# Educational Statistics- Essay type questions

You have just graduated from a College of Education. Explain to an untrained teacher, using
appropriate examples, five reasons why it is important for teachers to study statistics in
education.

a. Using appropriate statistics to describe performance

b. Understanding information from test scores

d. Reading and understanding professional journals in education

c. Carrying out research in education

2. i. State three weaknesses of the mean as a measure of location.

a. It is influenced by extreme scores

b. it is very sensitive to a change in the value of any score

c. It cannot be computed if a score is missing and the sum of the scores or observations cannot be obtained.

ii. Explain, using examples, three properties of the mean.

AMSWER

a. The mean is influenced by every score or values that makes it up. If a score is
changed, the values of the mean change.

b. The mean is very sensitive to extreme scores which are called outliers.

c. The mean is a function of the sum (or aggregate or total) of the scores. This
implies that one cannot obtain the mean without knowing the sum of the scores. If one number is missing, the mean cannot be obtained.

d. If the mean is subtracted from each individual score and the difference are
summed, the result is 0

e. If the same value is added to or subtracted from every number in a set of scores,
the mean goes up or goes down by the value of the number

f. If each score is multiplied or divided by the same value, the mean increases or
decreases by the same value.

iii. In an end of semester examination, a mean of 60 and a standard deviation of 5 were
obtained.

a. Obtain the coefficient of variation

CV = 8.3%

b. What information do you derive from the value of the coefficient of variation
concerning the nature of the class?

The class is homogeneous since the value of CV is less than 33%

c.State one use of the coefficient of variation in teaching and learning.

a. It is used to determine whether a group is homogeneous or heterogeneous. If the value of
the CV is 33% or less, then the group is homogeneous, otherwise, it is heterogeneous.

b. It is used to compare variations within or between groups where there are different units of measurement.

c. it is used to compare variations within or between group where there are different means
but with the same unit of measurement.

3.i What is a Z standard score?
It represents an individual raw score that has been transformed into a common
standard based on a mean of O and a standard deviation of 1.

ii. State two differences between Z and T standard scores.

a. Z score has a mean of 0 while T score has a mean of 50

b. Z score has a standard deviation/variance of 1 while T score has a standard
deviation of 10

c. Z score ranges from – 4 to +4 while T score ranges from 10 – 90

d. Z score could be positive or negative but T score is always positive.

iii. In an entrance examination a student obtained a raw score of 72. It is known that the
student’s Z score was 3.0. if the standard deviation for the group is 5, calculate the
mean score for the group.

x = 57

iv. Describe, with examples three ways by which the classroom teacher can improve
teaching and learning by the use of Z scores.
Ways

a. It helps the teacher to know an individual’s position in relation to the rest of the
class

b. It enables the teacher to compare student’s performances in different subjects to
know the individual strengths and weaknesses

c. It helps the teacher to guide and counsel the student to choose the correct course
for a future career and vocation

4. i. State three strengths of the variance as a measure of dispersion

a. It uses every score in the distribution

b. It is used a lot for further statistical analysis

c. It is the most appropriate measure of variability for scores that are normally
distributed

ii. Explain, using examples, three properties of the variance.

a. The variance of the constant is zero

b. Variance is not resistant. It is affected by extreme scores.

c. Variance is independent of change of scale

iii. In an end-of-semester examination, a mean of 40 and a standard deviation of 4 were
obtained
a. Obtain the coefficient of variation

CV = 10.0%

b.What information do you derive from the value of the coefficient of variation
concerning the nature of the class?

The class is homogeneous since the value of CV is less than 33%

c. State one strength of the coefficient of variation as a measure of relative
position.

a. It is easy to compute

b. It is unitless and this makes it possible to compare variability for different
distributions

c. It is based on every score in the distribution where the distribution is normal.

d. It is easy to interpret

5. What is standard score?

A standard score indicates the number of standard deviation units an individual score
is above or below the mean of each group.
It represents an individual score that has been transformed into a common standard
using the mean and the standard deviation

Kindly take note of the following;

a. Learn the reasons of studying Educational Statistics

b. Solve and learn all the questions in the book you are using or the pdf. You can download the pdf below if you don’t have.

c. Learn the Mid-semester examination and how to calculate. You can get it in the link below. All questions have been correctly answered.

d. Look at the properties of mean, median and their uses/importance

e. Pearson, Spearman and Phi coefficients

f. Difference between Descriptive and Inferential Statistics.

Kindly take note of them. Wishing you all Good Luck!!! #### Qweku Styles

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