Assume, if 10 patient calves were admitted to veterinary clinic you are working on took the age of animals in years from all patient calves that recorded as 7, 9, 7, 7, 7, 6, 6, 6... Assume, if 10 patient calves were admitted to veterinary clinic you are working on took the age of animals in years from all patient calves that recorded as 7, 9, 7, 7, 7, 6, 6, 6 on the scores of age of the patient animals listed above, find: A. The mean B. The median C. The mode and its type also D. The range E. The variance
Understand the Problem
The question asks to calculate the mean, median, mode, range and variance of the provided dataset which represents ages of calves.
Answer
A. Mean = 7 B. Median = 7 C. Mode = 7, Unimodal D. Range = 3 E. Variance = 0.8
Answer for screen readers
A. Mean = 7 B. Median = 7 C. Mode = 7, Unimodal D. Range = 3 E. Variance = 0.8
Steps to Solve
- Calculate the Mean
The mean is the average of all the numbers. To calculate it, we add all the numbers together and then divide by the total number of numbers. The ages of the calves are: 7, 9, 7, 7, 7, 6, 6, 6, 8, 7. Thus we have 10 calves.
$$ Mean = \frac{7 + 9 + 7 + 7 + 7 + 6 + 6 + 6 + 8 + 7}{10} = \frac{70}{10} = 7 $$
- Calculate the Median
The median is the middle value when the numbers are arranged in order. First, sort the numbers in ascending order: 6, 6, 6, 7, 7, 7, 7, 7, 8, 9. Since there are 10 numbers (an even number), the median is the average of the two middle numbers. In this case, the two middle numbers are the 5th and 6th numbers, which are both 7.
$$ Median = \frac{7 + 7}{2} = \frac{14}{2} = 7 $$
- Determine the Mode
The mode is the number that appears most frequently. In the dataset 6, 6, 6, 7, 7, 7, 7, 7, 8, 9, the number 7 appears 5 times, which is more than any other number. Therefore, the mode is 7. This is a unimodal distribution because there is only one mode.
- Calculate the Range
The range is the difference between the largest and smallest numbers. The largest number is 9, and the smallest number is 6.
$$ Range = 9 - 6 = 3 $$
- Calculate the Variance
The variance measures how spread out the numbers are. Here's how to calculate it:
a. Find the mean (already calculated in step 1): $Mean = 7$
b. Subtract the mean from each number and square the result: $(6-7)^2 = 1$ $(6-7)^2 = 1$ $(6-7)^2 = 1$ $(7-7)^2 = 0$ $(7-7)^2 = 0$ $(7-7)^2 = 0$ $(7-7)^2 = 0$ $(7-7)^2 = 0$ $(8-7)^2 = 1$ $(9-7)^2 = 4$
c. Add up all the squared differences: $1 + 1 + 1 + 0 + 0 + 0 + 0 + 0 + 1 + 4 = 8$
d. Divide by the number of values (10) to get the variance: $$ Variance = \frac{8}{10} = 0.8 $$
A. Mean = 7 B. Median = 7 C. Mode = 7, Unimodal D. Range = 3 E. Variance = 0.8
More Information
The mean, median, and mode are all measures of central tendency. The range and variance are measures of dispersion or spread.
Tips
- Forgetting to sort the data before finding the median.
- Incorrectly calculating the variance by not squaring the differences or dividing by the wrong number.
- Confusing mean, median, and mode.
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