It looks like you have a dataset of numerical values. Based on the data you've provided, we can perform various analyses or calculations, such as finding measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), and other descriptive statistics. Below are some analyses we can perform on this data set:
1. Sorting the Data:
The data is already sorted in ascending order.
2. Count of Numbers:
The total count of numbers in your dataset is 24.
3. Measures of Central Tendency:
- Mean: Sum of all values divided by the count of values.
- Median: The middle value when the data is arranged in order. Since there are 24 values (even number), the median will be the average of the 12th and 13th values.
- Mode: The value(s) that appear most frequently.
4. Measures of Dispersion:
- Range: The difference between the maximum and minimum values.
- Variance: The average of the squared differences from the mean.
- Standard Deviation: The square root of the variance.
Calculations:
Mean:
\[ \text{Mean} = \frac{159 + 175 + 189 + 190 + 191 + 202 + 208 + 210 + 218 + 220 + 232 + 234 + 234 + 253 + 253 + 261 + 265 + 275 + 295 + 295 + 304 + 305 + 308 + 308}{24} \] \[ = \frac{6276}{24} \approx 261.5 \]
Median:
The 12th and 13th numbers are 234 and 253: \[ \text{Median} = \frac{234 + 253}{2} = \frac{487}{2} = 243.5 \]
Mode:
The modes are 234 and 253 (they each appear twice).
Range:
\[ \text{Range} = 308 - 159 = 149 \]
Variance and Standard Deviation:
- Calculate each data point's deviation from the mean, square it, sum the squared deviations, then divide by the number of data points (for sample variance, divide by \(n - 1\)).
\[ \text{Variance} = \frac{\sum{(x_i - \text{mean})^2}}{n} \]
Calculating each deviation from the mean can be tedious without the exact calculations, but using the mean we found:
- Standard Deviation: \[ \text{Standard Deviation} = \sqrt{\text{Variance}} \]
Feel free to let me know if you want me to compute any specific stat or if you have any other questions regarding this dataset!