Basic statistics and Normal Distribution
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What type of variable is weight of patient (kg)?
Continuous.
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?
Discrete.
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)?
Continuous.
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?
Ordinal.
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)
7 9 9 10 10 10 11 11 11 11 12 12 12 12 13 14 12.
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.
11.
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.
7 9 9 10 10 10 11 11 11 11 12 12 12 12 13 14 11.
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).
117.5
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)
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
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
10 29 34 34 35 35 42 43 45 50 52 56 Median = 35 +42 /2 = 38.5
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
10 29 34 34 35 35 42 43 45 50 52 56 L25 = 25/100 (12+1) = 3.25 Q1 = 34
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
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
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.
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
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
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
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.
10 29 34 34 35 35 42 43 45 50 52 56 Upper fence = Q3 + (1.5IQR) = 48.8 + (1.514.8) = 71.0
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?
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.
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?
The samples are negatively skewed because Mean