This document contains data on the number of home appliances owned by 60 Grade 7 students. It includes tables showing the frequency distribution and calculations of measures of central tendency (mean, median, mode) and variation (range, variance, standard deviation). The modal class is 1-10 appliances, with a frequency of 28. The median is in the class range of 21-30 appliances. The mean number of appliances is 15.66. The range of appliances owned is from 1 to 70, with a standard deviation of 14.08 from the mean.

1. Names: Fernandez, Roiden Fredrich Section: IX- Krypton
Sundo, Christine Kate Subject: Math9a
Tanacio, Shekinah Teacher: Lester Lou Segumpan
Tayong, Cryschia Faye Date: July 6, 2014
The following are data on the observed number of home appliances
of 60 samples of Grade 7 Topaz CMULHS Students.
Number of
Tally
ClassBoundaries
Class Mark <cf >cf fx fx²Appliances LB UB
61 - 70 2 60.5 70.5 65.5 60 2 131 8580.5
51 - 60 0 50.5 60.5 55.5 58 2 0 0
41 - 50 2 40.5 50.5 45.5 58 4 91 4140.5
31 - 40 4 30.5 40.5 35.5 56 8 142 5041
21 - 30 5 20.5 30.5 25.5 52 13 127.5 3251.25
11 - 20 19 10.5 20.5 15.5 47 32 294.5 4564.75
1 - 10 28 0.5 10.5 5.5 28 60 154 847
c=10 n=60 ∑fx=940 ∑fx²=26425
Solutions:
R = 70-2= 68
m = 1 + 3.3 log 60 = 6.86= 7 classes
c = 68/7 = 9.71
Use c= 10 since the data values are nearest ones.
The lowest value is 2. It is convenient to start with 1 as the lower limit of the 7th class.

2. Measures of Central Tendency
1. Mean
2. Median
To find median class, we need
𝑥̅ =
∑ 𝑓𝑥
𝑛
𝑥̅ =
940
60
𝑥̅ = 15.66
𝑥̃ = 𝐿 + (
𝑛
2
− 𝐹
𝑓𝑚
) 𝐶
𝑥̃ = 20.5 + (
30 − 47
5
) 10
𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 =
𝑛
2
𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 =
60
2
𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 = 30
𝑥̃ = 20.5 + (
−17
5
) 10
𝑥̃ = 20.5 + (−3.4) 10
𝑥̃ = 20.5 − 34
𝑥̃ = −13.5

3. 3. Mode
To identify the modal class, choose the class with the highest frequency:
The Modal Class is the class 1-10 because it has the highest frequency.
𝑥̈ = 𝐿 + (
𝑓𝑚𝑜 − 𝑓1
2𝑓𝑚𝑜 − 𝑓1− 𝑓2
) 𝐶
𝑥̈ = 0.5 + (
28 − 0
2(28) − 0 − 19
) 10
𝑥̈ = 0.5 + (
28
56 − 19
) 10
𝑥̈ = 0.5 + (
28
37
) 10
𝑥̈ = 0.5 + (0.756) 10
𝑥̈ = 0.5 + (0.76) 10
𝑥̈ = 0.5 + 7.6
𝑥̈ = 8.1

4. Measures of Variation
1. Range
2. Variance
3. Standard Deviation
𝑅 = 𝑈𝐵 𝑢 − 𝐿𝐵𝑙
𝑅 = 70.5 − 0.5
𝑅 = 70
𝑠2
=
𝑛 ∑ −(∑ 𝑓𝑥)²
𝑛( 𝑛 − 1)
𝑠2
=
60(26425)− (940)²
60(60 − 1)
𝑠2
=
1585500 − 883,600
60(59)
𝑠2
=
701900
3540
𝑠2
= 198.2768362
𝑠2
= 198.28
𝑠 = 14.08108079
𝑠 = √
𝑠 = √198.2768362
𝑠 = 14.08