To analyze the personal income per capita data provided, let’s first summarize the values:
Data: 39, 39, 28, 26, 38, 36, 50, 34, 36, 44, 32, 39, 28, 26, 27, 31, 35, 33, 46, 45, 40, 47, 30, 43, 30
(a) Calculate the Mean
To find the mean, we sum all the values and divide by the number of values (n = 25).
Sum of values: \( 39 + 39 + 28 + 26 + 38 + 36 + 50 + 34 + 36 + 44 + 32 + 39 + 28 + 26 + 27 + 31 + 35 + 33 + 46 + 45 + 40 + 47 + 30 + 43 + 30 = 894 \)
Mean: \[ \text{Mean} = \frac{\text{Sum}}{n} = \frac{894}{25} = 35.76 \] Rounded to one decimal place, the mean state income is 35.8 thousand dollars.
(b) Calculate the Median
To find the median, we first need to sort the data in ascending order.
Sorted data: 26, 26, 27, 28, 28, 30, 30, 31, 32, 33, 34, 35, 36, 36, 38, 39, 39, 39, 39, 40, 43, 44, 45, 46, 50
Since there are 25 values (an odd number), the median is the middle value, which is the 13th value in the sorted list.
Median: The 13th value is 36.
Rounded to one decimal place, the median state income is 36.0 thousand dollars.
(c) Determine Skewness
To assess whether the data is skewed to the left, to the right, or approximately symmetric, we can compare the mean and median:
- Mean: 35.8
- Median: 36.0
Since the mean (35.8) is slightly less than the median (36.0), this indicates that the distribution is likely to be skewed to the left (also known as negatively skewed).
In summary:
- (a) Mean: 35.8 thousand dollars
- (b) Median: 36.0 thousand dollars
- (c) The data is likely skewed to the left.