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3 partsStep-by-step solution
7 stepsHere's an explanation of the columns in your frequency table:
- (Variable Value): This column lists the distinct values or categories observed in your dataset.
- (Frequency): This column shows how many times each specific value appears in the dataset.
- CF (Cumulative Frequency): This is the running total of the frequencies. For each row, it represents the total number of observations that are less than or equal to the current value.
- (Product): This column is the result of multiplying each variable value () by its corresponding frequency (). The sum of this column is used to calculate the mean.
Now, let's calculate the mode, mean, and median, and then present the frequency table.
The data from the table is:
| CF (calculated) | |||
|---|---|---|---|
| 2 | 2 | 2 | 4 |
| 4 | 1 | 3 | 4 |
| 6 | 5 | 8 | 30 |
| 7 | 7 | 15 | 49 |
| 9 | 3 | 18 | 27 |
| 12 | 2 | 20 | 24 |
| Total | 20 | 138 |
Part a· 2 steps
What is the mode?
Identify the highest frequency
Looking at the column, the highest frequency is 7.
Determine the corresponding value
The value that corresponds to the frequency of 7 is 7.
The mode is .
Part b6.9
Mean
Use the formula for the mean
The mean () is calculated by dividing the sum of the products by the sum of the frequencies .
Substitute the sums from the table
From the table:
Calculate the result
The mean is .
Part c7
Median
Determine the position of the median
The total number of observations is .
Since is an even number, the median is the average of the -th and -th values.So, we need to find the 10th and 11th values.
Use cumulative frequencies to find the corresponding values
Using the calculated cumulative frequency (CF) column:
- The first 2 values are 2.
- The values from the 3rd to the 3rd are 4.
- The values from the 4th to the 8th are 6.
- The values from the 9th to the 15th are 7. Therefore, the 10th value is 7. And the 11th value is also 7. The median is the average of these two values:
The median is .
Part d
Draw a frequency table to show the distribution
Here is the frequency table showing the distribution, with the correct cumulative frequencies:
| CF | |||
|---|---|---|---|
| 2 | 2 | 2 | 4 |
| 4 | 1 | 3 | 4 |
| 6 | 5 | 8 | 30 |
| 7 | 7 | 15 | 49 |
| 9 | 3 | 18 | 27 |
| 12 | 2 | 20 | 24 |
| Total | 20 | 138 |
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