Answer:
a.
Sample mean = 3.2 seconds
Sample variance = 0.4975
b. Median = 3.1
c. Mode = 2.5, 3.6, 3.1, 4.3, 2.9, 2.3, 2.6, 4.1, 3.4
d.
Upper quartile = Q3 --> 3.85
Lower quartiles = Q1 --> 2.55
IQR = 1.3
e. Manually, construct a boxplot of the data
Step-by-step explanation:
Step 1
Rearrange the numbers
a. Sample mean and sample variance
2.3, 2.5, 2.6, 2.9, 3.1, 3.4, 3.6, 4.1, 4.3
i) Sample Mean =
2.3+ 2.5+ 2.6+ 2.9+ 3.1+ 3.4+3.6+ 4.1+ 4.3/9 = 28.8/9
= 3.2 seconds
ii) Sample Variance
Formula =
(x - Mean)²/n - 1
n = 9
= (2.3 - 3.2)²+(2.5 - 3.2)²+ (2.6 - 3.2)² + (2.9 - 3.2)² +(3.1 - 3.2)² + (3.4 - 3.2)² +(3.6 - 3.2)² +(4.1 - 3.2)² + (4.3 - 3.2)²/9 - 1
= 0.81 +0.49 + 0.36 + 0.09 + 0.01 + 0.04 + 0.16 + 0.81 + 1.21/8
= 3.98/8
= 0.4975
b. Median.
2.3, 2.5, 2.6, 2.9, 3.1, 3.4, 3.6, 4.1, 4.3
Since the total number of reaction times = 9
This is an odd number.
The median formula = 1/2 (n + 1) value
= 9 + 1/2
= 10/2
= 5th value
2.3, 2.5, 2.6, 2.9,) 3.1,( 3.4, 3.6, 4.1, 4.3
The 5th value = 3.1 seconds
c. Mode.
Mode is the number that occurs the most
Each reaction time occurs only once, hence the mode = all of the above
2.3, 2.5, 2.6, 2.9, 3.1, 3.4, 3.6, 4.1, 4.3
d. Upper and lower quartiles and IQR.
2.3, 2.5, 2.6, 2.9, 3.1, 3.4, 3.6, 4.1, 4.3
Upper quartile
The formula for upper quartile
= 3/4(n + 1)value
= 3/4(9 + 1)value
= 3/4(10) value
= 30/4 value
= 7.5th value
This means, the value that fall between 7th and 8th value
7th value = 3.6
8th value = 4.1
Upper quartile = 3.6 + 4.1/2
= 7.7/2
= 3.85
Lower quartile
The formula for lower quartile
= 1/4(n + 1)value
= 1/4(9 + 1)value
= 1/4(10) value
= 10/4 value
= 2.5th value
This means, the value that fall between 2nd and 3rd value
2nd value = 2.5
3rd value = 2.5
Lower quartile = 2.5 + 2.6/2
= 5.1/2
= 2.55
Interquartile Range
= Formula = Upper quartile - Lower quartile
= 3.85 - 2.55
= 1.3
e. Manually, construct a boxplot of the data
Please find attached to this answer the diagram of the box plot
