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What is the modal range of the students? Find the mean and median age. Construct a frequency table for the data. Use your table to calculate the mean & median. State what is the mode of the distribution?
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2 partsStep-by-step solution
2 stepsHere's the solution for question 4:
Part i
Construct a frequency table for the data.
First, we list the scores and count their frequencies. The scores are:
12, 26, 15, 14, 14, 12, 16, 26, 12, 15, 15, 14, 26, 26, 15, 14, 19, 12, 26, 19, 19, 19, 14, 15, 26, 12, 14, 26, 12, 15, 26, 12
Let be the score and be the frequency. We also calculate and the cumulative frequency (CF).
| Score () | Frequency () | Cumulative Frequency (CF) | |
|---|---|---|---|
| 12 | 8 | 96 | 8 |
| 14 | 7 | 98 | 15 |
| 15 | 7 | 105 | 22 |
| 16 | 1 | 16 | 23 |
| 19 | 4 | 76 | 27 |
| 26 | 8 | 208 | 35 |
| Total | 35 | 599 |
Part ii17.11
Use your table to calculate the mean and median.
To calculate the mean (), we use the formula , where is the total number of students.
From the table, and .
Calculate the mean.
The mean score is (rounded to two decimal places).
Calculate the median.
The total number of data points is . The position of the median is given by .
We look at the cumulative frequency column to find the score at the 18th position.
- The first 8 scores are 12.
- The scores from 9 to 15 are 14.
- The scores from 16 to 22 are 15. Since the 18th position falls within the range of scores that are 15, the median is 15. The median score is .
Part iii
State what is the mode of the distribution?
The mode is the score that appears most frequently in the data.
From the frequency table:
- Score 12 has a frequency of 8.
- Score 14 has a frequency of 7.
- Score 15 has a frequency of 7.
- Score 16 has a frequency of 1.
- Score 19 has a frequency of 4.
- Score 26 has a frequency of 8. The highest frequency is 8, which corresponds to two scores: 12 and 26. The distribution is bimodal. The mode of the distribution is .
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