What is the mean of the range, median and modeofthe data given below? 1, 2, 5, 9, 6, 3, 9, 7, 4, 3, 9, 1, 9, 6, 8, 1

Options

A. `7 (1)/(2)`
B. `8`
C. `8 (1)/(2)`
D. 7

Answer

To find the mean of the range, median, and mode of the given data set: 1, 2, 5, 9, 6, 3, 9, 7, 4, 3, 9, 1, 9, 6, 8, 1, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the data in ascending order:
1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 9

### Step 2: Calculate the Range
The range is calculated as the difference between the maximum and minimum values in the data set.
- Maximum value = 9
- Minimum value = 1
- Range = Maximum - Minimum = 9 - 1 = 8

### Step 3: Calculate the Median
To find the median, we need to locate the middle value of the ordered data. Since there are 16 values (an even number), the median will be the average of the 8th and 9th values.
- 8th value = 4
- 9th value = 5
- Median = (4 + 5) / 2 = 9 / 2 = 4.5

### Step 4: Calculate the Mode
The mode is the value that appears most frequently in the data set.
- The number 9 appears 4 times, which is more than any other number.
- Mode = 9

### Step 5: Calculate the Mean of Range, Median, and Mode
Now we will calculate the mean of the three values we found: range, median, and mode.
- Range = 8
- Median = 4.5
- Mode = 9
- Mean = (Range + Median + Mode) / 3
- Mean = (8 + 4.5 + 9) / 3
- Mean = 21.5 / 3 = 7.1667 (or 7.17 when rounded to two decimal places)

### Final Answer
The mean of the range, median, and mode is approximately 7.17.

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