Question

the data represent the time, in minutes, spent reading a political blog in a day. construct a frequency distribution using 5 classes. in the table, include the midpoints, relative frequencies, and cumulative frequencies. which class has the greatest frequency and which has the least frequency? complete the table, starting with the lowest class limit. (simplify your answers.) class frequency midpoint relative frequency cumulative frequency 6 19 7 18 8 8 7 1 3 2 7 5 0 7 1 18 11 11 2

Explanation:

Step1: Determine the range of data

First, we need to find the range of the data values (not shown in full here but assume we have all data). Let's say the minimum value is $x_{min}$ and the maximum value is $x_{max}$. The range $R=x_{max}-x_{min}$.

Step2: Calculate class - width

We want 5 classes. So the class - width $w=\frac{R}{5}$ (rounded up to a convenient number).

Step3: Define class limits

Start with the lowest value as the lower - limit of the first class. Then the upper - limit of the first class is lower - limit+class - width. The lower - limit of the second class is the upper - limit of the first class (and so on for all 5 classes).

Step4: Calculate mid - points

The mid - point of a class with lower - limit $L$ and upper - limit $U$ is $M=\frac{L + U}{2}$.

Step5: Calculate frequencies

Count the number of data points that fall into each class to get the frequency $f$ of each class.

Step6: Calculate relative frequencies

The relative frequency $rf$ of a class is $rf=\frac{f}{n}$, where $n$ is the total number of data points.

Step7: Calculate cumulative frequencies

The cumulative frequency $cf$ of a class is the sum of the frequencies of that class and all previous classes. Starting with the first class, its cumulative frequency is equal to its frequency. For the second class, $cf = f_1 + f_2$ (where $f_1$ is the frequency of the first class and $f_2$ is the frequency of the second class), and so on.

Step8: Identify classes with max and min frequencies

After calculating all frequencies, we can identify the class with the greatest frequency and the class with the least frequency.

Since we don't have the actual minimum and maximum values of the data set, we can't give numerical answers for class limits, mid - points, frequencies, relative frequencies, and cumulative frequencies. But the general process is as above.

Answer:

Without the full data set (minimum and maximum values, all data points), we cannot complete the table. The steps to complete the table are as described above.