The document discusses different ways to calculate averages (means) from raw data sets and grouped data sets. It provides examples of calculating the mean from sets of individual scores, grouped frequency tables where only interval midpoints and frequencies are given, and formulas for estimating the mean from grouped data. It also presents practice problems asking to calculate means from sets of individual data and grouped data on people's ages and students' weights.

2. WHAT IS MEAN?
•The mean of a set of data is the sum of the data divided by the number of items in
the data set.
•The mean is also referred to as average.

3. MINI LAB
The number of marbles in each cup represents Jack’s scores for five math quizzes.
Move the marbles among the cups so that each cup has the same number of
marbles.

4. •What was Jack’s average score for the five quizzes?
Answer: 8
•If Jack scores 14 points on the next quiz, how many marbles would be in each
cup?
Answer: 9

5. The table shows the points scored by Manny Pacquiao over his opponent Adrien
Broner for the WBA “Regular” Welterweight Title. Pacquiao vs. Broner’s fight
reached up to 12 rounds. How many points need to be scored by Pacquiao during
the last round so that the average number of points scored is 9.75?
Answer: 10
Boxing Scene Scoreboard
Manny Pacquiao
10 10 10 9 10 10
10 10 9 10 9 ?

6. THE RACE AND THE NAUGHTY PUPPY
Edimar timed 21 people in a 10-meter race, to the nearest second: 59, 65, 61, 62, 53,
55, 60, 70, 64, 56, 58, 58, 62, 62, 68, 65, 56, 59, 68, 61, 67.
Mean: 61.38

7. THE RACE AND THE NAUGHTY PUPPY
Edimar then makes a grouped frequency table:

8. THE RACE AND THE NAUGHTY PUPPY
Suddenly all the original data gets lost (naughty puppy!)
Only the Grouped Frequency Table survived ...
... can we help Edimar calculate the Mean, Median and Mode from just that table?

10. Formula: 𝑥 =
𝑓𝑥
𝑛
where: 𝑥 = mean
f = frequency
x = midpoint
n= sum of frequency
ESTIMATING THE MEAN OF GROUPED DATA

11. 1. Calculate the midpoint of all intervals, denoted by x.
2. Multiply each midpoint by the corresponding frequency, denoted by fx.
3. Find the sum of these products, 𝑓𝑥.
4. Divide this sum by n.
STEPS IN COMPUTING THE MEAN OF
STATISTICAL GROUPED DATA

12. ESTIMATING THE MEAN OF GROUPED DATA
So all we have left is: •The groups (51-55, 56-60, etc), also called
class intervals, are of width 5
•The midpoints are in the middle of each
class: 53, 58, 63 and 68

13. Then we add them all up and divide by 21. The quick way to do it is to multiply each
midpoint by each frequency:
And then our estimate of the mean
time to complete the race is:
𝑥 =
𝑓𝑥
n
𝑥 =
1288
21
= 61.33
Seconds
(Class
Intervals)
Frequency
f
Midpoint
x
Frequency
x Midpoint
fx
51 – 55 2 53
56 – 60 7 58
61 – 65 8 63
66 – 70 4 68
106
406
504
272
= 1288= 21

14. Compute the mean of the following sets of data.
1. The people living together on a small town are grouped according to age as
follows:
Age Number of People
41 - 50 25
31 - 40 22
21 - 30 25
11 - 20 20
0 - 10 15

15. Compute the mean of the following sets of data.
2. Find the mean weight of Grade 7 students.
Weight in kg Frequency
75 – 79 1
70 – 74 4
65 – 69 10
60 – 64 14
55 – 59 21
50 – 54 15
45 – 49 14
40 – 44 1

16. ASSIGNMENT
Research about the median of statistical grouped data. How to find the median of
grouped data?