in a set of numbers {78, 79, 81, 82, 85} find
a) mean
b) median
c) standard deviation
is a) 81 b) 81 c) 2.74
mean will be 81
meadian will 81
stadndard deviation is wrong ..
i forgot how to calculate
a is-81
b is-81
c is 2.738613
are you sure that the standard deviation is wrong? because to figure it out, you have to get the mean which is 81. then subtract it from 78, 79, 81, 82, and 85. and square them and would get 4, 9, 0, 1, and 16. then you have to add them and divide by 5 - 1 which is 7.5 and get the square root which is 2.738 and rounded is 2.74
To find the mean, median, and standard deviation of a set of numbers {78, 79, 81, 82, 85}, follow these steps:
a) Mean:
The mean is calculated by taking the sum of all the numbers in the set and dividing it by the total count of numbers in the set.
Mean = (78 + 79 + 81 + 82 + 85) / 5
Mean = 405 / 5
Mean = 81
Therefore, the mean of the given set is 81.
b) Median:
The median is the middle number of a set of numbers when they are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle numbers.
Arranging the numbers in ascending order: 78, 79, 81, 82, 85
Since there are 5 numbers in the set, the middle number will be the third number, which is 81.
Therefore, the median of the given set is 81.
c) Standard Deviation:
To find the standard deviation, follow these steps:
1. Find the mean of the set.
2. Subtract the mean from each number in the set to get the deviations.
3. Square each deviation.
4. Find the mean of the squared deviations.
5. Take the square root of the mean squared deviation to get the standard deviation.
Step 1: Find the mean (already calculated as 81).
Step 2: Calculate the deviations:
Deviations = (78 - 81), (79 - 81), (81 - 81), (82 - 81), (85 - 81)
Deviations = -3, -2, 0, 1, 4
Step 3: Square each deviation:
Squared Deviations = (-3)^2, (-2)^2, (0)^2, (1)^2, (4)^2
Squared Deviations = 9, 4, 0, 1, 16
Step 4: Find the mean of the squared deviations:
Mean Squared Deviation = (9 + 4 + 0 + 1 + 16) / 5
Mean Squared Deviation = 30 / 5
Mean Squared Deviation = 6
Step 5: Take the square root of the mean squared deviation:
Standard Deviation = sqrt(6)
Standard Deviation ≈ 2.45
Therefore, the standard deviation of the given set is approximately 2.45.
In conclusion:
a) The mean of the set {78, 79, 81, 82, 85} is 81.
b) The median of the set {78, 79, 81, 82, 85} is 81.
c) The standard deviation of the set {78, 79, 81, 82, 85} is approximately 2.45.