Basic statistics and Normal Distribution

Question 1

What type of variable is weight of patient (kg)?

Answer 1

Continuous.

Question 2

A researcher uses a haemocytometer to count the number of cells in a cell culture plate. What sort of variable is the number of cells?

Answer 2

Discrete.

Question 3

The force of impact (Newtons) of a bullet can be measured by firing the bullet at a transducer coated with a ballistic gelatine. What sort of variable is force of impact (Newtons)?

Answer 3

Continuous.

Question 4

Participants in a food consumer study are asked to rank their opinion of a new product on a Likert scale of 1 to 5 where 1 is dislike extremely and 5 is like extremely. What sort of variable is the Likert scale?

Answer 4

Ordinal.

Question 5

A group of 16 fingerprint analysts was asked to count the number of Galton details in a partial fingermark. The data are shown below.
9 12 10 11 10 13 12 14 11 12 7 12 11 9 10 11.

What is the HIGHER of two modes of the dataset? (N.B. Answer in this example is a whole number)

Answer 5

7 9 9 10 10 10 11 11 11 11 12 12 12 12 13 14

12.

Question 6

A group of 16 fingerprint analysts was asked to count the number of Galton details in a partial fingermark. The data are shown below.
9 12 10 11 10 13 12 14 11 12 7 12 11 9 10 11.

Calculate the mean of the dataset to the nearest whole number.

Answer 6

11.

Question 7

A group of 16 fingerprint analysts was asked to count the number of Galton details in a partial fingermark. The data are shown below.
9 12 10 11 10 13 12 14 11 12 7 12 11 9 10 11.

Calculate the median of the dataset to the nearest whole number.

Answer 7

7 9 9 10 10 10 11 11 11 11 12 12 12 12 13 14

11.

Question 8

Total serum iron concentration was measured in blood from 10 men. The concentrations (µg/dL) were
88; 103; 150; 136; 105; 98; 117; 125; 142; 111

Calculate the mean total serum iron concentrations in the 10 blood samples. Give your answer to one decimal place. (N.B. Units are µg/dL).

Answer 8

117.5

Question 9

Total serum iron concentration was measured in blood from 10 men. The concentrations (µg/dL) were
88; 103; 150; 136; 105; 98; 117; 125; 142; 111

Calculate the standard deviation of the total serum iron concentrations in the 10 blood samples. Give your answer to one decimal place. (N.B. Units are µg/dL)

Answer 9

x1 = 88 103 150 136 105 98 117 125 142 111
(x1-x) = -29.5  -14.5  32.5  18.5  -12.5  -19.5  -0.5  7.5  24.5  -6.5
(xi-x)2 = 870.25  210.25  1056.25  342.25  156.25  380.25  0.25  56.25  600.25  42.25
Total of (xi-x) = -83+83=0
Total of (xi-x)2 = 3714.5
s2 = Σ (x1-x)2/10-1 = 3714.5/9 = 412.72
s = square root of 412.72 = 20.3

Question 10

Blood Vitamin D levels were measured in a group of 12 individuals living in Scotland. The Vitamin D levels in ng/ml from the 12 samples were
35; 50; 52; 56; 10; 45; 34; 29; 43; 42; 35; 34

Calculate the median. Give your answer to one decimal place

Answer 10

10 29 34 34 35 35 42 43 45 50 52 56

Median = 35 +42 /2 = 38.5

Question 11

Blood Vitamin D levels were measured in a group of 12 individuals living in Scotland. The Vitamin D levels in ng/ml from the 12 samples were
35; 50; 52; 56; 10; 45; 34; 29; 43; 42; 35; 34

Calculate the Lower quartile. Give your answer to one decimal place

Answer 11

10 29 34 34 35 35 42 43 45 50 52 56
L25 = 25/100 (12+1) = 3.25
Q1 = 34

Question 12

Blood Vitamin D levels were measured in a group of 12 individuals living in Scotland. The Vitamin D levels in ng/ml from the 12 samples were
35; 50; 52; 56; 10; 45; 34; 29; 43; 42; 35; 34

Calculate the upper quartile. Give your answer to one decimal place

Answer 12

10 29 34 34 35 35 42 43 45 50 52 56 
L75 = 75/100 (12+1) = 9.75
Q3 = 45 + 0.75 X (50-45) = 
45 + 0.75 X 5 = 
45 + 3.75 = 
48.75 = 
48.8

Question 13

Blood Vitamin D levels were measured in a group of 12 individuals living in Scotland. The Vitamin D levels in ng/ml from the 12 samples were
35; 50; 52; 56; 10; 45; 34; 29; 43; 42; 35; 34

Calculate the interquartile range (IQR). Give your answer to one decimal place.

Answer 13

10 29 34 34 35 35 42 43 45 50 52 56

L50 = 50/100 (12+1) = 6.5
Q2 = 35 + 0.5 x (42-35) =
38.5

Question 14

Blood Vitamin D levels were measured in a group of 12 individuals living in Scotland. The Vitamin D levels in ng/ml from the 12 samples were
35; 50; 52; 56; 10; 45; 34; 29; 43; 42; 35; 34

Calculate the lower inner fence (LIF). Give your answer to one decimal place

Answer 14

10 29 34 34 35 35 42 43 45 50 52 56

Lower fence = Q1 – (1.5*IQR)
IQR = L75 - L25
IQR = 48.8 - 34 = 14.8
Lower fence = 34 - (1.5 * 14.8)
Lower fence = 34 - 22.2 
Lower fence = 11.8

Question 15

Blood Vitamin D levels were measured in a group of 12 individuals living in Scotland. The Vitamin D levels in ng/ml from the 12 samples were
35; 50; 52; 56; 10; 45; 34; 29; 43; 42; 35; 34

Calculate the upper inner fence (UIF). Give your answer to one decimal place.

Answer 15

10 29 34 34 35 35 42 43 45 50 52 56

Upper fence = Q3 + (1.5IQR)
= 48.8 + (1.514.8)
= 71.0

Question 16

Blood Vitamin D levels were measured in a group of 12 individuals living in Scotland. The Vitamin D levels in ng/ml from the 12 samples were
35; 50; 52; 56; 10; 45; 34; 29; 43; 42; 35; 34

There are outliers in the dataset?

Answer 16

Lower Outlier = Q1 – (1.5 * IQR)
= 34 - (1.5*14.8) 
= 11.8
Higher Outlier = Q3 + (1.5 * IQR)
= 48.8 + (1.5*14.8)
= 71
True.

Question 17

A food technologist measured the mean fructose concentration in 20 samples of apples. The mean fructose concentration was 5.9%, the median of the 20 samples was 6.3% and the mode was 6.4%.

What are the samples?

Answer 17

The samples are negatively skewed because Mean