B.Ed.104 unit4.5,4.6.4.7.4.8 statistics

1. MAEER’s
MIT SaintDnyaneshwarB.Ed.College,
Alandi(Devachi),Pune.
B.Ed. 104
ASSESSMENT AND EVALUATION FOR
LEARNING
Unit 4- INTERPRETING TEST SCORES
(Statistics): (4.5,4.6,4.7,4.8)
By.
Asst.Prof. Gangotri V. Rokade

2. UNIT4 INTERPRETINGTESTSCORES
(1 CREDIT)
Statistical measures to interpret the test scores (Meaning,
Characteristics, and Uses)
4.1 Measures of Central Tendency : Mean, Median, Mode
4.2 Measures of Variability : Quartile Deviation, Standard
Deviation
4.3 Percentile and Percentile Rank
4.4 Co-efficient of correlation by Spearman’s Rank Difference
method
4.5 Standard Scores: Z and T (Concept Only)
4.6 Graphical representation of data : Histogram, Frequency
polygon
4.7 Normal Probability Curve : Properties, Uses
4.8 Skewness and Kurtosis

3. UNIT 4 INTERPRETING TESTSCORES
4.5 Standard Scores: Z and T (Concept Only)
Standard scores are also known as derived scores from the raw
scores./ Z-scores/ T-scores.
By assuming Mean as a reference point, the raw scores are
converted. These converted scores are known as standard scores or
derived scores.
Types of standard scores:
1. Z-scores
2. T-scores

4. Computation of Z-scores
X- M X= Raw score
Z= --------- M= Mean
SD SD= standard deviation
Eg. Nisha obtained 70 marks in mathematics, mean of the class
for maths is 66 and SD is 10. compute the Z-score of Nisha.
X- M X= Raw score =70
Z= --------- M= Mean= 66
SD SD= standard deviation= 10
70-66 4
Z= ----------- = ------- = 0.4 = Nisha’s Z-score
10 10

5. Sometimes, Z-scores are obtained in d form of fractions or
sometimes negative. So it becomes difficult to interpret them.
Therefore Z-score are converted into T-scores.
T-scores:
T = Z x 10 + 50
Eg. Sarang obtained 90 marks in mathematics out of 100.
For mathematics, the Mean of the class is 80 and SD is 5.
Calculate T-scores of Sarang.
X- M X= Raw score =90
Z= --------- M= Mean= 80
SD SD= standard deviation= 5

6. 90-80 10
Z= ----------- = ------- = 2 = Sarang’s Z-score
5 5
T = Z x 10 + 50
= 2 x 10 + 50
= 20 + 50
= 70
T scores of Sarang is 70.

7. UNIT 4 INTERPRETING TESTSCORES
4.6 Graphical representation of data : Histogram,
Frequency polygon
Types of Graph:
1. Histogram:
2. Frequency Polygon
Histogram:

8. Draw a Histogram:
C.I f
40- 44 2
35- 39 5
30- 34 8
25- 29 9
20-24 12
15- 19 10
10- 14 7
05- 09 4
00- 04 3
N= 60

9. Characteristics of Histogram
1. Area of histogram is in proportion to that of frequencies.
2. CI having maximum and minimum f can be immediately
identified with the help of histogram.
3. The no. of frequencies in each class interval can be easily
known by the help of histogram.
4. We can compare frequencies in different CI s of a given
distribution with the help of histogram.
5. Range of the scores can be easily found out.
6. Easy to understand.

10. 2. Frequency Polygon

11. UNIT 4 INTERPRETING TESTSCORES
4.7 Normal Probability Curve : Properties, Uses
Normality: The tendency of scores to concentrate around the
Mean is known as Normality.
Probability: Possibility of an event occur in the same type of
several events is known as Probability.
Normal Probability Curve (NPC)
If a graph is drawn from the scores of a group of students then
its shape appears like a Bell and this bell-shaped graph is
known as the normal probability curve.
The credit of developing the theory of probability goes to Gauss,
a great mathematician of 19th century.

12. Normal Probability Curve (NPC)

13. Characteristics of Normal Probability Curve (NPC)
1. NPC is bell shaped.
2. Values of all 3 measures of Central tendency i.e. mean,
median and mode appear at the same point.
3. The point at which perpendicular from zero point on X-
axis intersect the curve is called the crest of curve.
4. In NPC, 50 % scores fall in each of the left and right
sides.
5. As the curve extended further it comes nearar to X-axis
but it never touches the same.
6. Skewness of NPC is zero.

14. UNIT 4 INTERPRETING TESTSCORES
4.8 Skewness and Kurtosis
Skewness: The distribution in which Mean and median fall on
different points is known as Skewed distribution and this
tendency of the distribution is Skewness.
Types of Skewed curves:
1. Positively Skewed curve: The distribution in which most of
the frequencies are concentrated in the class intervals having
lower values is known as positively skewed distribution and
the curve is called as Positively skewed curve
2. Negatively skewed curve: The distribution in which most of
the frequencies are concentrated in the class intervals having
higher values is known as negatively skewed distribution and
the curve is called as negatively skewed curve

15. M< Mdn< Mo M> Med> Mo

16. Kurtosis: In some distribution, the values of Mean, Median and
Mode are the same. But the height of the curve is either more or
less than NPC.
Two types of curves:
1. Leptokurtic curve: If maximum frequencies are
concentrated around the mean, then the frequencies falling
between -1σ and +1σ are more than in NPC.
2. Platykurtic curve: If scores are not concentrated around the
mean, then the frequencies falling between -1σ and +1σ are
less than in NPC.

17. M= Mdn = Mo