The reaction times, for a random sample of 9 subjects to a stimulant were recorded as follows: 2.5, 3.6, 3.1, 4.3, 2.9, 2.3, 2.6, 4.1, and 3.4 seconds.

Calculate:
a. Sample mean and sample variance.
b. Median.
c. Mode.
d. Upper and lower quartiles and IQR.
e. Manually, construct a boxplot of the data

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