Make a Frequency Distribution with 5 classes18, 19, 20, 20, 21, 22, 22, 24, 25, 25, 26, 27, 28, 30, 30, 31, 33, 34, 35, 37, 37, 38, 39, 40, 41, 42, 56, 62, 73
What is the class width?
List the midpoints, relative frequency, and cumulative relative frequency
Make a relative frequency ogive
Make a frequency polygon
Calculate the mean
Calculate the median
Calculate the sample standard deviation (our data is sample from our class, not a population!)
Calculate the Q1 and Q3 values

Answers

Answer 1

Answer: The class width is calculated by dividing the range of the data by the number of classes. In this case, the range is 73-18=55. So, the class width is 55/5=11.

The midpoints are calculated by adding the lower and upper limits of each class and dividing by 2. The midpoints for each class are: 20.5, 31.5, 42.5, 53.5, and 64.5.

The relative frequency is calculated by dividing the frequency of each class by the total number of data points (28 in this case). The relative frequencies for each class are: 0.1071, 0.1071, 0.2143, 0.2857, and 0.2857.

The cumulative relative frequency is calculated by adding up the relative frequencies for each class and all previous classes. The cumulative relative frequencies for each class are: 0.1071, 0.2143, 0.4286, 0.7143, and 1.

To make a relative frequency ogive, you would plot the cumulative relative frequencies against the upper limits of each class.

To make a frequency polygon, you would plot the midpoints of each class against their respective frequencies.

The mean is calculated by adding up all the data points and dividing by the total number of data points (28 in this case). The mean is approximately 32.39.

The median is calculated by finding the middle value when all the data points are arranged in order from smallest to largest. Since there are an even number of data points (28), we take the average of the two middle values (25 and 30). So, the median is (25+30)/2=27.5.

The sample standard deviation is calculated using the formula: sqrt(sum((x-mean)^2)/(n-1)), where x is each data point, mean is the mean of all the data points, n is the total number of data points (28 in this case). The sample standard deviation is approximately 12.87.

The Q1 value (the first quartile) is calculated by finding the median of the lower half of the data points (14 in this case). Since there are an even number of data points in this half (14), we take the average of the two middle values (22 and 22). So, Q1 is (22+22)/2=22.

The Q3 value (the third quartile) is calculated by finding the median of the upper half of the data points (14 in this case). Since there are an even number of data points in this half (14), we take the average of the two middle values (34 and 35). So, Q3 is (34+35)/2=34.5.

Answer 2

Answer:

This mathematical question focused on descriptive statistics, such as calculating the class widths for a frequency distribution,

Determining the midpoints, relative frequency, and cumulative relative frequency, drawing a relative frequency ogive and frequency polygon, and calculating the mean, median, sample standard deviation, Q1, and Q3.First, to construct a frequency distribution with a total of 5 classes, we need to determine the class width. We get this by subtracting the smallest value from the largest value and dividing by the number of classes, then rounding up. In this case, (73-18)/5 = 11. Therefore, the class width is 11.Next, we calculate the midpoints of each class, relative frequency, and cumulative relative frequency. After that, we create the relative frequency and frequency polygon. Unfortunately, without a greater context, these cannot be shown here.For the mean, we sum up all the numbers and divide by the number of observations. In this case, the mean is the sum of the values divided by 29.We calculate the median, which is the middle value when the numbers are arranged in ascending order. For this dataset, the median would be the 15th data value.The sample standard deviation is a little more complex. It involves finding the mean, subtracting each value from the mean and squaring the result, summing these squared values, dividing by the number of observations minus 1, and taking the square root. This gives the sample standard deviation.Lastly, Q1 and Q3 are the 25th and 75th percentiles, respectively. Q1 and Q3 can be calculated by sorting the data in ascending order and taking the 25th and 75th percentile positions.

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