Given the list 10,7,5,3,-6
find by hand, mean,meadian, midrange, mode(s), range, popvar, and sample standard deviation.
(seven problems)
Find the mean first = 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
There is no mode for these 5 scores (most frequently observed score).
Range = highest score - lowest.
Median: arrange scores in order of value, score that divides highest 50% from lowest 50% = median.
I'll let you do the calculations.
consider a football team whom the numbers on active players' jersey are 29,41, 50, 58, 79,..., 10 (listed in alphabetical order of the players' names) Does it make sense to calculate the mean of those numbers? why or why not?
To find the mean, median, midrange, mode(s), range, population variance (popvar), and sample standard deviation of a given list, follow these steps:
Step 1: Start by arranging the numbers in ascending order: -6, 3, 5, 7, 10.
Step 2: Calculate the Mean:
- The mean is the average of all the values in the list.
- Add up all the numbers in the list: -6 + 3 + 5 + 7 + 10 = 19.
- Divide the sum by the total number of values in the list (which is 5): 19 ÷ 5 = 3.8.
- So, the mean of the given list is 3.8.
Step 3: Calculate the Median:
- The median is the middle value in the list.
- Since the list has an odd number of values (5), the median is the middle value, which is 5.
- So, the median of the given list is 5.
Step 4: Calculate the Midrange:
- The midrange is the average of the largest and smallest values in the list.
- The smallest value is -6, and the largest value is 10.
- Add the smallest and largest values together: -6 + 10 = 4.
- Divide the sum by 2: 4 ÷ 2 = 2.
- So, the midrange of the given list is 2.
Step 5: Calculate the Mode(s):
- The mode is the value(s) that occur most frequently in the list.
- In this case, none of the values repeat, so there is no mode.
- Therefore, there are no modes in the given list.
Step 6: Calculate the Range:
- The range is the difference between the largest and smallest values in the list.
- The smallest value is -6, and the largest value is 10.
- Subtract the smallest value from the largest value: 10 - (-6) = 16.
- So, the range of the given list is 16.
Step 7: Calculate the Population Variance (popvar):
- The population variance measures how spread out the data is from the mean.
- Subtract the mean from each value in the list, square the result, and sum all the squares:
((-6 - 3.8)^2 + (3 - 3.8)^2 + (5 - 3.8)^2 + (7 - 3.8)^2 + (10 - 3.8)^2) ÷ 5 = 42.56
- Divide the sum by the total number of values in the list (which is 5): 42.56 ÷ 5 = 8.512.
- So, the population variance of the given list is 8.512.
Step 8: Calculate the Sample Standard Deviation:
- The sample standard deviation is the square root of the population variance.
- Take the square root of the population variance: √8.512 ≈ 2.916.
- So, the sample standard deviation of the given list is approximately 2.916.
In summary, the results for the given list are as follows:
- Mean: 3.8
- Median: 5
- Midrange: 2
- Mode(s): No mode(s)
- Range: 16
- Population Variance: 8.512
- Sample Standard Deviation: Approximately 2.916