Answer:
Explanation:
Using limit grouping with a first class of 10-16 and a class width of 7, the frequency distribution for the given data is as follows:
Class Tally Frequency
10-16 4
17-23 4
24-30 4
31-37 7
38-44 4
45-51 3
52-58 1
59-65 0
66-72 1
73-79 1
To construct this table, we first start with the first class of 10-16. The lower limit of the first class is 10, and the upper limit is 16, so any value in the data set that falls between 10 and 16 (inclusive) is assigned to this class. We use a tally mark to indicate each value that falls within this range, and then count the number of tally marks to get the frequency.
We then move on to the next class, which has a lower limit of 17 and an upper limit of 23, and repeat the process until we have accounted for all the values in the data set.
here are the step-by-step instructions for constructing the frequency distribution using limit grouping:
Determine the range of the data set by subtracting the smallest value from the largest value. In this case, the smallest value is 11 and the largest value is 70, so the range is 70 - 11 = 59.
Choose a convenient class width. In this case, we are given a class width of 7.
Determine the number of classes needed by dividing the range by the class width, and rounding up to the nearest whole number. In this case, the range is 59 and the class width is 7, so we need 9 classes.
Determine the lower limit of the first class by choosing a value that is less than or equal to the smallest value in the data set. In this case, the smallest value is 11, and the first class has a width of 7, so we can choose 10 as the lower limit of the first class.
Determine the upper limit of each class by adding the class width to the lower limit. In this case, the class width is 7, so we can add 7 to 10 to get 17 as the upper limit of the first class.
Create a table with columns for the class limits, the tally marks, and the frequency.
For each value in the data set, determine which class it belongs to by finding the class whose limits contain the value. Mark a tally in the corresponding row for that class.
Count the number of tally marks in each row to determine the frequency for that class.
Record the frequency for each class in the table.
The frequency distribution is now complete.
Note that in step 5, the upper limit of each class is not the same as the lower limit of the next class. This is because the classes are not overlapping, and we want to ensure that each value in the data set falls into exactly one class. In this case, the lower limit of the second class is 17, which is not the same as the upper limit of the first class (16).
Using limit grouping with a first class of 10-16 and a class width of 7, the frequency distribution for the given data is:
Class Tally Frequency
10-16
17-23
24-30
31-37
38-44
45-51
52-58
59-65
66-72
73-79