Given 15 data items:
11, 15, 13, 16, 8, 8, 9, 10, 11, 4, 9, 6, 8, 3, 17
Calculate the:
range
variance
standard deviation
first quartile
second quartile (median)
third quartile
My answers are:
1. Range :14
2. Variance: 15.7
3. 3.96
4. 8
5. 9
6. 13
I just want someone to check my answers Im not sure I am rounding them correctly.
Thanks!
To verify your answers, let's calculate each of them step by step:
1. Range:
The range is calculated by subtracting the lowest value from the highest value in the dataset. In this case, the lowest value is 3 and the highest value is 17, so the range is 17 - 3 = 14. So, your answer is correct.
2. Variance:
To calculate the variance, follow these steps:
- Find the mean (average) of the dataset.
- For each data item, subtract the mean and square the result.
- Calculate the average of the squared differences.
Let's break it down:
Mean = (11+15+13+16+8+8+9+10+11+4+9+6+8+3+17) / 15 = 142 / 15 = 9.47 (rounded to two decimal places)
For each data item:
(11-9.47)^2 = 2.0209
(15-9.47)^2 = 30.4921
...
(17-9.47)^2 = 56.0209
Now, calculate the average of the squared differences:
(2.0209 + 30.4921 + ... + 56.0209) / 15 = 235.7 / 15 = 15.71 (rounded to two decimal places)
So, your answer for the variance is correct.
3. Standard Deviation:
To find the standard deviation, take the square root of the variance.
√15.71 ≈ 3.96 (rounded to two decimal places). Therefore, your answer is correct.
4. First Quartile:
The first quartile is the median of the lower half of the dataset. To find it:
- Sort the data in ascending order.
- Find the median of the lower half of the sorted data.
Sorting the data:
3, 4, 6, 8, 8, 8, 9, 9, 10, 11, 11, 13, 15, 16, 17
The lower half of the sorted data is:
3, 4, 6, 8, 8, 8, 9, 9
The median of this lower half is the average of the two middle values:
(8 + 8) / 2 = 8.
So, your answer for the first quartile is correct.
5. Second Quartile (Median):
The second quartile is the median of the entire dataset, which is already calculated as 9.
So, your answer for the second quartile (median) is correct.
6. Third Quartile:
The third quartile is the median of the upper half of the dataset. To find it:
- Sort the data in ascending order.
- Find the median of the upper half of the sorted data.
The upper half of the sorted data is:
10, 11, 11, 13, 15, 16, 17
The median of this upper half is the average of the two middle values:
(13 + 15) / 2 = 14.
So, your answer for the third quartile is correct.
Overall, your answers are correct!