Measures of Central Tendency
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4. An MM207 statistics class surveyed 24 students to find out how many hours they spent doing homework during the previous week.
10 11 10 8 10 10 15 12 10 8 13 11
11 13 10 11 13 10 11 12 11 13 12 8
a. Calculate the mean for these data. (Round to 2 decimal places)
b. Determine the median for these data
Measures of Variation
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5. A placement test has a mean of 65 and a standard deviation of 2. A histogram of the data shows that the distribution is bell-shaped. Using the Empirical Rule, what two values have about 95% of the curve between them?
A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20 – 29 age groups, the heights were normally distributed, with a mean of 69.7 inches and a standard deviation of 3.0 inches. A study participant is randomly selected.
Find the probability that his height is less than 68 inches
To calculate the mean for these data, follow these steps:
1. Add up all the values:
10 + 11 + 10 + 8 + 10 + 10 + 15 + 12 + 10 + 8 + 13 + 11 + 13 + 10 + 11 + 13 + 12 + 11 + 13 + 12 + 8 = 238
2. Divide the sum by the total number of values:
238 / 24 = 9.92
So, the mean for these data is 9.92 (rounded to 2 decimal places).
To determine the median for these data, follow these steps:
1. Arrange the values in ascending order:
8, 8, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 15.
2. Since the total number of values is even (24 in this case), find the average of the two middle values. In this case, the middle values are the 12th and 13th values, which are both 11.
So, the median for these data is 11.