43) Twelve randomly-chosen students were asked how many times they had missed class during a certain semester, with this result: 2, 1, 5, 1, 1, 3, 4, 3, 1, 1, 5, 18.
To analyze the given data, the first step is to arrange the numbers in ascending order:
1, 1, 1, 1, 2, 3, 3, 4, 5, 5, 18
Next, you can calculate some measures of central tendency to summarize the data:
1) Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is 1, as it appears four times.
2) Median: The median is the middle value in the data set. If there is an even number of data points, the median is the average of the two middle values. In this case, there are 11 data points, so the median is the 6th value, which is 3.
3) Mean: The mean is the average of all the data points. To calculate it, sum up all the numbers and divide by the total count. In this case, the sum is 1 + 1 + 1 + 1 + 2 + 3 + 3 + 4 + 5 + 5 + 18 = 44. Dividing by 12 (the total count) gives a mean of approximately 3.67.
These measures can give you an idea of the typical number of times a student missed class during the semester, as well as any extreme values that might indicate outliers.
To analyze the data given, we need to calculate some statistical measures.
First, let's arrange the data in ascending order: 1, 1, 1, 1, 2, 3, 3, 4, 5, 5, 18.
Next, we can calculate the measures of central tendency (mean, median, and mode) and dispersion (range and standard deviation).
Mean: To find the mean, we sum up all the values and divide by the total number of values. Summing up the values: 1 + 1 + 1 + 1 + 2 + 3 + 3 + 4 + 5 + 5 + 18 = 44.
Dividing by the total number of values: 44 / 12 = 3.67 (rounded to two decimal places).
Median: The median is the middle value when the data is arranged in ascending order. In this case, we have an odd number of values, so the middle value is the one at the 6th position (counting from 1), which is 3.
Mode: The mode is the value that appears most frequently in the set of data. In this case, the mode is 1 as it appears 4 times, more frequently than any other number.
Range: The range is the difference between the maximum and minimum values in the data set. In this case, the minimum is 1, and the maximum is 18. So, the range is 18 - 1 = 17.
Standard Deviation: Standard deviation measures the spread or dispersion of the data. To calculate it, we first find the deviations of each value from the mean, square them, calculate the average of those squared deviations, and finally take the square root. The calculations for standard deviation can be complex, so using software or a calculator that supports statistical functions is recommended.