The following tables shows the hourly wages of all workers in a certain hospital. Determine the pearsonian coefficient of skewness (population data).

Hourly wages frequency
90-99 5
100-109 9
110-119 5
120-129 7
130-139 5
140-149 3

My answers:
mean = 116.56
s = 15.72
But i don't know how to solve for the mdn and the pearsonian coefficient of skewness. thank you:D

http://https://www.easycalculation.com/statistics/skewness-coefficient.php

To calculate the median and the Pearsonian coefficient of skewness, follow these steps:

Step 1: Find the Median
The median represents the middle value of a set of data when ordered. To find the median, you need to arrange the data in ascending order. In this case, the data is already given in intervals, so we can use the midpoint of each interval as an approximate value for calculations.

Hourly Wages Frequency Midpoint (x) fx
90-99 5 94.5 472.5
100-109 9 104.5 940.5
110-119 5 114.5 572.5
120-129 7 124.5 871.5
130-139 5 134.5 672.5
140-149 3 144.5 433.5

To find the median, we need to find the cumulative frequency (CF) and the median group.

Cumulative Frequency (CF) calculations:
For each row, add up the frequencies starting from the first row:

First row: CF = 5
Second row: CF = 5 + 9 = 14
Third row: CF = 14 + 5 = 19
Fourth row: CF = 19 + 7 = 26
Fifth row: CF = 26 + 5 = 31
Last row: CF = 31 + 3 = 34

Since the total frequency (sum of all the frequencies) is 34, the median group will be the one where the cumulative frequency (CF) crosses half the total frequency. In this case, CF = 17, which lies in the second row (100-109 interval).

Now we can calculate the median:
Median = Lower Bound +[(0.5 * n - CF) / Frequency] * Width

Lower Bound = 100 (from the median group)
n = Total Frequency = 34
CF = Cumulative Frequency of previous group = 14
Frequency = Frequency of the median group = 9
Width = Range of the interval = 109 - 100 = 9

Median = 100 + [(0.5 * 34 - 14) / 9] * 9
Median = 100 + [(17 - 14) / 9] * 9
Median = 100 + (3/9) * 9
Median = 100 + 3
Median = 103

Therefore, the median value is 103.

Step 2: Calculate the Pearsonian Coefficient of Skewness (Population Data)
The Pearsonian Coefficient of Skewness is calculated using the formula:

Coefficient of Skewness = 3 * (Mean - Median) / Standard Deviation

Given:
Mean (x̄) = 116.56
Median (Md) = 103
Standard Deviation (s) = 15.72

Coefficient of Skewness = 3 * (116.56 - 103) / 15.72
Coefficient of Skewness = 3 * 13.56 / 15.72
Coefficient of Skewness = 2.598

Therefore, the Pearsonian Coefficient of Skewness for the population data is approximately 2.598.

Note: The Pearsonian Coefficient of Skewness helps to determine the skewness (symmetry or asymmetry) of a distribution. A positive value indicates a right skew (tail to the right), a negative value indicates a left skew (tail to the left), and a value close to zero indicates near symmetry.