Final answer:
To find the class width for a range of data from 10 to 91 divided into 6 classes, subtract the minimum from the maximum and divide by the number of classes. This gives a class width of 13.5, which can be rounded to 14. Construct lower and upper class limits by adding the class width to the previous lower limit for the next set of classes.
Step-by-step explanation:
To find the class width, lower class limits, and upper class limits given a minimum data entry of 10 (a), a maximum data entry of 91 (b), and the number of classes being 6 (c), you should first calculate the range by subtracting the minimum value from the maximum value (91 - 10 = 81).
Next, to find the class width, divide the range by the number of classes (81 ÷ 6 = 13.5). To ensure that all values are included and that the minimum value is the start of a class interval, it's common to round the class width up to the next whole number if necessary. In this case, the class width is 13.5, which we could round up to 14 for simplicity.
Starting with the minimum value as the first lower class limit and adding the class width each time will give you the lower class limits, and then adding one less than the class width to each lower class limit will provide the upper class limits. The lower class limits will be 10, 24, 38, 52, 66, and 80. The corresponding upper class limits are 23, 37, 51, 65, 79, and 93.
In constructing a histogram, remember that data values falling on the right boundary are counted in the class interval, while those on the left are not, except for the first interval where both boundaries' values are included.