how find median when one frequency is zero
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Answer:
To create a histogram, you first must make a quantitative frequency distribution. The following list of steps allows you to construct a perfect quantitative frequency distribution every time. Other methods may work sometimes, but they may not work every time.
1. Find the smallest data value (low score) and the largest data value (high score).
2. Select the number of classes you want. Usually, this number is between 3 and 7. (The number of classes may be given in the instructions to the problem.)
3. Determine the accuracy of the data. That is, look at the data to see how many places to the right of the decimal point are used.
4. Compute the following two numbers:
5. The class width is now chosen to be any number greater than the lower bound, but not more than the upper bound. The class width may have more accuracy than the original data, but should be easy to use in calculations. Since there may be more than one possible class width, there can be many correct frequency distributions with the same number of classes.
6. Next you compute the lower class limits. Starting with the low score, repeatedly add the class width until - including the low score - you have one lower class limit for each class.
7. The upper class limit for the first class is the biggest number below the second lower class limit with the same accuracy as the class width. To obtain the other upper class limits, you repeatedly add the class width to the first upper class limit until - including the first upper class limit - you have one upper class limit for each class.
8. For each class, count the number of data values in the class. This is the class frequency. You can do this by going through the data values one by one and making a tally mark next to the class where the data value occurs. Counting up the tallies for each class gives the class frequency. The class frequencies should be recorded in their own column.
Tally marks are optional, but you must show the class frequencies. The frequencies of the first and last class must be greater than zero. The frequency of any other class may be zero. If you tallied correctly, the sum of all the frequencies should equal the total number of data values.
Example: The following data represents the actual liquid weight in 16 "twelve-ounce" cans. Construct a frequency distribution with four classes from this data.
11.95 11.91 11.86 11.94 12.00 11.93 12.00 11.94
12.10 11.95 11.99 11.94 11.89 12.01 11.99 11.94
Solution: First we use the steps listed above to construct the frequency distribution.
Step 1: low score = 11.86, high score = 12.10
Step 2: number of classes = 4 (given in problem)
Step 3: The accuracy is two decimal places.
Step 4: Compute the lower and upper bounds.
Step 5: We can use any number bigger than 0.06, but not more than 0.08. If we restrict our attention to the simplest numbers, either 0.07 or 0.08 will work. I chose 0.08 because I think it is easier to work with than 0.07.
Step 6: By adding 0.08 to 11.86 repeatedly, we obtain the lower class limits: 11.86, 11.94, 12.02, 12.10. Notice there are 4 numbers because we want 4 classes.
Step 7: The first upper class limit is the largest number with the same accuracy as the data that is just below the second lower class limit. In this case, the number is 11.93. The other upper class limits are found by adding 0.08 repeatedly to 11.93, until there are 4 upper class limits.
Step 8: Next, for each member of the data set, we decide which class contains it and then put a tally mark by that class. The numbers corresponding to these tallies gives us the class frequencies.
Class
Tally
Frequency
11.86-11.93
||||
4
11.94-12.01
|||| |||| |
11
12.02-12.09
0
12.10-12.17
|
1
The tallies in the last step are optional, but the frequency column is required. Notice that the frequency of the third class is zero. Since this is not the first or last class, this is not a problem. Notice also that the sum of the frequencies is 16, which is the same as the number of data values.
For more examples of making a quantitative frequency distribution, go to the GeoGebra applet Quantitative Frequency Distributions
B. Making a Histogram from a
Step-by-step explanation: