Measures of Spread
The marks for the last 10 matches are listed below:
Cricketer 1
100 | 85 | 86 | 79 | 80 |
80 | 80 | 88 | 75 | 87 |
Cricketer 2
150 | 0 | 1 | 298 | 2 |
10 | 0 | 250 | 0 | 129 |
Cricketer 1
75 | 79 | 80 | 80 | 80 |
85 | 86 | 87 | 88 | 100 |
The decimal point is 1 digit(s) to the right of the |
7 | 59
8 | 0005678
9 |
10 | 0
Cricketer 2
0 | 0 | 0 | 1 | 2 |
10 | 129 | 150 | 250 | 298 |
The decimal point is 1 digit(s) to the right of the |
0 | 00012
1 | 0
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 | 9
13 |
14 |
15 | 0
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 | 0
26 |
27 |
28 |
29 | 8
Bidwidth: 1 (Bins: 1, 2, 3,..)
Cricketer 1
75 | 79 | 80 | 80 | 80 |
85 | 86 | 87 | 88 | 100 |
Cricketer 2
0 | 0 | 0 | 1 | 2 |
10 | 129 | 150 | 250 | 298 |
Cricketer 1
75 | 79 | 80 | 80 | 80 |
85 | 86 | 87 | 88 | 100 |
Cricketer 2
0 | 0 | 0 | 1 | 2 |
10 | 129 | 150 | 250 | 298 |
Cricketer 1
75 | 79 | 80 | 80 | 80 |
85 | 86 | 87 | 88 | 100 |
\[\text{Range} = 100-75 = 25\]
Cricketer 2
0 | 0 | 0 | 1 | 2 |
10 | 129 | 150 | 250 | 298 |
\[\text{Range} = 298-0 = 298\]
Advantages
Easy measure
Easy to understand
Disadvatages
It only takes into account the maximum and the minimum value.
Highly sensitive to outliers.
Does not provide information about the spread of data between the minimum and maximum values, nor does it indicate whether the data points are clustered or evenly distributed.
Variance is the mean squared deviations from the mean.
Measure of the spread of the data around the mean.
\[\text{Population variance} = \sum_{i=1}^N \frac{(x_i-\mu)^2}{N}\]
\(N\) - population size
\(\mu\) - population mean
\[\text{Sample variance} = \sum_{i=1}^n \frac{(x_i-\bar{x})^2}{n-1}\]
\(n\) - sample size
\(\bar{x}\) - sample mean
Cricketer 1
75 | 79 | 80 | 80 | 80 |
85 | 86 | 87 | 88 | 100 |
Cricketer 2
0 | 0 | 0 | 1 | 2 |
10 | 129 | 150 | 250 | 298 |
10:00
Advantages:
Disadvantages:
Sensitive to outliers/ extreme values.
The units of variance are the square of the units of the original data, which can make interpretation difficult. For example, if the data are in meters, the variance will be in square meters.
Variance is less intuitive to understand than other measures of dispersion like the range or interquartile range. People often find the concept of squared deviations harder to grasp.
\[\text{Standard deviation} = \sqrt{Variance}\]
The variance and the standard deviation are measures of the spread of the data around the mean. They summarise how close each observed data value is to the mean value.
Standard deviation is expressed in the same units as the original values (e.g., minutes or meters)
Cricketer 1
75 | 79 | 80 | 80 | 80 |
85 | 86 | 87 | 88 | 100 |
Cricketer 2
0 | 0 | 0 | 1 | 2 |
10 | 129 | 150 | 250 | 298 |
02:00
If the variance of a dataset is 0, what can you conclude about the values within the dataset?
02:00
Other measures of central tendency and measures of dispersion
Interpretation of measurements
Other methods of visualizing numerical data