Science 7 - LAND and SEA BREEZE and its Characteristics
Β
Measures of Spread and Central Tendency
1. Measures of Spread
Range: -The range is the highest value minus
the lowest value.
The interquartile range is the third quartile
minus the first quartile
Mean deviation:- This tells us on the average,
how far all the values are from the center.
Variance: -The variance is the average of the
squares of the distance each value is from the
2. Standard deviation:
1. Use π =
π₯β π₯ 2
π
, if the data set is in discrete form
2. Use π =
ππ π
π
β
ππ
π
2
, if the data set is in
frequency table
3. Use π =
ππ π
π
β
ππ
π
2
, if you know the assumed
mean
3. 1. Mean deviation =
|πΏβ πΏ|
π
, if the data
set is in discrete form
2. ππππ πππ£πππ‘πππ =
π|πΏβ πΏ|
π
, if the data
set is in frequency table
MEAN DEVIATION
5. The distribution of scores in a class test are as follows: 2,8,6,5,8,6,6,5,6 and 5. Find
the product of the modal and the median score
JAMB 2018
SOLUTION
6 occurs most
Modal mark= 6
For median mark, we arrange the numbers in order:
2,5,5,5,6,6,6,6,8,8
Median mark =
6+_6
2
12
2
= 6
Their product = 6 Γ 6 = 36
6. 1. The standard deviation of the data set 21,15, π₯, πππ 18 is
5 3
4
. Find the
value of π₯.
A. 15
B. 16
C. 17
D. 19
E. 20
The correct answer is 17
7. 2. Compute the variance of 21,15,22, πππ 18.
A. 3.5
B. 4.5
C. 5.5
D. 6.5
E. 7.5
The correct answer is 7.5
8. 3. The table below is a distribution of marks scored by 20 students out 10.
Calculate the range
A. 4
B. 5
C. 6
D. 7
E. 8
The range is 4
π΄ππππ (π) π π π π π
ππ. ππ π π‘π’ππππ‘π 6 3 4 3 4
9. 4. The table below is a distribution of marks scored by 20 students out 10.
Calculate the standard deviation correct to 2 decimal places?
A. 1.50
B. 2.50
C. 3.50
D. 4.50
E. 5.50
The correct answer is 1.50
π΄ππππ (π) π π π π π
ππ. ππ π π‘π’ππππ‘π 6 3 4 3 4
10. 5. The histogram represents the distribution of marks scored by students in a test.
Calculate the variance of the distribution.
A. 1.25
B. 2.25
C. 3.25
D. 4.25
E. 5.25
The correct answer is 2.25
11. 6. The table below is a distribution of marks scored by 20 students out 10.
Calculate the inter-quartile range?
A. 1.0
B. 2.0
C. 3.0
D. 4.0
E. 5.0
The correct answer is 3.0
π΄ππππ (π) π π π π π
ππ. ππ π π‘π’ππππ‘π 6 3 4 3 4
12. 7. The histogram represents the distribution of marks scored by students in a test.
Calculate the semi interquartile range.
A. 1.5
B. 2.5
C. 3.5
D. 4.5
E. 5.5
The correct answer is 1.5
13. 8. The table below is a distribution of marks scored by students in a test.
Calculate the third quartile?
A. 1.50
B. 2.50
C. 3.50
D. 4.50
E. 5.50
The correct answer is 4.50
π΄ππππ (π) π π π π π
ππ. ππ π π‘π’ππππ‘π 3 2 4 3 4
14. 9. The table below is a distribution of marks scored by students in a test.
Calculate the first quartile?
A. 1.0
B. 2.0
C. 3.0
D. 4.0
E. 5.0
The correct answer is 2.0
π΄ππππ (π) π π π π π
ππ. ππ π π‘π’ππππ‘π 3 2 4 3 4
15. 10. The table below is a distribution of marks scored by students in a test.
Calculate the inter-quartile range?
A. 1.5
B. 2.5
C. 3.5
D. 4.5
E. 5.5
The correct answer is 2.0
π΄ππππ (π) π π π π π
ππ. ππ π π‘π’ππππ‘π 3 2 4 3 4
16. Summary
1. The first quartile is in
1
4
π π‘β position
2. The median is in
1
2
π π‘β position
3. The third quartile is in
3
4
π π‘β position