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1. Define Descriptive statics

Descriptive statistics are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Measures of central tendency include the mean, median, and mode, while measures of variability include standard deviation, variance, minimum and maximum variables, kurtosis, and skewness.

2. What are the three tools used descriptive data analysis

The three tools used in descriptive statistics include;

• Numerical central tendency measures like; mean, median and mode
• Numerical Measures of variability like standard deviation, variance, kurtosis and skewedness
• Graphical tools like scatter plots, histogram, pie charts and bar graphs

3. Tools for analyzing frequency tabular data.

• Measures of Central Tendency

It is a single measure that tries to describe the set of data through a value that represents the central position within that data set. Most popular measures of central tendency used for frequency analysis are Mean, Median and Mode. While the mean is the average value of the data set, the median is the middle observation (observation which has an equal number of values lying above and below it) in the data set. Mode is the value that occurs the most number of times in a data set.

• Measures of Dispersion

These reflect the spread or variability of data within a data set. Most popular measures of dispersion used for frequency analysis are Standard Deviation, Variance and Range.

• Percentile Values

A percentile value shows what percent of values in a data set fall below a certain percent. Frequency Analysis commonly uses percentile values like Quartiles, Deciles, Percentiles, etc. While the 10th percentile value shows that 10% of the observations fall below it in a data set, it is also called the 1st Decile (where the data set is divided into 10 Deciles at intervals of 10% each). Similarly the 25th, 50th and 75th percentiles are also called the 1st, 2nd and 3rd Quartile respectively (where the data set is divided into 4 Quartiles at intervals of 25% each).

4. Calculating relative frequency

5. Calculation of relative frequency and cumulative frequency

6. What is a normal frequency distribution of a numerical variable?

Is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

7. What is analysis of central tendency?

This can be defined as the analysis of mean, median and the mode of a given data set.

It can also be defined as; the analysis of the average the middle and number of occurrence in a data set. Measures of central tendency help you find the middle, or the average, of a data set. The 3 most common measures of central tendency are the mean, median and mode. The mode is the most frequent value. The median is the middle number in an ordered data set.

8. what are the measures of central tendency

Mean

Median

Mode

9. Rita scored the following marks.

1. What is the modal number and why.

The modal score is 72 because it appears the most times.

1. Median score

Solution

Her median score is 72. This is because 72 is the number in the middle.

• Mean score and why

Mean = total sum/ number of occurance

Mean =649/9

Mean =72.

The reason is because 72 is the average mark

9. What is the analysis of dispersion?

Analysis of dispersion is a statistical method that measures the amount of  variations in a  given data set like variancess, range and standard deviation.

10. what are the measures of variation ?

The measures of variation are; ;variance’,standard deviation , kurtosis and skewedness.

12. Consider a comparative performance of a student in two sittings (all marks are %)

Perfotm the measures of dispersion of cooperative performance and interprete results.

Range

Standard deviation

Standard deviation and variance

Variance

Semester one =1612/5-1

Semester two=

Standard deviation

QUESTION 13

Table showing marks obtained from research methods examination

Therefore,

MEAN=fx/f

Fx=1445

f=20

1445/20=72.25.

MEDIAN

=48,49,50,64,64,67,67,68,72,74,74,76,79,79,81,82,84,85,87,88

14. Inferential statistics

Inferential statistics are often used to compare the differences between the treatment groups. Inferential statistics use measurements from the sample of subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects.

15. Basic concepts useful in inferential data analysis regarding the

(i) Population and its parameters

• Mean
• Median
• modee

 (ii) Sample and its statistics

1. T-test
2. Pearson correlation

• Bi-variate regression

16. What is estimation of parameters? Support your answer with an example.

Estimation of parameters is branch of statistics that involves using sample data to estimate the parameters of distribution, for example A point estimation.

1. ii) Discuss two types of estimation in research

Appoint estimate; is a value of sample statistics that is used as a single estimate of population parameter.

Interval estimate: is the use of sample data to estimate an interval of plausible values of parameter of interest.

iii) What is the commonly used type of estimation in social science research?

Interval estimation

17. What is standard error and how can we numerically estimate it?

The standard error (SE) of a statistic is the approximate standard deviation of a statistical sample population. The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error of the mean.

The formula for standard error,

The standard error of the mean is usually estimated by replacing σ {\displaystyle \sigma } with the sample standard deviation. σ x {\displaystyle \sigma _{x}}

19. What is hypothesis?

Hypothesis is an expert guess of an event.

20. Explain two types of research.
21. a) Null hypothesis; This type of hypothesis expects a negative outcome of an event.
22. b) Alternative hypothesis; this type of hypothesis expects a positive outcome of an event.

21) Write two hypothesis.

1. All men with big stomachs are not rich
2. All men with big stomachs are rich.
3. ii) Hypothesis

H_o All maize sold in Kikubo have a less than 50kg means from the imported maize.

H₁ All maize sold in Kikubo have a more than 50kg means from the imported maize.

iii) How to symbolically state that the mean performance of males is different from that of females

let males be M

Females be F

22) When do we reject or accept hypothesis?

We accept the hypothesis when the P-value is less than 0.05 and reject the hypothesis when the P-value is greater than 0.05.

23) What do you understand by significant level?

Significance level is the point of confidence

24) Categorical Independent Variable:

A categorical variable is a discrete variable that captures qualitative outcomes by placing observations into fixed groups (or levels). The groups are mutually exclusive, which means that each individual fits into only one category.

Categorical dependent variable

The categorical dependent variable here refers to as a binary, ordinal, nominal or event count variable. When the dependent variable is categorical, the ordinary least squares (OLS) method can no longer produce the best linear unbiased estimator (BLUE); that is, the OLS is biased and inefficient.

25) Numerical Independent variable

An independent variable, sometimes called an experimental or predictor variable, is a variable that is being manipulated in an experiment in order to observe the effect on a dependent variable, sometimes called an outcome variable and the values are quantifiable in numbers.

Numerical dependent variable

A numeric variable (also called quantitative variable) is a quantifiable characteristic whose values are numbers and are affected by the Independent variable for their outcome.

Ranked or ordinal data IV

An ordinal variable is a categorical variable for which the possible values are ordered and they have influence on the outcome of dependent variable.

Ranked or ordinal data DV

An ordinal variable is a categorical variable for which the possible values are ordered and they have influenced by Independent variable.

Binary categorical IV

Binary variable (such as yes/no question) is a categorical variable having two categories (yes or no) and there is no intrinsic ordering to the categories and the variable influences the dependent variable.

Numerical DV

A numeric variable (also called quantitative variable) is a quantifiable characteristic whose values are numbers and are affected by the Independent variable for their outcome.

Categorical Independent variable and Numerical DV

The categorical Independent variable here refers to as a binary, ordinal, nominal or event count variable. When the dependent variable is categorical, the ordinary least squares (OLS) method can no longer produce the best linear unbiased estimator (BLUE); that is, the OLS is biased and inefficient and have influence the numerical set of data.

25. Null hypothesis
26. i) Sex is not a determinant of performance of students in mathematics
27. ii) Testing null hypothesis at 98%

27. i) H_O: Students’ achievement is not related to the number of research methods’ lecturers attended.

1. ii) Test the null hypothesis

P-value, 0.000<0.05, null hypothesis and alternative hypothesis is accepted.

• Making an inference

According to the findings in the study the P-value, 0.000<0.05, INDICATING THAT the null hypothesis is rejected and accepting the alternative hypothesis therefore concluding that Students’ achievement is related to the number of research methods’ lecturers attended.