5.2 Approach
5.2.2 Data Collection
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Th~ data collected was presented in tabular forms, which was
t
ana lysed to answer the research questions raised early and to test the null hypotheses. The pattern of the results presentation IS In
I accordance with the formulated research questions and
I hypotheses. The presentation was done by taking each question and hypothesis one at a time.
Research Question 1
Goes rural and urban location influence students' achievement in
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mathematics?
The accompanying research hypothesis is
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Hypothesis 1
There is no significant difference in the means scores between students located in rural areas and students located in urban areas in mathematics achievement.
Table 4.1 and 4.2 below show students scores with respect to rural and urban factor.
Table 4.1 Class intervals, number of students, mean deviation and mean squared deviation of the test scores of rural students
Class No. of Class
- (X_X)2 f (X_X)2 interval students marks fx (x - x)
0-4 50 2 100 -5.64 31.81 1590.5
5-9 98 7 686 -0.64 0.416 40.18
10 -14 47 12 564 4.36 19.096 6893.45
15 -19 15 17 255 9.36 87.16 1314.15
TOTAL 210 1605 3838.25
The computed me.an and the standard deviation were 7.64 and 4.3 respectively.
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Table 4.~ Class intervals, number of students, mean deviation
and mean squared deviation of the test scores of urban students
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f--- --- --- --- --- --- ---
---~--Class No. of Class
5 - 9 114 7 798 -0_57 0.3249 37.0386
---.- .... - -.- --- ---.--- -'----'--- --- ---
---1---10-14 33 12 _ 396 4.43 19.62 1647.46
, .__._.__. . . J _
15- 19 14 17 238 9.43 88.92 1244.88
Total 210
interval students marks Fx
---,- ----
---0-4 46 2 92
20 - 24 03 22
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__ ,. " .__ • ._---_· .0 -__ - •. _
4.43 208.22 624.66
, ..l --'-_
66 1590
(x-
X) __(x-~l~ _ _.!Jx-~L
-5.57 31.02 1426.92
3980.9586
_____ . L
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The mean and standard deviation of urban students' scores was
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, found to be 7.57 and 4.35 respectively. t-test statistics was
I employed and the calculated value was found to be 0.39
Table 4.3 gives the summary of the t-test analysis of rural-urban scores.
Table 4.3 Mean, Standard deviation and t - test comparison between rural and urban students
CATEGORY N SD DF CALCULATED CRITICAL
X t-VALUE t-VALUE
Rural 210 7.64 4.35
418 0.39 1.96
Urban 210 7.57 4.3
From table 4.3 the calculated value of 0.39 was found to be lower than critical value of 1.96. The null hypothesis was therefore accepted. Hence there is no significant difference in the mean score between students located in urban-rural areas in mathematics achievement.
Research question 2
Is there any significant difference between boys and girls In mathematics achievement?
The accompanying research hypothesis is;
Hypothesis 2
There is no significant different in the performance of boy and girls in mathematic achievement.
Table 4.4 and 4.5 Displays examination score of boys and girls respectively.
Table 4.4 Class intervals, number of students, mean deviation and mean squared deviation of the test scores of boys students
Class No. of Class
- (X_X)2 f(x-x)2 interval students marks fx (x - x)
X
0-4 25 2 50 -7.3 53.29 1332.25
5-9 98 7 686 -2-3 5.29 518.42
--10 - 14 56 12 672 2.7 7.29 408.24
15 - 19 28 17 476 7.7 59.29 1660.12
20 - 24 03 22 06 12.7 161.29 483.87
Total 210 1950 4402.9
The mean and standard deviation were calculated to be 9.29 and 4.58 respectively.
Table 4.5: Class intervals, number of students, mean deviation and mean squared deviation of the test scores of girls students
Class No. of Class
interval students marks fx (x - x) (X_X)2 f(x-x)2
X
0-4 71 2 '. 142 -4.21 17.72 1258.12
5-9 108 7 756 0.79 0.62 66.96
10 - 14 24 12 288 5.79 33.52 804.48
15 - 19 07 17 119 10.79 116.42 814.94
Total 210 1303 2944.5
and 3.74. t-test statistics was employed to compute calculated The calculated mean and standard deviation were found to be 6.21
boys and girls students scores value it was found to be 7.5.
Table 4.6 give summary of table 4.4 and 4.5
Table 4.6: Mean, standard deviation and t - test comparison of
CATEGORY N - SO OF CALCULATED CRITICAL
X t-VALUE t-VALUE
Boys 210 9.29 4.58
418 7.5 Girls 210 6.21 3.74 1.96
Hence, there is significant differences in the performance of boys From table 4.6 the calculated value of 7.5 was found to be greater than the table value (1.96). We therefore, reject the null hypothesis.
and girls in mathematics achievement.
Research question 3
Is there any significant difference between boys in rural areas and girls in urban areas in mathematics achievement?
The accompanying hypothesis is Hypothesis 3
There is no significant difference in the means scores of boys in rural areas and girls in urban areas in mathematics achievement.
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Table 4.7 and 4.8 gives test score of boys in rural areas and girls urban area.
Table 4.7: Class intervals, number of students, mean deviation and mean squared deviation of the test scores of boys in rural areas
Class No. of Class
interval students marks fx (x -
Xl
(X_X)2 f(x-x)2F
0-4 06 2 12 -87.6 57.76 346.56
5-9 43 7 301 -2.6 6.76 290.68
10 - 14 29 12 406 2.4 5.76 167.04
15 - 19 12 17 2094 7.4 54.76 657.72
Total 90 865 1461.4
The mean scores of boys in the test was 9.6 and the standard deviation was found to be 4.0
Table 4.8: Class intervals, number of students, mean deviation and mean squared deviation of the test scores of girls in urban areas
Class No of Class -
-(X_X2) f (X-X) 2 interval Student marks fx (X-X)
0-4 27.,
,
2 54 -3.8 14.44 389.885-9 57 7 399 1.2 1.44 82.08
10-14 06 12 72 6.7 38.44 1477.63
Total 90 525 1949.29
The computed mean score of the girls and standard deviation were 5.8 and 4.6 respectively. t-test statistic was used to find the
boys in rural areas and girls in urban areas performance.
calculated value, it was found to be 5.8. Table 4.9 give the summary of 4.7 and 4.8
Table 4.9: Mean, standard deviation, t - test comparison for
CATEGORY N SD DF CALCULATED CRITICAL
-X t-VALUE t-VALUE
Boys in rural 90 9.6 4.0
areas 178 5.8 1.96
Girls In 90 5.8 4.6 urban areas
Research question 4
From the table above the calculated value of 5.8 was found to be greater than the table value of 1.96. The null hypothesis was therefore rejected. Hence there was significant difference in the means scores of boys in the rural areas and girls in urban areas in mathematics achievement.
Is there any significant difference In mathematics achievement between girls in rural areas and girls in urban areas?
The accompanying research hypothesis is
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Hypothesis 4
There is no significant difference in mathematics achievement scores between girls in rural areas and girls in urban areas
Tables 4.10 and 4.11 display test scores of girls in rural areas and girls in urban areas.
Table 4.10: Class intervals, number of students, mean deviation and mean squared deviation of the test scores of
. I· I .
glr s In rura areas
Class No of Class
- (X_X)2
-interval Student marks fx (x-x) f(x-x) 2
0-4 23 2 46 -5.5 30-25 695.75
5-9 42 7 294 10.5 0.25 10.5
10-9 18 12 216 4.7 20.25 364.5
15-19 07 17 119 9.5 90.25 1534.25
Total 90 675 2605
5.3 respectively.
The calculated mean score and standard deviation were 7.5 and
Table 4.11: Class intervals, number of students, mean
deviation and mean squared deviation of the test scores of . I· b
glr s In ur an areas
Class No of Class
- (X_i)2 f (x-xl
interval Student marks fx (x - x)
0-4 27 2 54 -3.8 14.44 389.88
5-9 57 7 399 1.2 1.44 82.08
10-14 06 12 72 6.2 38.44 1477.65
Total 90 525 1949.29
The mean and standard deviation of the girls in urban areas test score were 5.6 and 4.6. respectively.
t-test statistics was employed where 2.3 was found as calculated value.
Tables 4.12 display the summary of tables 4.10 and 4.11
Table 4.12: Mean, standard deviation and t - test comparison for girls in rural areas and girls in urban areas performance
CATEGORY N SO OF CALCULATED CRITICAL
-X t-VALUE t-VALUE
Girls in rural 90 7.5-- 5.3 areas
Girls In 90 5.8 4.6 178 2.3 1.96
urban areas
From table 4.12 above the calculated t-value of 2.3 found was greater than table value of 1.96. We therefore reject the null hypothesis. Hence, there is significant difference in mathematics
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achievement scores between girls in rural areas and girls in urban areas.
Research question 5
Is there any significant difference between boys in rural areas
and boys in urban areas in mathematics achievement?
The accompanying research hypothesis is Hypothesis 5
There is no significant difference between boys in rural areas and boys in urban areas in mathematics achievement.
Table 4.13 and 4.14 gives rural and urban boys test scores.
Table 4.13: Class intervals, number of students, mean deviation and mean squared deviation of the test scores of rural boys students
Class No of Class
Mark Student mark fx (x - x) (X_i)2 f (X_X)2
0-4 06 2 12 -7.6 57.76 346.56
5-9 43 7 301 -2.6 6.76 290.68
10-14 29 12 348 2.4 5.76 167.04
-.
15-19 12 17 204 7.4 54.76 657.12
., "
Total 90 865 1461.4
The mean and standard deviation were found to be 9.6 and 4.0 respectively.
Table 4.14 Class intervals, number of students, mean deviation and mean squared deviation of the test scores of urban boys students
Class No of Class
- (X_X)2 f (X_X)2
Mark Student marks fx (x - x)
0-4 18 2 36 -6.4 40.96 737.28
5-9 42 7 274 -1.4 1.96 82.32
10-14 18 12 216 3.6 12.96 233.28
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15-19 10 17 170 8.6 73.96 739.6
20-24 02 22 44 13.6 184 369.92
Total 760 2162.4
The mean score and standard deviation were calculated to be 8.4 and 4.9 respectively. t-test statistics was also used, the calculated value was found to be 1.2
Table 4.15 display the summary of 4.13 and 4.14
Table 4.15 Mean, standard deviation and t - test comparison for rural boys and urban boys performance
CATEGORY - N'- SO OF CALCULATED CRITICAL
X T-VALUE T-VALUE
Boys in rural' 9.6' 90' 4.9
areas 178 1.2 1.96
Boys In 8.4 90 4.0 urban areas
From table 4.15 above the calculated value of 1.2 is lower than critical value of 1.96. we therefore accept the hypothesis.
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Hence, there was no significant different between boys in rural areas and boys in urban areas in mathematics achievement.
Research question 6
To what extent sex difference, rural and urban location when taken together affects students' achievement in mathematics?
The accompanying research hypothesis is Hypothesis 6
There is no significant difference between students' sex and location of school (environment) in mathematics achievement.
Table 4.3 and 4.6 gives the summary of the calculation. In other word, table 4.3 and 4.6 answers the research question raised.
At 0.05 level of significance we accept the null hypothesis one and we also reject the null hypothesis two.
In general, there is no significant difference in the mean score between student located in rural areas and urban areas in mathematics achievement. On the other hand, we replace hypothesis tw6'with alter~ative hypothesis.
Hence, there IS significant difference between the performance of boys and girls in mathematics achievement.
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