The document discusses skewness, a measure of the asymmetry of a probability distribution. It provides formulas to calculate skewness based on the mean, median, and standard deviation of a data set. Skewness values between -1 and 1 indicate a symmetrical distribution, between -1 and -0.5 or 0.5 and 1 indicate moderate skewness, and outside that range indicates high skewness. Examples are given to classify distributions as positively or negatively skewed based on the relationship between the mean and median. The document then provides example data sets and problems to calculate skewness and classify the distributions.

1. Mr. Anthony F. Balatar Jr.
Subject Instructor

2. Skewness – the measure of symmetry or asymmetry
of the probability distribution of a random variable
about the mean.
To find the skewness, subtract the median from the
mean, multiply the difference by 3, and divide the
product by the standard deviation.
In symbols,
[3(mean–median)]/standard deviation

3. If skewness is -1> x > 1, the distribution is highly
skewed.
If skewness is between -1 and -0.5 or between 0.5
and 1, then the distribution is moderately skewed.
If skewness is between -0.5 and 0.5, then the
distribution is approximately normal or
symmetrical.

4. If the mean is equal to the median, the distribution
is symmetrical.
If the mean is less than the median, the
distribution is concentrated on the right side and
the left tail is longer. This is a negatively skewed
distribution.
If the mean is greater than the median, the
distribution is concentrated on the left side and the
right tail is longer. This is a positively skewed
distribution.

5. Compute the skewness and determine the kind of
distribution of the data sets given the following
characteristics: Mean Median Standard Deviation
1. 45 44 6
2. 68 70 15
3. 23.75 23.75 2.5
4. 102.5 104.32 5.35
5. 12.52 13.40 4.65
6. 800 785 100
7. 1050 1100 200
8. 0.89 0.86 0.25
9. 74 74 7
10. 13.86 13.86 3.79

6. Solve the following problems.
1. A manufacturer of flashlight batteries took a
sample of 10 batteries from a day’s production and
used them continuously until they were drained.
The time (in hours) the batteries were used until
failure is listed below. Describe the data using the
value of skewness.
397 355 415 395 352 436 327 417 276 461

7. Solve the following problems.
2. After receiving his first salary, Jerome went to the
mall to buy a pair of shoes. He visited different
stores and found out that the shoes he wants to
buy is being sold at the following prices:
₱1,500 ₱1,650 ₱1,480 ₱1,400 ₱1,450 ₱1,550 ₱1,600
Determine what type of distribution is being
described by the prices using the value of skewness.