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3 partsStep-by-step solution
8 stepsHere's an explanation of the columns in your frequency table:
- (Variable Value): These are the distinct data points or categories.
- (Frequency): This shows how many times each value appears.
- CF (Cumulative Frequency): This is the running total of frequencies, indicating the count of observations less than or equal to the current .
- (Product): This is the product of each and its , used for calculating the mean.
Let's solve for the mode, mean, and median using the provided table.
The data from the table is:
| 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 |
Part a· 2 steps
What is the mode?
Identify the highest frequency
The highest value in the column is 7.
Find the corresponding value
The value corresponding to the frequency of 7 is 7.
The mode is .
Part b6.9
Mean
Use the formula for the mean
The mean () is given by the sum of divided by the sum of .
Substitute the sums from the table
From the table, and .
Calculate the mean
The mean is .
Part c7
Median
Determine the position of the median
The total number of observations is . Since is even, the median is the average of the -th and -th values.
We need the 10th and 11th values.
Find the values using cumulative frequency (CF)
Looking at the CF column:
- The 10th value falls within the range where CF is 15, which corresponds to .
- The 11th value also falls within this range, corresponding to . The 10th value is 7. The 11th value is 7.
Calculate the median
The median is .
Part d
Draw a frequency table to show the distribution
Here is the frequency table:
| 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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