6,12,6,8,10,12,8,14,16 find mean medion mode and standerd deviation
Arrange the collection data values in order with their corresponding frequently: 2 6 5 8 5 5 3
1. What score frequently appears?
2. What score appears to be in the middle?
3. How many students fall below the middle?
Arrange the collection data values in ascending order with their corresponding frequently: 2 6 5 8 2 5 5 3
Questions:
1. What score frequently appears?
2. What score appears to be the middle?
3. How many students fall below the middle score?
To find the mean, median, mode, and standard deviation of the given set of numbers: 6, 12, 6, 8, 10, 12, 8, 14, 16, we can follow these steps:
Mean:
1. Add up all the numbers in the set: 6 + 12 + 6 + 8 + 10 + 12 + 8 + 14 + 16 = 92.
2. Divide the sum by the number of values in the set, which is 9: 92 / 9 = 10.22 (rounded to two decimal places).
So, the mean of the given set is 10.22.
Median:
1. Arrange the numbers in ascending order: 6, 6, 8, 8, 10, 12, 12, 14, 16.
2. Since the set has an odd number of values (9 in total), the median is the middle value.
In this case, the middle value is the 5th number, which is 10.
So, the median of the given set is 10.
Mode:
1. The mode is the value that appears most frequently in the set.
2. In this case, the numbers 6 and 12 occur twice, while the rest occur once.
Therefore, the modes are 6 and 12.
So, the modes of the given set are 6 and 12.
Standard Deviation:
1. Find the mean of the set. In this case, we already calculated the mean as 10.22.
2. Subtract the mean from each value in the set and square the result.
For each value: subtract mean, then square the result.
(6 - 10.22)^2 = 18.08
(12 - 10.22)^2 = 3.14
(6 - 10.22)^2 = 18.08
(8 - 10.22)^2 = 4.92
(10 - 10.22)^2 = 0.05
(12 - 10.22)^2 = 3.14
(8 - 10.22)^2 = 4.92
(14 - 10.22)^2 = 14.35
(16 - 10.22)^2 = 33.23
3. Find the mean of the squared differences: (18.08 + 3.14 + 18.08 + 4.92 + 0.05 + 3.14 + 4.92 + 14.35 + 33.23) / 9 = 10.49 (rounded to two decimal places).
4. Take the square root of the mean calculated in step 3: sqrt(10.49) ≈ 3.24 (rounded to two decimal places).
So, the standard deviation of the given set is approximately 3.24.
Mode = most frequently occurring score(s)
Median = arrange in order of value, then find middle-most score.
Mean = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
I'll let you do the calculations.