1. The document presents data on the heights of 25 students. It includes frequency distributions, measures of central tendency (mean, median, mode), measures of dispersion (standard deviation, variance), and other statistical analyses. 2. The mean height is 168.9 cm, median is 169.5 cm, and mode is 171.5 cm. Standard deviation is 6.086 cm. 3. The distribution is found to be negatively skewed.

1. Welcome to our presentation
STUDENT HEIGHT

2. Group Members:
1.Golam Mostafa Imran(161-15-6930).
2.Raseduzzaman(161-15-7494).
3.Monirul Awal(161-15-7501).
4.Asrafuzaman(161-15-7507).

3. Overview:
1.Frequency Distribution of Students.
2.Compute AM,GM,HM of Students.
3.Compute Median, Mode of Students.
4.Compute Standard and mean deviation of Students.
5.Compute Coefficient Of Variable and Skewness of Students.

4. Collection of data & Frequency distribution
Collected data:
 155,170,171,158,160,168,169,170,170,172,1
61, 166,182,166,167,168,173,173,173,
162,163,164,174,176,179
Frequency distribution:
 Step-1: Organize the data into ascending order,
 155,158,160,161,162,163,164,166,166,167,168,1
68,169,170,170,170,171,172,173,173,173,174,17
6,179,182
 Step-2: Determine the number of class,
 2 𝑘
>=n
 Where ,
 K= the number of classes.
 n = total number of observation.

5. Frequency distribution:
 Step-3: Determine the class interval (H-L)/K>=i
 Where ,
 K=the number of classes
 H=Highest value
 L=lowest value
 I=class interval

6. Step-4: Set up the classes:
class f F xi fixi filogxi
155-160 2 2 157.5 315 4.39 11.4 129.96 259.92
160-165 5 7 162.5 812.5 11.05 6.4 40.96 204.8
165-170 6 13 167.5 1005 13.34 1.4 1.96 11.76
170-175 9 22 172.5 1552.5 20.13 3.6 12.96 116.64
175-180 2 24 177.5 355 4.5 8.6 73.96 147.92
180-185 1 25 182.5 182.5 2.26 13.6 184.96 184.96
25 1020 4222.5 55.67 45 926
|𝑥𝑖 − 𝑥| |𝑥𝑖 − 𝑥|² fi|𝑥𝑖 − 𝑥|²

7. Graph of Frequency polygon :

8. **Measures of central tendency
Measures of central tendency is the measurement of the data set
or observations to cluster around a central value.
Kind of Measures of central tendency:
1.Mean
i. Arithmetic mean:
𝑥 =
∑𝑓𝑖𝑥𝑖
𝑁
ii. Geometric mean
GM= antilog[
∑𝑓𝑖𝑙𝑜𝑔𝑥𝑖
𝑁
]
iii. Harmonic mean
HN=
𝑁
∑
𝑓𝑖
𝑋𝑖
2.Median
Me=L0 +
𝑖
𝑓
(
𝑁
2
− 𝐹)
3.Mode
Mo= L0+
⧍1
⧍1+⧍2
*i

9. *** Measure of location:
 Measures of location summarize a list of numbers by a "typical" value. The three most common measures of
location are the mean, the median, and the mode. The mean is the sum of the values, divided by the number of
values.
 Kind of Measure of location:
 Quartile
 Qj=L0+
𝑖
𝑓
(
𝑗𝑁
4
-F)
 Decile
 Dj=L0+
𝑖
𝑓
(
𝑗𝑁
10
-F)
 Percentile
 Pj=L0+
𝑖
𝑓
(
𝑗𝑁
100
-F)

10. Measures of central tendency
Arithmetic mean:
Given that,
 ∑fixi = 4222.5
 𝑥 =4222.5/25
 N = 25
 We know,
 𝑥 =
∑𝑓𝑖𝑥𝑖
𝑁
 𝑥=168.9
 The arithmetic mean of our data is 168.9 cm
Geometric mean:
 Given that,
 filogxi=55.67
 N=25
 We know,
 GM= antilog[
∑𝑓𝑖𝑙𝑜𝑔𝑥𝑖
𝑁
]
 GM= antilog (55.67/25)
 GM=168.57
 The Geometric mean of our data is 168.57 cm

11. Measures of central tendency
Harmonic mean:
 Given that,
 N=25
 ∑
𝑓𝑖
𝑋𝑖
= 0.025
 We know,
 HM=
𝑁
∑
𝑓𝑖
𝑋𝑖
 HM=25/0.025
 HM=1000
 The Harmonic mean of our data is 1000 cm

12. Measures of central tendency
2.Median:
Me=L0 +
𝑖
𝑓
(
𝑁
2
− 𝐹) Here,
Me = 165+5/6(25/2-7) N/2=25/2=12.5≈13th observation line in the (165-170) class
Me =169.5 So (165-170) is the median class
L0 =165
i= 5
f= 6
N=25
F=7
The median of our data is 169.5 cm

13. Measures of central tendency
3.Mode:
Mo= L0+
⧍1
⧍1+⧍2
*i Here,
Mo = 170+(3/10)*5 The frequency of class(170-175) is heigst so (170-175) class is Modal class
Mo = 171.5 L0 =170 i= 5
⧍1=3
⧍2=7
The mode of our data is 170 cm

14. Measures of location
Measures of location summarize a list of numbers by a "typical" value. The three most common measures of
location are the mean, the median, and the mode. The mean is the sum of the values, divided by the number
of values.
Kind of Measure of location:
1.Quartile Here,
Qj=L0+
𝑖
𝑓
(
𝑗𝑁
4
-F) Let, j=1.
Qj=160+5/6(25/4-2) Nj/4=(25*1)/4=6.25 ≈ 7th observation line is(160-165)
Qj= 172.5 Class, so (160-165) is quartile class,

15. Measures of location
2.Decile:
 Dj=L0+
𝑖
𝑓
(
𝑗𝑁
10
-F)
 Dj=165+5/5(25*5/10-7)
 Dj=170.5
 Let,
 j=5.
 Nj/10=(25*5)/10=12.5 ≈ 13th observation line
is(165-170) Class, so (165-170) is Decile class,

16. Measures of location
3.Percentail:
Pj=L0+
𝑖
𝑓
(
𝑗𝑁
100
-F)
Pj=160+5/5(25*25/100-2)
Pj=164
 let j=25.
 Nj/100=(25*25)/10=≈ 7th observation line
is(160-165) Class, so (160-17165) is percentile
class.

17. *** Measures of Dispersion:
 Mean deviation
 MD=
(∑|𝑋𝑖−𝑋 |)
𝑁
 Standard deviation
 ∂= √
∑𝑓𝑖𝑋𝑖2
𝑁
- 𝑋2
 Variance
 ∂2
 Coefficient of variation
 CV=
𝜕
𝑥
*100

18. *** Measures of Dispersion:
Mean deviation:
 Given that,
 ∑|xi- 𝑥| = 45
 N = 25
 We know,
 MD=
(∑|𝑋𝑖−𝑋 |)
𝑁
= 45/25
= 1.8
Standard deviation:
 Given that,
 ∑𝑓𝑖 𝑥𝑖 − 𝑥 2
= 926
 𝑋² = 28527.21
 N = 25
 We know,
 ∂ =
∑ 𝑓𝑖 𝑥𝑖− 𝑥 2
𝑁
 ∂ = 6.086

19. *** Measures of Dispersion:
Variance:
 Given that,
∂ = 6.086
 We know,
 Variance = ∂2
= 37.039
Coefficient of variation:
 Given that,
 ∂ = 6.086
 𝑥 = 168.9
 We know,
 CV=
𝜕
𝑥
*100
=3.60%

20. ***Skewness:
 Given that,
 Mo = 171.5
 𝑥 = 168.9
 ∂ = 6.086
 We know,
 Skp =
𝑥−𝑚𝑜
𝜕
= -0.427
Comment: This distribution is negatively skewed.