - 46.26)²) / (12 - 1)]
s = 9.96 inches
Comparing the means, we can see that City A has a higher average annual precipitation than City M.
Comparing the standard deviations, we can see that City A has a larger variability in annual precipitation than City M.
To determine whether Travis' histogram is correct, we need to check if it accurately represents the data provided.
A histogram is a graphical representation of the distribution of data. It consists of a series of bars, where the height of each bar represents the frequency or count of data falling within a certain range or category.
To create a histogram, we first need to determine the intervals or bins. These are the ranges within which we group the data. The frequency of data falling within each interval will be represented by the height of the corresponding bar.
Let's examine the data and compare it to Travis' histogram:
Data provided:
236 240 232 242 238 235 228 245
247 239 234 238 241 227 243 238
Based on the data, we can see that the minimum value is 227 and the maximum value is 247. We can use these values to determine the range of the histogram.
If we decide to use a range of 5 for each interval, we can create the following intervals:
225-229, 230-234, 235-239, 240-244, and 245-249.
Now, let's count the frequency of data falling within each interval:
225-229: 1
230-234: 3
235-239: 6
240-244: 4
245-249: 2
Based on the frequency counts, we can now create the histogram.
Travis' histogram:
There is no histogram provided in the question, so we cannot evaluate if it is correct or not.
To create a histogram from the frequency counts, we would need to plot the counts on the vertical (y-axis) and the intervals on the horizontal (x-axis). Each interval would be represented by a bar with a height equal to its corresponding frequency count.
If you need further clarification or if Travis' histogram was provided, please provide more information, and I would be happy to assist you further.