Here is a data set on wing lengths in cm: 8, 9, 10, 10, 12, 13, 13, 14, 15, 15, 15, 19, 22, 25, 25. For this sample data set, the mean, median and mode are _________,_________and_________ respectively.
Wing Length Data Set: Mean, Median, Mode Calculation
This solution calculates the mean, median, and mode for the provided sample data set of wing lengths.
Mean Calculation for Wing Lengths
The mean represents the average value.
- Sum all data points: $8 + 9 + 10 + 10 + 12 + 13 + 13 + 14 + 15 + 15 + 15 + 19 + 22 + 25 + 25 = 225$.
- Count the number of observations: $n = 15$.
- Calculate the mean: $\text{Mean} = \frac{\sum x}{n} = \frac{225}{15} = 15$.
Median Calculation for Wing Lengths
The median is the middle value when the data is ordered.
- The data set is already sorted: $8, 9, 10, 10, 12, 13, 13, 14, 15, 15, 15, 19, 22, 25, 25$.
- Determine the position of the median for $n=15$ (odd number): Position $= \frac{n+1}{2} = \frac{15+1}{2} = 8$.
- The 8th value in the sorted list is 14.
- Median = 14.
Mode Determination for Wing Lengths
The mode is the most frequently occurring value.
Observe the frequency of each value in the data set:
- 15 appears 3 times.
- 10 and 25 appear 2 times each.
- Other values appear once.
The value 15 occurs most often.
Mode = 15.
Final Results: Mean, Median, Mode
The calculated values are: Mean = 15, Median = 14, and Mode = 15.
Important Questions from Mean Median Mode
- The median of the following set of numbers: 154, 130, 144, 137, 156, 146, 138, 149, 160, 138 is:
- Let $X$ be a continuous random variable whose cumulative distribution function (CDF)
$F_X(x) = \begin{cases} 0 & x < t \\ \frac{x-t}{4-t} & t \le x \le 4 \\ 1 & x \ge 4 \end{cases}$
If the median of $X$ is $3$, then what is the value of $t$? - The elements of the dataset $\{-5,1, a, 5, b\}$ are in ascending order. If both mean and median of the dataset are equal to 3, what is the value of $b$?
- The sample average of 50 data points is 40. The updated sample average after including a new data point taking the value of 142 is ________.
The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT?
