This document discusses using appropriate statistical measures to analyze and interpret statistical data. It introduces common measures of central tendency (mean, median, mode) and measures of variability (range, average deviation, variance, standard deviation). Examples are provided to illustrate calculating and applying these statistical measures to different datasets. The document concludes with an activity that prompts the reader to determine and apply the right statistical measure to analyze given data sets.

1. Analyzing and
Interpreting Statistical
Data
STATISTICS

2. Uses appropriate statistical measures in
analyzing and interpreting statistical data
Today we will...

3. Solve the puzzle by providing the words defined in each number.
Activity 1

4. ACROSS:
1. ________________ deviation of a set of scores is calculated by computing the mean and
then the specific distance
between each score and that mean without regard to whether the score is above or below the
mean.
3. ________________ deviation is a measure of variation of the set of data in terms of the
amounts by which the individual
values differ from their mean.
4. ________________ is generally considered the best measure of central tendency and the
most frequently used one.
5. ________________ is the middle value in the set of data arranged in increasing or
decreasing order.
DOWN:
2. _______________ is the difference between the highest and lowest values.
4. _______________ is the most frequently occurring number or score in a data set.

5. Analyzing and Interpreting Statistical Data
When to use Measures of Central Tendency
One of the most important and useful numerical
descriptive measures are the Measures of Central
Tendency. Measures of Central Tendency are
numerical descriptive measures used to describe the
center of a given set of data. Three common
measures of central tendency are: the mean, the
median, and the mode.

6. Analyzing and Interpreting Statistical Data
The mean is the most reliable. It is
used when the data are of interval or
ratio scale. The median is generally
used when the data are of ordinal
scale. The mode is commonly used
when the data are of nominal level.

7. Examples:
1. Due to the pandemic, many students had difficulties in studying on
their own. Yvonne, a consistent honor student, wants to find out if
her grades still meet the mark this year. She got 87 in Filipino, 92 in
English, 92 in Mathematics, 88 in Science, 90 in Araling Panlipunan,
94 in Edukasyon sa Pagpapakatao, 90 in Technology and Livelihood
Education, and 87 in MAPEH. Is she qualified for honors? Why do you
say so?
To find out if Yvonne is still an honor student, we can use the mean,
solving for the mean, we get 90. Since honor students must have an
average of 90 and above, Yvonne is still With Honors.

8. Examples:
2. Obina Family drove through 7 cities on their summer
vacation. Gasoline prices varied from city to city. The price of
the gasoline are as follows: ₱48, ₱55, ₱50, ₱52, ₱47, ₱53, ₱49.
They want to know the middle price of their gasoline.
To find the middle price of the gasoline, they can use the
median. To determine the median of the given set, arrange the
data values from lowest to highest (increasing order). The value
that divides the distribution in half is the median. In this case,
the median price of gasoline is 50.

9. Examples:
3. The manager of a video shop wants to know the most common
number of blank tapes he sold in his shop. So, he recorded the
number of blank tapes sold per day in 2 weeks. What do you think
should he use to find the most common number of blank tapes he
sold in 2 weeks?
132, 121, 119, 116, 130, 121, 131, 117, 119, 135, 121, 129, 119, 134
To find the most common number of blank tapes he sold, he will get
the mode of the given data. The mode is 119, because it appears
three times in the given data. Since 119, appearing three times it is
the most common blank tape the manager sold in his shop.

10. When to use Measures of Variability
Measures of Variability are the measures of the average distance of
each observation from the center of the distribution. The goal for
variability is to obtain a measure of how spread out the scores are in
distribution. The range is the difference between the highest and
lowest values. The average deviation is the average value by which any
value in a set of data or distribution differs from the mean. Variance is
the average of the squared deviation from the mean. Standard
deviation determines the location of every value in the set of data
related to the mean, and it is the most important and most applied
measure of variability. Standard deviation is also used to compare two
sets of data.

11. Examples:
1. A marathon race was completed by 5 participants. 3.7 hours,
6.3 hours 2.9 hours, 4.1 hours, and 7.3 hours are the recorded
time of the participants. The organizer wants to know the
difference between the first and the last to finish.
To find the difference, we use the range. It is the difference
between the highest and lowest value in a data set. In this
example, the range is 4.4 hours. The winner of the race is faster
by 4.4 hours from the last to finish.

12. Examples:
2. Jeff and James measured the height of the dogs (in millimeters).
The height is: 600 mm, 470 mm, 170 mm, 430 mm, and 300 mm. If
they want to know the average dog’s height from the mean, they can
use average deviation, because average deviation is telling us how far,
on average, all values are from the middle. The average deviation is
127.2 mm.
This average deviation indicates that the heights of the dogs are
127.2 mm far from the mean which is 394 mm. You can also infer that
the heights of the dogs are scattered because the average deviation is
too high.

13. Examples:
3. Two groups of students competed for the championship. The First
Group scored 70, 95, 60, 80 and 100 while the Second Group scored
82, 80, 83, 81 and 79. Which group performed better together?
We can use the variance. From the given, the variance of the first
group is 280 square units while the second group is 2.5 square units.
Using the variance as a measure of variability for the sets of scores,
the first group showed more variability in performance. Note that the
higher the variance, the more variable or far apart the values are
from each other. So that means, the second group has closer scores
than the first. Thus, they performed better together.

14. Examples:
4. Chris wants to know how consistent his bowling
scores have been during the past seasons. What
measures of variability would provide the most
appropriate answer to his questions?
The most appropriate is standard deviation because it
uses all data points in its calculation, it is the best
measure of variability for Chris to calculate. Also, the
standard deviation is used to compare sets of data.

15. Activity 2
Determine the appropriate statistical measure to be used and analyze the statistical
data. Write your answer on a separate answer sheet.
For numbers 1 to 5, refer to the table below.
The table shows the grades of the students in 5 subject areas.
Let us determine the appropriate Statistical Measure to be used in order to answer
the following questions on a separate answer sheet.

16. 1. What is the average grade of each student?
2. What is the grade did most of the students have?
3. Are the grades of Benj close or spread out?
4. If the students will be ranked according to their
average grade, who will be in the middle?
5. What is the difference between Cris' highest
grade
and lowest grade?

17. Learning Task
Determine the appropriate statistical measure to be used and analyze the statistical
data. Write your answer on a separate answer sheet.
If you were the store manager, analyze and interpret the data using the appropriate
statistical measure.

18. Learning Task
6. What cellphone brand has the most sales?
7. What is the average sale of iPhone for the three
months?
8. Are the sales of Huawei for three months close or spread
out?
9. By how much is the highest sale of Samsung differ from
its lowest sale?
10. If the data will be arranged from highest sale to lowest
sale, combining all brands, what value will be in the
middle?

19. Thank You!