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Maris conducted a study on the effect that playing video games has on memory recall. As part of her study, she compiled the following data:
Hours Teenagers Spend on Video Games | Number of Teenagers |
---|---|
0–3.5 | 3 |
3.5–7.5 | 7 |
7.5–11.5 | 12 |
11.5–15.5 | 7 |
15.5–19.5 | 9 |
What is the best estimate for the mean number of hours spent playing video games?
Find the midpoint of each interval, multiply by the corresponding number of teenagers, add the results and then divide by the total number of teenagers
The midpoints are 1.75, 5.5, 9.5, 13.5,17.5.
Mean = (1.75)(3) + (5.5)(7) + (9.5)(12) + (13.5)(7) + (17.5)(9) = 409.75
Data from The World Bank, available online at http://www.worldbank.org (accessed April 3, 2013).
“Demographics: Obesity – adult prevalence rate.” Indexmundi. Available online at http://www.indexmundi.com/g/r.aspx?t=50&v=2228&l=en (accessed April 3, 2013).
The mean and the median can be calculated to help you find the "center" of a data set. The mean is the best estimate for the actual data set, but the median is the best measurement when a data set contains several outliers or extreme values. The mode will tell you the most frequently occuring datum (or data) in your data set. The mean, median, and mode are extremely helpful when you need to analyze your data, but if your data set consists of ranges which lack specific values, the mean may seem impossible to calculate. However, the mean can be approximated if you add the lower boundary with the upper boundary and divide by two to find the midpoint of each interval. Multiply each midpoint by the number of values found in the corresponding range. Divide the sum of these values by the total number of data values in the set.
$\mu =\frac{{\displaystyle \sum fm}}{{\displaystyle \sum f}}$ Where f = interval frequencies and m = interval midpoints.
Find the mean for the following frequency tables.
Grade | Frequency |
---|---|
49.5–59.5 | 2 |
59.5–69.5 | 3 |
69.5–79.5 | 8 |
79.5–89.5 | 12 |
89.5–99.5 | 5 |
Daily Low Temperature | Frequency |
---|---|
49.5–59.5 | 53 |
59.5–69.5 | 32 |
69.5–79.5 | 15 |
79.5–89.5 | 1 |
89.5–99.5 | 0 |
Points per Game | Frequency |
---|---|
49.5–59.5 | 14 |
59.5–69.5 | 32 |
69.5–79.5 | 15 |
79.5–89.5 | 23 |
89.5–99.5 | 2 |
Use the following information to answer the next three exercises: The following data show the lengths of boats moored in a marina. The data are ordered from smallest to largest:
Calculate the mean.
Mean: 16 + 17 + 19 + 20 + 20 + 21 + 23 + 24 + 25 + 25 + 25 + 26 + 26 + 27 + 27 + 27 + 28 + 29 + 30 + 32 + 33 + 33 + 34 + 35 + 37 + 39 + 40 = 738;
$\frac{738}{27}$ = 27.33
Identify the median.
Identify the mode.
The most frequent lengths are 25 and 27, which occur three times. Mode = 25, 27
Use the following information to answer the next three exercises: Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Calculate the following:
sample mean = $\overline{x}$ = _______
mode = _______
Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed 100 shoppers. The samples yielded the following information.
Javier | Ercilia | |
---|---|---|
$\overline{x}$ | 6.0 miles | 6.0 miles |
$s$ | 4.0 miles | 7.0 miles |
Use the following information to answer the next three exercises : We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.
Number of years | Frequency | Number of years | Frequency |
---|---|---|---|
Total = 20 | |||
7 | 1 | 22 | 1 |
14 | 3 | 23 | 1 |
15 | 1 | 26 | 1 |
18 | 1 | 40 | 2 |
19 | 4 | 42 | 2 |
20 | 3 |
What is the mode?
Is this a sample or the entire population?
b
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